Question 1

In the following question, a matrix of numbers is given. These numbers follow a certain pattern either row wise or column wise. Study the pattern carefully and then choose the correct answer for the missing number. The matrix is: 72   24   6; 96   1…

Accepted Answer

Introduction / Context: This is a missing number puzzle based on a 3 by 3 numerical matrix. Each row appears to follow a specific mathematical relationship among its three entries. Our job is to identify this relationship from the known rows and apply it to find the missing number in the third row. Such problems assess numerical pattern recognition and the ability to test and confirm a suspected rule. Given Data / Assumptions: The matrix has three rows: (72, 24, 6), (96, 16, 12), and (108, ?, 18). One number in the third row, middle column, is missing and denoted by a question mark. The pattern is consistent across the rows. We assume simple arithmetic operations such as addition, subtraction, multiplication, division, or combinations of these. Concept / Approach: To find the hidden pattern, we compare the structure of the first two rows where all entries are known. A useful idea is to see how the first, second, and third elements of each row relate to each other. For example, we check if the first number can be expressed in terms of the second and third numbers using multiplication or division. Once a relationship is identified that works for the first two rows, we apply it to the third row to find the missing middle element. Step-by-Step Solution: Step 1: Observe the first row: 72, 24, 6. If we multiply the second and third entries we get 24 * 6 = 144. Step 2: Notice that 72 is exactly half of 144. So, for the first row, first entry = (second entry * third entry) / 2. Step 3: Check the second row with this rule. The second row is 96, 16, 12. Multiply the second and third entries: 16 * 12 = 192. Step 4: Half of 192 is 192 / 2 = 96, which matches the first entry of the second row. So the same rule holds for the second row. Step 5: Apply this rule to the third row. The first entry is 108 and the third entry is 18. Let the missing middle entry be x. Then, according to the rule, 108 = (x * 18) / 2. Step 6: Rearranging gives x * 18 = 108 * 2 = 216, so x = 216 / 18 = 12. Step 7: Therefore, the missing number is 12. Verification / Alternative check: We can verify by reapplying the pattern. For the completed third row 108, 12, 18, the product of the second and third is 12 * 18 = 216. Half of 216 is 108, which matches the first number in the third row. Since the same relationship now holds for all three rows, the pattern is consistent and the solution is reliable. Why Other Options Are Wrong: If we substitute 16, 18, or 20 for the missing value, the relationship first entry = (second entry * third entry) / 2 would not hold. For example, with 16 we would get 16 * 18 / 2 = 144 which is not 108. Similarly, 18 * 18 / 2 = 162 and 20 * 18 / 2 = 180, both of which fail to match 108. Hence those options do not fit the discovered pattern. Common Pitfalls: Students sometimes look only at column wise relationships or simple differences and miss the more direct row wise pattern. Others might attempt addition based patterns instead of checking products. A systematic approach tries products, ratios, and sums row by row until a clear consistent rule emerges for all given rows. Final Answer: The number that should replace the question mark in the matrix is 12.

Question 2

In the following question, a matrix of letters is given. These letters follow a particular alphabetical pattern row wise or column wise. Study the pattern carefully and choose the missing character accordingly. The rows are: B   G   N; D   J   R; G …

Accepted Answer

Introduction / Context: This is a letter based missing character puzzle, where each row contains three letters that follow a pattern. We must determine the missing letter in the third row by discovering the alphabetical rule that connects the letters in each row. Such questions measure familiarity with alphabet positions and recognition of regular jumps in letter sequences. Given Data / Assumptions: The matrix has three rows: (B, G, N), (D, J, R), and (G, N, ?). Letters follow a pattern, most likely involving fixed steps in the alphabet. B is the 2nd letter, D is 4th, G is 7th, J is 10th, N is 14th, and R is 18th in the English alphabet. We need to find the letter represented by the question mark in the third row. Concept / Approach: A common pattern in such matrices is that the letters in each row increase by a fixed number of positions in the alphabet from left to right, and this increment itself might follow a pattern from row to row. So we convert letters into their numeric positions, examine the differences between consecutive letters in the same row, and check if these differences form a simple increasing sequence down the rows. Step-by-Step Solution: Step 1: Consider the first row: B, G, N. In numeric positions, B is 2, G is 7, and N is 14. Step 2: Compute the differences: from 2 to 7 is +5, and from 7 to 14 is +7. Step 3: Now examine the second row: D, J, R. In numeric positions, D is 4, J is 10, and R is 18. Step 4: Compute the differences: from 4 to 10 is +6, and from 10 to 18 is +8. Step 5: Observe the pattern. The first jump in row 1 is +5, and in row 2 it is +6. The second jump in row 1 is +7, and in row 2 it is +8. This shows that as we go from row 1 to row 2, both jumps increase by 1. So in row 3, the first jump should be +7 and the second jump should be +9, continuing this pattern. Step 6: In the third row, the first two letters are G and N. G is 7 and N is 14. From 7 to 14 is +7, which matches the expected first jump for row 3. Step 7: The second jump in row 3 should therefore be +9. So the missing letter numeric position should be 14 + 9 = 23. Step 8: The 23rd letter of the alphabet is W. Therefore, the missing letter is W. Verification / Alternative check: We can summarise the pattern: row 1 jumps are +5, +7; row 2 jumps are +6, +8; row 3 jumps are +7, +9. Thus, each row increases both jumps by 1 compared with the previous row. Checking with the filled third row G, N, W: positions 7, 14, 23 have differences 7 and 9, fitting perfectly with the expected pattern. Why Other Options Are Wrong: If we try U, V, or X, the second jump from N would be 7, 8, or 10 respectively, which would break the smooth sequence of +7 and +9 in the third row. Only W gives the correct increment of +9 from N, matching the established pattern across all rows. Common Pitfalls: A typical mistake is to treat each row as independent without comparing the size of the jumps between rows, or to check only one difference in each row instead of both. Another error is to count alphabet positions incorrectly or ignore the possibility of increasing jump sizes between rows. Careful counting and looking for simple arithmetic progressions of differences usually leads to the correct solution. Final Answer: The missing letter in the matrix is W.

Question 3

In the following question, a matrix of numbers is given. These numbers follow a particular numerical trend row wise or column wise. Study this trend carefully and choose the missing number accordingly. The matrix is: 1   7   9; 2   14   ?; 3   105  …

Accepted Answer

Introduction / Context: This is a three row numerical matrix puzzle with one missing value in the second row. Each column seems to connect its three elements through a multiplicative relationship. Our goal is to identify a rule that holds for all three columns, and then use that rule to compute the missing entry in the central position of the matrix. Given Data / Assumptions: Row 1: 1, 7, 9. Row 2: 2, 14, ?. Row 3: 3, 105, 117. The missing number is the third element of the second row. The pattern is likely consistent down each column. We can use basic multiplication and addition to search for the rule. Concept / Approach: Rather than only looking row wise, we can treat each column as a mini sequence with three values. The top two values may be combined through multiplication and addition to generate the third value in the same column. By examining columns where all three entries are known, we can infer the relationship and apply it to the column that contains the missing value. Step-by-Step Solution: Step 1: Consider the first column: 1, 2, 3. The numbers 1 and 2 combine to form 3 by the equation 1 * 2 + 1 = 3. That is, third element = first element * second element + first element. Step 2: Now consider the second column: 7, 14, 105. Test the same pattern: 7 * 14 + 7 = 98 + 7 = 105. This matches the actual third element in the second column. Step 3: Thus, the rule third element = first element * second element + first element works for column 1 and column 2. Step 4: Apply this rule to the third column, where the first and third elements are known: 9 is the first element of the first row, the missing number is in the second row, and 117 is the third element in the same column. Step 5: Let the missing number be x. According to the rule, 117 = 9 * x + 9. Step 6: Solve for x. First subtract 9 from both sides: 117 − 9 = 108, so 9 * x = 108. Step 7: Divide both sides by 9: x = 108 / 9 = 12. Step 8: Hence, the missing number in the second row, third column is 12. Verification / Alternative check: We can quickly check consistency. For column 3 with values 9, 12, 117, applying the rule 9 * 12 + 9 gives 108 + 9 = 117, which matches the third entry. Since the same rule holds for all three columns, it confirms that we have identified the correct pattern and that 12 is the only number that fits. Why Other Options Are Wrong: If we substitute 26, 20, or 16 for the missing value, the rule 9 * x + 9 would give 243, 189, or 153 respectively instead of 117. None of these match the actual third column entry. Therefore those options do not satisfy the pattern that automatically holds for the first two columns. Common Pitfalls: Many candidates first look for a simple row wise progression and may miss a more structured column wise relationship. Others may try only addition or only multiplication rather than a combined form like first * second + first. Practising conversion between compact formulas and observed numeric patterns helps build confidence for such questions. Final Answer: The missing number in the matrix is 12.

Question 4

In the following question, a matrix of numbers is given. These numbers follow a certain pattern row wise or column wise. Study this trend carefully and choose the missing number accordingly. The matrix is: 11   6   8; 17   12   ?; 25   34   19; 19  …

Accepted Answer

Introduction / Context: This is a four row numeric matrix with one missing entry in the second row. The numbers exhibit a symmetric pattern when we compare the first two rows with the last two rows. By identifying how the rows differ from each other, we can determine the missing middle value in the second row. Solving this requires attention to consistent differences across corresponding elements. Given Data / Assumptions: Row 1: 11, 6, 8. Row 2: 17, 12, ?. Row 3: 25, 34, 19. Row 4: 19, 28, 11. The missing number is the third entry in row 2. The pattern may involve constant increases or decreases between rows. Concept / Approach: A useful strategy is to examine the differences between consecutive rows in each column. If we notice that one pair of rows shows a certain amount of increase, and another pair shows the symmetric decrease with the same amount, we can infer the missing middle value. In this puzzle, rows 1 and 2 form a pair, and rows 3 and 4 form a mirror pair with consistent differences. Step-by-Step Solution: Step 1: Compare row 1 and row 2 element wise in the first column: 11 to 17 is an increase of +6. Step 2: Compare row 3 and row 4 element wise in the first column: 25 to 19 is a decrease of −6. Step 3: Now compare row 1 and row 2 in the second column: 6 to 12 is again an increase of +6. Step 4: Compare row 3 and row 4 in the second column: 34 to 28 is a decrease of −6, mirroring the pattern from the first column. Step 5: This suggests that from row 1 to row 2 the entries increase by (6, 6, x), and from row 3 to row 4 they decrease by exactly the same amounts with signs reversed. Step 6: Now examine the third column where we know row 1 and rows 3 and 4: row 1 third element is 8 and row 3 third element is 19, row 4 third element is 11. Step 7: The difference between row 3 and row 4 in the third column is 19 to 11, which is −8. So in the top pair from row 1 to row 2 we expect a symmetric increase of +8. Step 8: Therefore, the third element of row 2 should be 8 + 8 = 16. Verification / Alternative check: Summarise the differences. Row 1 to row 2: each column increases by (+6, +6, +8). Row 3 to row 4: each column decreases by (−6, −6, −8). This symmetric pattern agrees with all known values and uniquely determines the missing entry as 16. No other number would preserve these neat and consistent differences across both pairs of rows. Why Other Options Are Wrong: If we choose 15, 13, or 9 as the missing number, the increase from row 1 to row 2 in the third column would be +7, +5, or +1 respectively. None of these magnitudes match the corresponding decrease of −8 observed from row 3 to row 4 in the third column. Hence they break the symmetry of the pattern and cannot be correct. Common Pitfalls: A frequent error is to look only row wise or only column wise without comparing the top and bottom halves of the matrix. Others attempt to find a formula within each row, ignoring the possibility of a neat pattern in the differences between rows. Checking both directions and especially checking differences is often the key for such puzzles. Final Answer: The number that should replace the question mark is 16.

Question 5

In the following question, a matrix of numbers is given. These numbers follow a specific pattern row wise or column wise. Study the matrix carefully and choose the missing pair of numbers accordingly. The matrix is: Row 1: 1   4   9   ?; Row 2: 1   …

Accepted Answer

Introduction / Context: This puzzle presents a 3 by 4 matrix where two entries are missing, one in the first row and one in the third row. The second row is fully known and provides a base sequence of simple increasing numbers. By examining how the first and third rows are related to this middle row, we can deduce the rules that generate them and then fill in the missing numbers. Given Data / Assumptions: Row 1: 1, 4, 9, ?. Row 2: 1, 2, 3, 4. Row 3: 2, 4, 6, ?. The missing numbers are the fourth entry of row 1 and the fourth entry of row 3. The second row looks like a simple sequence 1, 2, 3, 4. Concept / Approach: The middle row forms the base: 1, 2, 3, 4. It is common in such puzzles that one row may contain squares of these numbers while another row may contain some simple multiple, such as double. We test whether the first row entries correspond to squares of the second row, and whether the third row entries correspond to twice the second row. If these relationships hold for the known columns, we can confidently extend them to the unknown entries. Step-by-Step Solution: Step 1: Examine row 2, which is 1, 2, 3, 4. This is a simple increasing sequence of natural numbers. Step 2: Compare row 1 with row 2 column wise. Row 1 entries for the first three columns are 1, 4, 9 while row 2 entries are 1, 2, 3. Step 3: Notice that 1 is 1 squared, 4 is 2 squared, and 9 is 3 squared. Thus row 1 appears to be the squares of row 2: n^2 for each corresponding n. Step 4: If this pattern continues, the fourth entry of row 1 should be 4 squared, which is 16. Step 5: Now compare row 3 with row 2. Row 3 entries for the first three columns are 2, 4, 6, while row 2 entries are 1, 2, 3. Step 6: We see that 2 is 2 * 1, 4 is 2 * 2, and 6 is 2 * 3. So each entry in row 3 is double the corresponding entry in row 2. Step 7: Therefore, the missing fourth entry of row 3 should be 2 times the fourth entry of row 2, that is 2 * 4 = 8. Verification / Alternative check: With the missing values filled, the matrix becomes: Row 1: 1, 4, 9, 16. Row 2: 1, 2, 3, 4. Row 3: 2, 4, 6, 8. Row 1 is clearly 1^2, 2^2, 3^2, 4^2. Row 3 is clearly 2 * 1, 2 * 2, 2 * 3, 2 * 4. Since the relationships hold across all columns, the pattern is neat and internally consistent, confirming the correctness of 16 and 8 as the missing numbers. Why Other Options Are Wrong: If we choose 49, 7 then the first row would suddenly jump from 9 to 49, which is 7 squared, breaking the clear square pattern of 1^2, 2^2, 3^2, 4^2. The options 36, 4 and 25, 5 similarly do not align the first row with squares of the second row and the third row with doubles of the second row. Therefore, they disrupt the simple and elegant pattern observed across multiple columns. Common Pitfalls: Some learners focus only row wise or only on differences between numbers and may miss the square and double relationships. Others search for an overly complicated rule when a simple square and doubling pattern fits perfectly. Always check for basic arithmetic and algebraic patterns like squares, cubes, and multiples before trying more complex ideas. Final Answer: The two missing numbers are 16 in the first row and 8 in the third row, so the correct pair is 16, 8.

Question 6

In the following sentence, choose the pair of words that best completes the blanks to form a meaningful, grammatically correct sentence. A four-year-old girl ______ her life after she was _____ from a 400 ft deep borewell she had slipped into.

Accepted Answer

Introduction / Context: This question tests vocabulary, collocations and the ability to select a pair of words that fits both the meaning and the grammar of a real-life news style sentence. The scene describes a tragic accident involving a small child who fell into a very deep borewell and was later brought out. The correct option must therefore match the emotional tone, the time sequence and the typical English expressions used in such reports. Given Data / Assumptions: - The subject is a four-year-old girl who had slipped into a 400 ft deep borewell. - There are two blanks in the sentence: one before “her life” and one before “from a 400 ft deep borewell”. - The second blank clearly goes with a passive construction “she was _____ from a 400 ft deep borewell”. - We assume the sentence describes what happened after she was brought out. Concept / Approach: The approach is to check (1) meaning, (2) grammar and (3) natural collocations. For the first blank, we need a verb that commonly combines with “her life”. Common newspaper phrases include “lost her life” (died), “saved her life”, “risked her life”, and so on. For the second blank, typical verbs with “from a borewell” are “rescued”, “pulled out”, “taken out”. Among the options, we have to identify the pair that produces a natural sounding and logically correct sentence. Step-by-Step Solution: Step 1: Focus on the second blank: “she was _____ from a 400 ft deep borewell”. Step 2: The only option that makes sense here is “rescued”. People are usually “rescued from” dangerous places. Step 3: Now look at the first blank: “A four-year-old girl ______ her life after she was rescued …”. Step 4: In tragic accident reports, the standard expression is “lost her life”, meaning “died”. Step 5: Combine the two: “A four-year-old girl lost her life after she was rescued from a 400 ft deep borewell she had slipped into.” Step 6: Check tense consistency (simple past), subject–verb agreement and logical sequence of events. Everything fits. Verification / Alternative check: Read the full sentence aloud: “A four-year-old girl lost her life after she was rescued from a 400 ft deep borewell she had slipped into.” This is exactly the kind of sentence that appears in news reports. It is grammatically correct, logically ordered and sounds natural. No other option gives this level of correctness and natural usage. Why Other Options Are Wrong: - “Defaulted, released”: “defaulted her life” is meaningless, and “released from a borewell” is not a natural collocation here. - “Made, treated”: “made her life” does not describe death, and “treated from a borewell” is grammatically wrong. - “Maintained, sustained”: “maintained her life” is unusual and “sustained from a borewell” is incorrect usage. Common Pitfalls: Students sometimes focus only on one blank and ignore the other, choosing a pair where one word fits loosely but the second does not. Another mistake is to pick words based only on emotional tone (for example, “treated” sounds medical) without checking collocations like “rescued from” or “lost her life”. Always read the complete sentence after inserting the pair, and check both meaning and natural usage. Final Answer: The only option that produces a natural, grammatically correct and meaningful sentence is “Lost, rescued”.

Question 7

Choose the pair of words from the options that best completes the sentence meaningfully and correctly: We were thinking ______ it ______ something like a requiem for our age.

Accepted Answer

Introduction / Context: This question checks a very common English prepositional phrase: “think of something as something”. It tests whether you can choose the correct pair of small words that together create a natural idiomatic expression. Such questions are frequent in competitive exams because prepositions look simple but carry subtle meaning and must be used in fixed patterns. Given Data / Assumptions: - The sentence is: “We were thinking ______ it ______ something like a requiem for our age.” - There are two blanks to be filled with a pair of words from the options. - “Requiem for our age” describes a serious, reflective piece of art or music representing an entire era. - We assume the speaker is describing how they regarded or viewed “it” (probably a film, book or project). Concept / Approach: The key is to recall the correct idiomatic frame: “think of it as X”. The verb “think” here does not mean “consider an idea” in general, but “regard” or “view”. English has stable patterns such as “think of him as a friend” or “think of this as a warm-up”. Hence the correct combination is “of” for the first blank and “as” for the second blank. Other prepositions like “for”, “since” or “because” either change the meaning or break the grammar. Step-by-Step Solution: Step 1: Focus on the structure “thinking ______ it ______ something”. It suggests “thinking of it as something”. Step 2: For the first blank, the natural verb–preposition combination is “think of something”, not “think for” or “think about it because something like a requiem”. Step 3: For the second blank, we need a word that links “it” and “something like a requiem”. We usually say “consider it as something” or “think of it as something”. Step 4: The pair “of, as” exactly matches this structure: “We were thinking of it as something like a requiem for our age.” Step 5: Read the sentence fully with this pair to ensure that tone and meaning are coherent. Verification / Alternative check: Insert “of, as” and read: “We were thinking of it as something like a requiem for our age.” The sentence now clearly states that they regarded that work as a kind of requiem. This is grammatically correct and idiomatically natural. No other combination gives this clarity and correctness simultaneously. Why Other Options Are Wrong: - “For, because”: “thinking for it because something” is ungrammatical and does not express “regarding it as”. - “For, as”: “thinking for it as something” still sounds wrong; “think for” is not the right verb–preposition pair here. - “Of, since”: “thinking of it since something like a requiem” breaks the meaning and uses “since” incorrectly as a conjunction of time or reason. Common Pitfalls: A common trap is to select prepositions only by rough sense (“for” looks related to “for our age”) without checking fixed expressions like “think of it as”. Another pitfall is ignoring the entire structure and focusing only on one blank. Always recall standard English patterns and read the entire sentence after inserting the chosen pair. Final Answer: The pair that correctly completes the idiomatic phrase is “Of, as”, giving the sentence: “We were thinking of it as something like a requiem for our age.”

Question 8

Fill in the blank with the most appropriate preposition in the following sentence: ____ the two, I prefer tea.

Accepted Answer

Introduction / Context: This question tests correct use of basic prepositions in a very common comparative structure. Even though words like “of”, “between”, “among” and “from” look easy, each of them is used in specific patterns. Competitive exams often check whether a candidate knows the exact phrase used when choosing one thing out of two. Given Data / Assumptions: - The sentence is: “____ the two, I prefer tea.” - The speaker is clearly choosing one item (tea) out of exactly two options. - No other context is given, so the answer must rely on standard English usage. Concept / Approach: There are two important patterns that students confuse: - “Of the two, I prefer X.” - “Between X and Y, I prefer Z.” When “two” is used as a noun (“the two”), the fixed phrase is “of the two”. When we name the two alternatives explicitly, we use “between”. Therefore, the correct preposition before “the two” is “of”, not “between”, “among” or “from”. Step-by-Step Solution: Step 1: Identify what “the two” refers to. It represents two options, for example coffee and tea. Step 2: Recall common English sentences. We say “Of the two, I prefer tea” and “Between tea and coffee, I prefer tea”. Step 3: Check each option in the sentence: - “Of the two, I prefer tea.” sounds natural and correct. - “Between the two, I prefer tea.” is heard in informal speech but is not the standard textbook pattern with the noun “the two”. - “Among the two, I prefer tea.” is wrong because “among” is used for more than two items. - “From the two, I prefer tea.” is unnatural in modern English. Step 4: Select the option that matches the standard comparative expression. Verification / Alternative check: Try to convert the sentence into the second pattern: “Between tea and coffee, I prefer tea.” This confirms that when we use the pronoun phrase “the two” instead of listing the items, we switch the preposition to “of”. The meaning of the sentence is now crisp and idiomatic. Why Other Options Are Wrong: - “Between”: Correct with explicit items (“between tea and coffee”), but not the best choice with “the two” as a standalone phrase in formal usage. - “Among”: Used for three or more items, so it conflicts with the idea of only two choices. - “From”: Usually used when selecting from a group as in “choose from the menu”, but “from the two” is not the standard idiomatic pattern. Common Pitfalls: Students often overuse “between” whenever they see the number two, without checking the complete phrase. Others confuse “between” and “among” and treat them as interchangeable. Always remember: “between A and B” but “of the two”. Keeping these two templates in mind will prevent most mistakes. Final Answer: The correct preposition is “Of”, giving the natural sentence: “Of the two, I prefer tea.”

Question 9

A letter series is given with one term missing. Select the letter that will complete the series: A, D, I, P, ?

Accepted Answer

Introduction / Context: This question belongs to the category of alphabet series. Instead of numbers, letters are arranged in a particular logical order. You must identify the hidden pattern and then use it to find the missing letter. Here, the pattern is based on the positions of letters in the English alphabet and the sequence of perfect squares. Given Data / Assumptions: - The given series is: A, D, I, P, ? - We know the positions of these letters in the alphabet: A = 1, D = 4, I = 9, P = 16. - We need to find the fifth letter that logically continues this pattern. Concept / Approach: For alphabet series questions, a very useful strategy is to convert letters into their numeric positions: A = 1, B = 2, C = 3 and so on. Once we look at the numeric pattern, it is often easier to notice familiar number sequences like odd numbers, even numbers, prime numbers or perfect squares. After identifying the numeric pattern, we convert back to the corresponding letter for the final answer. Step-by-Step Solution: Step 1: Write the positions of the given letters. A → 1, D → 4, I → 9, P → 16. Step 2: Observe the numeric sequence: 1, 4, 9, 16. Step 3: Recognise that these are perfect squares: 1^2, 2^2, 3^2, 4^2. Step 4: The next number should naturally be the next perfect square, that is 5^2 = 25. Step 5: Find the 25th letter of the alphabet: A=1, B=2, ..., Y=25, Z=26. So the 25th letter is Y. Step 6: Replace the question mark with Y to complete the series. Verification / Alternative check: Check the consistency: 1^2 = 1 (A), 2^2 = 4 (D), 3^2 = 9 (I), 4^2 = 16 (P), 5^2 = 25 (Y). Each step follows the same pattern of perfect squares. No other option matches this clean and simple rule. This confirms that Y is the only valid continuation. Why Other Options Are Wrong: - U: Position 21, which is not a perfect square in this context. - R: Position 18, not a perfect square and does not follow the 1, 4, 9, 16 sequence. - W: Position 23, also unrelated to perfect squares. Since the underlying rule is based on perfect squares of natural numbers, any letter whose position is not a perfect square cannot be correct. Common Pitfalls: Many learners try to look only at the difference between positions (for example, +3, +5, +7) and may fail to generalise the rule. Others may guess based on visual familiarity with certain letter pairs. Always convert letters to numbers and search for known numerical patterns such as squares, cubes, primes or arithmetic progressions. This systematic approach quickly reveals the structure. Final Answer: The missing term in the series is the letter Y.

Question 10

In the following question, which one set of letters, when sequentially placed at the gaps in the given letter series, will complete it? b_d_ed_b_c_e

Accepted Answer

Introduction / Context: This is a letter-series completion problem. A sequence of letters is given with several blanks, and you are asked to choose one set of letters that, when inserted in order, makes the entire series follow a clear pattern. The difficulty here lies in noticing that the pattern involves letters going forward and backward in the alphabet in a symmetric way. Given Data / Assumptions: - Incomplete series: b_d_ed_b_c_e - There are five blanks in this series. - Each option provides a 5-letter string to be inserted, in order, into the blanks. - We must choose the set that creates a meaningful and consistent pattern through the whole series. Concept / Approach: The usual approach in such problems is: - Step 1: Write down the complete series after inserting the letters from each option. - Step 2: Look for simple alphabetical progressions or symmetrical patterns such as increasing then decreasing sequences. - Step 3: Select the option that produces a clean, repeating pattern without breaks or contradictions. Step-by-Step Solution: Step 1: Insert option (b) “cecbd” into the blanks. The series becomes: b c d e e d c b c d e. Step 2: Now observe the pattern. From the first letter: b, c, d, e form an ascending sequence in the alphabet. Step 3: Next, from position 5 to 8: e, d, c, b form a descending sequence, which is the reverse of b, c, d, e. Step 4: Finally, from position 8 to 11: b, c, d, e again form the same ascending sequence. Step 5: Thus, the complete pattern is: ascending (b c d e), then descending (e d c b), then ascending again (b c d e). Step 6: Check that no letter breaks this symmetry. The pattern is smooth and fully consistent. Verification / Alternative check: Test the other options quickly: - Option (a) produces “bcdeedbbcce”, which does not show a clean symmetrical pattern. - Option (c) and option (d) similarly create irregular sequences without a neat ascending–descending structure. Option (b) is the only one that gives the aesthetically clear pattern of b c d e, then e d c b, then b c d e. Why Other Options Are Wrong: - “cedbc”: The resulting series contains awkward repetitions and fails to form a simple, recognisable alphabet pattern. - “ceabc”: Produces a mixed sequence with no consistent ascending or descending order. - “cecdb”: Breaks the symmetry and injects letters at places where the pattern would otherwise rise or fall smoothly. Common Pitfalls: Students often try to match only local patterns (for example, looking at just three or four letters) instead of scanning the entire string. Another mistake is to focus only on frequency of letters rather than the order. For letter-series questions, think in terms of direction (forward or backward in the alphabet) and repetition of full blocks rather than isolated pairs. Final Answer: The set of letters that correctly completes the series is “cecbd”.

Question 11

In the following question, by using which mathematical operators will the expression become correct? 15 _ 3 _ 4 _ 20

Accepted Answer

Introduction / Context: This is a simple operator-insertion puzzle. We are given numbers in a fixed order and must choose a sequence of operators from the options so that the resulting mathematical statement is numerically correct. Such questions test understanding of the basic arithmetic operations and, very importantly, the rule of operator precedence: multiplication and division are done before comparison or equality checks. Given Data / Assumptions: - Expression skeleton: 15 _ 3 _ 4 _ 20 - The three blanks must be filled in order with the three operators given in one option. - Normal arithmetic precedence is assumed: division and multiplication first, then comparison or equality. - We must find the option that makes a true statement. Concept / Approach: The strategy is to test each option as a complete expression. For every option, substitute the operators into the blanks, simplify the left-hand side following arithmetic rules, and then check whether the relation with 20 is true. Because there are only four options, this trial-and-check method is quick and reliable. Step-by-Step Solution: Step 1: Test option (a): 15 × 3 ÷ 4 > 20. Compute: 15 × 3 = 45; 45 ÷ 4 = 11.25. The statement is “11.25 greater than 20”, which is false. Step 2: Test option (b): 15 ÷ 3 × 4 < 20. Compute: 15 ÷ 3 = 5; 5 × 4 = 20. The statement becomes “20 less than 20”, which is false. Step 3: Test option (c): 15 ÷ 3 × 4 = 20. Compute: 15 ÷ 3 = 5; 5 × 4 = 20. Now the statement is “20 equals 20”, which is true. Step 4: Test option (d): 15 + 3 × 4 = 20. Compute: 3 × 4 = 12 first; then 15 + 12 = 27. The statement becomes “27 equals 20”, which is false. Step 5: Since only option (c) produces a true equation, it must be the correct choice. Verification / Alternative check: We can verify option (c) directly: 15 ÷ 3 × 4 = 5 × 4 = 20; right side is 20, so both sides match exactly. The equality sign is therefore justified. No other option yields a valid comparison with 20. Why Other Options Are Wrong: - Option (a) gives 11.25 on the left side, which is not greater than 20, so the inequality fails. - Option (b) gives 20 on the left side, which is not less than 20, so the relation is false. - Option (d) produces 27 on the left side, which is not equal to 20, so the equation is incorrect. Common Pitfalls: A frequent mistake is to ignore operator precedence and, for example, compute “15 ÷ 3 × 4” from left to right but then incorrectly add before multiplying in option (d). Another pitfall is to judge correctness by rough estimation instead of performing exact calculations. Always apply the standard rule: perform multiplication and division before addition or subtraction, and only then evaluate the equality or inequality. Final Answer: The expression becomes correct with the operators “÷, x and =”, giving the true equation 15 ÷ 3 × 4 = 20.

Question 12

In the following question, from the given alternative words, select the word which cannot be formed using the letters of the given word: NIGHTWALKER.

Accepted Answer

Introduction / Context: This is a word-formation question based on letter availability. You are given one base word and several option words. The task is to decide which option word cannot be formed using the letters of the base word, where each letter of the base word can be used only as many times as it actually appears. Such questions test attention to detail and counting skills more than vocabulary knowledge. Given Data / Assumptions: - Base word: NIGHTWALKER. - Options: Talker, Tailer, Waller, Winer. - Each letter in NIGHTWALKER can be used at most once per occurrence in that word. - We assume standard English letter counts, ignoring case (treating all letters as uppercase or lowercase uniformly). Concept / Approach: The method is straightforward: - First, list the letters in the base word along with their frequencies. - Then, for each option word, check whether every required letter exists in the base word in at least the same quantity. - If any letter in the option requires more copies than available, that option cannot be formed and is therefore the answer. Step-by-Step Solution: Step 1: Write the letters of NIGHTWALKER: N, I, G, H, T, W, A, L, K, E, R. Step 2: Count frequencies: N(1), I(1), G(1), H(1), T(1), W(1), A(1), L(1), K(1), E(1), R(1). Every letter appears exactly once. Step 3: Check “Talker”: letters T, A, L, K, E, R. Each of these letters appears at least once in NIGHTWALKER, and none is repeated beyond the available count. So “Talker” can be formed. Step 4: Check “Tailer”: letters T, A, I, L, E, R. Again, each letter is present once in NIGHTWALKER, so “Tailer” can be formed. Step 5: Check “Waler” with an extra L to get “Waller”: letters W, A, L, L, E, R. Here the letter L appears twice, but NIGHTWALKER contains L only once. Therefore there are not enough Ls to spell “Waller”. Step 6: Check “Winer”: letters W, I, N, E, R. All of these letters exist once in the base word, so “Winer” can be formed. Verification / Alternative check: We can summarise quickly: the only problematic option is “Waller”, which demands two copies of L. Since the base word has just one L, forming “Waller” is impossible. All other options require each letter only once and match the available counts exactly. Why Other Options Are Wrong: - “Talker”: All letters (T, A, L, K, E, R) appear once each in NIGHTWALKER, so this word is formable. - “Tailer”: All letters (T, A, I, L, E, R) are present and used only once, so it is also formable. - “Winer”: Composed of W, I, N, E, R, each of which is available in the base word, so it can be formed. Common Pitfalls: The main mistake is to check only whether the letters occur at all and forget to check how many times they occur. Many learners see that L exists in NIGHTWALKER and assume it is enough, ignoring that “Waller” needs two Ls. Another pitfall is reading too fast and miscounting letters like N and M or confusing similar shapes. Always slow down, count carefully, and compare frequencies. Final Answer: The word that cannot be formed from the letters of NIGHTWALKER is “Waller” because it requires two Ls while the base word has only one.

Question 13

In the following question, which one set of letters, when sequentially placed at the gaps in the given letter series, shall complete it? JK_MJ_LM_KL_

Accepted Answer

Introduction / Context: This is another letter-series completion question in which you must insert a block of letters into several gaps so that the final series follows a clear pattern. The pattern here is particularly elegant: it is based on repeating the four-letter sequence J, K, L, M without any break. The correct option will reconstruct three full cycles of this sequence. Given Data / Assumptions: - Incomplete series: JK_MJ_LM_KL_ - There are four blanks in the series. - Each option gives a 4-letter block to be placed sequentially into these blanks. - We assume a simple pattern such as repetition of a short letter block is intended, which is typical for this type of question. Concept / Approach: The best approach is to try each option and then look for a recognisable letter pattern, especially repeating blocks like ABCD, JKL, or alternating sequences. When you see letters like J, K, L, M already present, suspect that the intended pattern may be a repetition of “JKLM”. The correct inserted letters should therefore restore or complete that repetition without introducing any irregularities. Step-by-Step Solution: Step 1: Consider the target pattern: J K L M. Step 2: Try option (c) “LKJM” in the blanks. Step 3: Substitute into the series: JK_MJ_LM_KL_ becomes J K L M J K L M J K L M. Step 4: Now the complete series is: J, K, L, M, J, K, L, M, J, K, L, M. Step 5: This is exactly three consecutive repetitions of the block “JKLM” with no gaps or disruptions. Step 6: Since the series is perfectly regular, option (c) is a strong candidate for the correct answer. Verification / Alternative check: Check other options briefly: - Option (a) “JKLL” gives J K J M J J L M L L with irregular sequences and duplicated letters where the pattern should be smooth. - Option (b) “LKKM” generates a mixed pattern that does not fit a clean repeating block. - Option (d) “KJLM” also disrupts the simple “JKLM” repetition. Only option (c) produces a complete, repeated “JKLM” sequence across all 12 positions. Why Other Options Are Wrong: - “JKLL”: breaks the order and introduces LL together, which does not match the alphabetical progression J, K, L, M. - “LKKM”: introduces repeated Ks and distorts the underlying order, so you no longer see neat cycles of any simple block. - “KJLM”: shuffles the letters in a way that prevents a regular pattern from emerging. Common Pitfalls: Some candidates focus too much on local pairs, such as trying to match only “JK” or “LM”, and miss the larger repeating structure. Another error is to accept a partially ordered fragment and ignore irregularities later. For letter-series questions, always look at the entire resulting sequence after substitution and check whether a simple, repeating rule explains all positions. Final Answer: The set of letters that correctly completes the series is “LKJM”, giving three full repetitions of the sequence J, K, L, M.

Question 14

In the following letter series, a _ c a a b _ a _ b c a a b _ a _ b _ a, which one set of letters, when placed sequentially in the blanks, will correctly complete the series and maintain a consistent repeating pattern?

Accepted Answer

Introduction / Context: This question tests the concept of letter series completion. A letter series is created according to a hidden pattern, and some positions are left blank. The task is to identify a single fixed sequence of letters that, when inserted in order into the blanks, restores a clean and consistent pattern across the entire series. Such problems are common in aptitude and competitive examinations because they check observation, pattern recognition, and systematic reasoning rather than mere memorisation. Given Data / Assumptions: The given series is: a _ c a a b _ a _ b c a a b _ a _ b _ a. There are six blanks, and each option provides six letters to be placed sequentially in those blanks. Only one option should generate a neat, repeating or logically consistent pattern for the entire series. Concept / Approach: The most reliable approach is to treat the series as a possible repetition of a short block of letters. Many letter series questions are formed by repeating a small pattern like ABC, ABCAAB, or similar units. We first note the positions of the fixed letters and then see how they may fit into a repeating block. Once we suspect a base block, we check each option by filling the blanks and seeing whether the resulting full series decomposes into equal segments with the same order of letters throughout. Step-by-Step Solution: Step 1: Mark the blanks at positions 2, 7, 9, 15, 17, and 19 in the series. Step 2: Fill these six blanks with the letters from option B (b c a c a c) in order. Step 3: The completed series becomes: a b c a a b c a a b c a a b c a a b c a. Step 4: Group the completed series as: abcaab abcaab abcaab abca. Step 5: Observe that the pattern ABCAAB is consistently repeated three times, and the remaining part also follows the same order. Step 6: This shows that option B generates a clean and consistent repeating structure, which is the hallmark of a correct answer in such questions. Verification / Alternative check: We can verify our choice by checking whether any other option yields a similarly regular structure. When option B is used, the sequence of letters always appears in the same order, without any irregularity or break. This symmetry strongly indicates that we have identified the intended pattern. A quick secondary check is to see that no adjacent group violates the sequence a, b, c and that the distribution of each letter across the series is balanced in line with the repeating block. This cross check confirms that option B uniquely fits the series. Why Other Options Are Wrong: Option A (cbacba) produces clusters where the letters do not follow a simple, repeated order; some segments show disruptions and the entire string cannot be partitioned into identical blocks. Option C (acbaca) results in irregular transitions where the letters do not repeat in a fixed pattern and some local groups contradict the surrounding structure. Option D (bbacaa) creates consecutive duplicate letters at positions where the underlying structure expects a different symbol; the series then fails to maintain a single repeating block. Hence these options do not generate a clean, systematic arrangement. Common Pitfalls: Many learners try to fill blanks locally by matching only the immediate neighbours, without checking the full series after insertion. This can produce a small portion that looks right but fails when extended to the entire pattern. Another common mistake is to focus only on frequencies of letters rather than the precise order in which they appear. In letter series questions, the order of letters is more important than simple counts. It is therefore essential to verify the completed series globally rather than relying on partial matches. Final Answer: The correct set of letters that completes the series is option B, bcacac.

Question 15

Which one set of letters, when placed sequentially in the blanks of the series x _ z x _ y _ z _ x _ x y y _ z z z, will correctly complete the letter pattern?

Accepted Answer

Introduction / Context: This problem belongs to the category of missing letter series. You are given a sequence of x, y, and z with some blanks, and you must choose one option that fills all blanks so that the overall sequence follows a clear and systematic pattern. Such questions train your ability to recognise structured repetition and increasing patterns in symbolic sequences, a key skill in aptitude tests and reasoning examinations. Given Data / Assumptions: Given series: x _ z x _ y _ z _ x _ x y y _ z z z. There are six blanks which must be filled sequentially by letters from one chosen option. The same underlying pattern should hold from the first letter to the last after filling the blanks. Concept / Approach: The letters used are only x, y, and z. A natural idea is to look for a pattern in the counts of each letter. On inspection, we suspect the series builds in groups where the number of x, y, and z increases gradually. A very neat pattern in such questions is to have one x, one y, one z, then two x, two y, two z, and then three x, three y, three z. If we can reconstruct the full sequence to match this idea, we have likely found the correct answer. We then test each option by filling the blanks and checking whether a simple progression appears. Step-by-Step Solution: Step 1: Assume the final series should perhaps show increasing runs of x, y, and z. Step 2: Fill the blanks with letters from option B, yxyzxy, in order. Step 3: The completed series becomes: x y z x x y y z z x x x y y y z z z. Step 4: Group the completed sequence as: x, y, z; then x x, y y, z z; then x x x, y y y, z z z. Step 5: Check the counts: each of x, y, and z appears once, then twice, then three times in consecutive blocks, exactly matching an elegant increasing pattern. Step 6: This confirms that option B produces a very regular and purposeful construction, which is typical of well-set reasoning questions. Verification / Alternative check: To verify, count the occurrences of each letter. There are 6 x letters, 6 y letters, and 6 z letters. Their arrangement is not random but ordered into segments that show the counts 1, 2, and 3 in sequence. Also, check that there is no sudden disruption where a different letter intrudes into these blocks. All transitions follow the idea of x block, then y block, then z block, for each size. No other option arranges the letters so neatly, which gives strong confirmation that we have the intended solution. Why Other Options Are Wrong: Option A (zxyxyz) generates a sequence where the distribution of x, y, and z does not form clean increasing blocks; the runs of each letter are irregular and do not follow a simple rule. Option C (xxyyxz) leads to overlapping segments with uneven counts, so the idea of one, two, and three successive occurrences is lost. Option D (yxyxyz) produces some repeated subpatterns but fails to achieve the beautiful progression in counts that is present with option B. Therefore these options do not supply a consistent structural rule across the whole sequence. Common Pitfalls: Learners often attempt to match small local fragments only, for example focusing on the first few letters and ignoring the tail of the series. That approach can mistakenly make an incorrect option appear acceptable. Another frequent error is to ignore the possibility of an increasing count pattern and instead look only at permutations of x, y, and z. Systematic reasoning requires checking the entire string for a uniform rule, such as gradually increasing runs or repeated fixed blocks. Taking time to visualise the full series avoids these mistakes. Final Answer: The correct set of letters is option B, yxyzxy.

Question 16

In the letter series r _ p r _ p _ q _ r _ p, which one set of letters, when inserted sequentially into the blanks, will correctly complete the pattern?

Accepted Answer

Introduction / Context: This question again deals with a missing letter series, but this time only three letters r, p, and q are involved. The task is to determine which sequence of letters completes the pattern when placed into the blanks in order. Such problems help evaluate how effectively you can detect underlying repetition and structure, even when letters repeat in a seemingly complex way. Given Data / Assumptions: The series is: r _ p r _ p _ q _ r _ p. There are five blanks; each option provides five letters that must be inserted sequentially. After filling, the final series should have a clear and consistent pattern, ideally in the form of a repeated block. Concept / Approach: Since the letters r, q, and p appear, a natural idea is that the series may be built from a small repeating unit such as rqp or rpq. To uncover this, we replace the blanks using each option and then examine the completed string. The correct option will give a simple repeated cycle that continues without disruption. This type of series is usually designed so that the completed pattern is obvious and compact once discovered. Step-by-Step Solution: Step 1: Identify blank positions at second, fifth, seventh, ninth, and eleventh places. Step 2: Try option B which supplies the letters q q r p q in order. Step 3: Insert them into the blanks to get: r q p r q p r q p r q p. Step 4: Group this series as r q p repeated four times: rqp rqp rqp rqp. Step 5: Observe that each block r q p is identical and follows immediately after the previous block, creating a neat cyclic pattern. Step 6: This shows that option B creates a perfectly regular repeating sequence, which is the hallmark of a correct completion. Verification / Alternative check: To verify, check that no letter appears in a position that breaks the r q p rotation. Starting at the first letter r, the sequence always progresses to q then to p, and then repeats from r again. There are no double q or double p blocks in places where the pattern would expect another letter. This uniformity confirms that option B fits the intended design of the question. A quick comparison with other options confirms that only option B leads to this clean repetition. Why Other Options Are Wrong: Option A (qrppq) leads to segments where double p appears and the rotation r q p is broken, so the series cannot be rearranged into identical blocks. Option C (qrprp) generates inconsistent transitions that do not match a single simple cycle. Option D (qrppr) produces an uneven distribution with extra p letters which again conflicts with any regular pattern. These irregularities show that these options do not create a consistent repeating sequence across all positions. Common Pitfalls: A common mistake is to choose an option that seems to make the first half of the series look reasonable without inspecting the entire completed sequence. Another pitfall is to focus on immediate neighbours but ignore longer cycles that extend over three or more positions. In letter series questions, it is very important to search for a small repeating block and verify that this block can be applied throughout the series without contradictions. Final Answer: The correct set of letters is option B, qqrpq.

Question 17

A series of three letter groups is given as dem, fgo, hiq, and one more missing term. Which of the following options correctly completes the series?

Accepted Answer

Introduction / Context: This is a classic alphabet series question involving three letter groups. You are given three terms dem, fgo, and hiq, and you must find the next term that continues the pattern. Each position in the triplet follows a separate rule based on the positions of letters in the English alphabet. Such questions check your understanding of alphabetical order and your ability to track multiple parallel patterns at the same time. Given Data / Assumptions: First term: dem. Second term: fgo. Third term: hiq. We need the fourth term that follows the same logical pattern as the previous ones. Concept / Approach: The key idea is to treat the first, second, and third letters of each group as three separate sequences. For each position, we convert the letters to their alphabet positions and look for a numeric pattern. We then apply the same increment to obtain the next letter in each position. If all three positions show a consistent rule, we can confidently generate the missing triplet. This structured approach avoids guesswork and ensures accuracy. Step-by-Step Solution: Step 1: Consider the first letters: d, f, h. Their positions are 4, 6, and 8, which increase by 2 each time. Step 2: The next first letter should be 8 plus 2, which is 10, corresponding to j. Step 3: Consider the second letters: e, g, i with positions 5, 7, and 9, again increasing by 2 each time. Step 4: The next second letter should be 9 plus 2, that is 11, corresponding to k. Step 5: Consider the third letters: m, o, q with positions 13, 15, and 17, increasing by 2 each time. Step 6: The next third letter should be 17 plus 2, which is 19, corresponding to s, so the required group is jks. Verification / Alternative check: We can quickly verify the choice jks by checking the increments again. For each position, we add 2 to the alphabet index and confirm that we obtain the letters in our answer. There is no deviation in the increment pattern, and the difference remains constant across all three positions. None of the other options produce consistent increments of plus two for every corresponding position of the triplets, which confirms that jks is the only valid continuation of the sequence. Why Other Options Are Wrong: Option A (jkt) has the correct first two letters j and k but ends with t, which represents position 20, not 19, and therefore breaks the plus two rule in the third position. Option B (ikp) changes the increments in more than one position and does not respect the constant difference of two. Option D (klt) alters both the starting letter and the pattern and fails to match any consistent progression from the previous terms. Thus none of these options aligns with the clear arithmetic structure observed in the series. Common Pitfalls: Learners sometimes focus only on visually similar letters or on one position of the triplet and ignore the others. This can lead to choosing an option that appears partially correct but fails under closer inspection. Another frequent mistake is to miscount letter positions in the alphabet, especially for letters nearer to the end. Writing down the index numbers and verifying the difference between consecutive terms helps avoid these errors and leads to a systematic solution. Final Answer: The correct missing term is jks, which corresponds to option C.

Question 18

Which number should come next in the series 1, 8, 27, 64, 125, 216, ______ so that the sequence follows the same pattern?

Accepted Answer

Introduction / Context: This question is a straightforward number series based on powers of integers. You are given a sequence of positive integers and must identify the next term by recognising the pattern. Such questions evaluate your familiarity with perfect cubes and perfect squares, as well as your ability to match each term to a simple mathematical rule. Given Data / Assumptions: Sequence: 1, 8, 27, 64, 125, 216, ? All numbers are positive integers. We expect a simple and consistent pattern, likely involving powers of small integers. Concept / Approach: A quick look suggests that these numbers are cubes. We check whether each term corresponds to n^3 for some integer n. If this is confirmed, then the next term should be the cube of the next integer in the sequence. The approach is to compute cube roots mentally or by recalling common cube values, then confirm the pattern and extend it by one more term. Step-by-Step Solution: Step 1: Recognise that 1 is 1^3. Step 2: Verify that 8 is 2^3, 27 is 3^3, and 64 is 4^3. Step 3: Check that 125 is 5^3 and 216 is 6^3. Step 4: Therefore the sequence can be written as 1^3, 2^3, 3^3, 4^3, 5^3, 6^3. Step 5: The next term must naturally be 7^3. Step 6: Calculate 7^3 = 7 * 7 * 7 = 49 * 7 = 343. Verification / Alternative check: To verify, confirm that no other pattern among the options fits as neatly. All given numbers are exactly cubes of consecutive integers, and only 343, which is 7^3, continues this rule. The other options do not correspond to 7^3 or to any obvious continuation of comparable simplicity. Since exam number series are usually based on a single clear idea, the cube pattern is the intended one and 343 is the only reasonable extension. Why Other Options Are Wrong: Option A (354) is not a cube of any integer and does not match 7^3. Option C (392) also does not equal 7^3 and fails to correspond to any simple power sequence consistent with the previous terms. Option D (245) is not the cube of 7 and has no direct relation to the displayed pattern. These numbers may appear close in magnitude but they do not fit the elegant n^3 structure visible in the given series. Common Pitfalls: A common mistake is to try differences between consecutive terms and misinterpret them as a primary rule, instead of checking for powers first. Learners sometimes overlook simple power patterns because they rush through the question. Another pitfall is confusing cubes with squares, which can lead to incorrect selections. Remembering standard cubes from 1^3 up to at least 10^3 makes such questions very quick to solve. Final Answer: The next term in the series is 343, so option B is correct.

Question 19

In the letter series T _ S T _ S _ U _ T _ S, which set of letters, when placed sequentially in the blanks, will correctly complete the pattern?

Accepted Answer

Introduction / Context: Here we have a missing letter series composed of the letters T, U, and S. Several blanks must be filled by choosing exactly one set of letters from the options. The goal is to produce a completed series that follows a simple and consistent pattern. These problems test letter pattern recognition and the ability to identify repeated cycles in symbolic data, skills that are important in many reasoning examinations. Given Data / Assumptions: Series with blanks: T _ S T _ S _ U _ T _ S. There are five blanks that must be filled in order by one of the given options. The final series should show a clear repeated pattern rather than a random arrangement. Concept / Approach: A helpful idea in such problems is to suspect that the full sequence is composed of repeated short blocks like TUS or TSU. By trying each option, we can see which one, after filling the blanks, yields a smooth repetition without contradictions. The correct pattern in this question turns out to be T U S repeated four times, giving a very elegant structure once completed. Step-by-Step Solution: Step 1: Place the blanks at positions 2, 5, 7, 9, and 11 within the series. Step 2: Choose option D, which supplies the letters U U T S U in that order. Step 3: Fill the blanks to obtain: T U S T U S T U S T U S. Step 4: Group the completed sequence as TUS TUS TUS TUS. Step 5: Note that the block T U S is repeated four times in succession without any break. Step 6: This regularity shows that option D is consistent with a simple and coherent underlying pattern. Verification / Alternative check: We verify by checking each group of three letters. Every triple, starting from the first, spells T U S in the same order: positions 1 to 3, 4 to 6, 7 to 9, and 10 to 12. There is no deviation in any of the blocks. If we tested another option, the resulting series would not yield such a neat repetition. Therefore, this property of forming four identical TUS blocks confirms that option D is the correct completion. Why Other Options Are Wrong: Option A (UUSTT) produces a mix where some T letters cluster together, breaking any simple cycle and preventing repetition of a short block. Option B (TUUTS) creates irregular segments with extra U letters, which do not allow equal sized repeating groups. Option C (TTSTU) leads to a structure with double T at unexpected positions and does not reduce to a simple pattern such as TUS. None of these options can be grouped into identical consecutive blocks across the full series, so they are incorrect. Common Pitfalls: Many learners attempt to judge options based on the first few positions only and thus accept a pattern that seems fine at the beginning but fails later. Another common error is to ignore symmetry and not try to partition the completed series into equal segments. In letter series questions, always examine the entire sequence after filling the blanks and see whether it suggests an obvious repeating unit. This habit greatly improves accuracy in similar problems. Final Answer: The correct set of letters is option D, UUTSU.

Question 20

In the letter series A _ B C _ B B C _ B B _, which one set of letters, when placed sequentially in the blanks, will correctly complete the pattern?

Accepted Answer

Introduction / Context: This question presents a letter series formed mainly from A, B, and C with several positions left blank. You must choose one option whose letters, inserted sequentially into the blanks, restore a smooth and regular pattern. These problems are designed to test how effectively you can detect repetition and structure in short strings of symbols, an ability that supports many higher order reasoning tasks. Given Data / Assumptions: The incomplete series is: A _ B C _ B B C _ B B _. There are four blanks that must be filled in order. Each option provides four letters which are to be used exactly once, in the given order. Concept / Approach: We expect the final series to consist of repeated blocks of letters. The visible parts suggest that the combination ABBC might be significant, since A is frequently followed by B B C in parts of the sequence. Therefore we try each option to see whether the completed string decomposes into identical blocks of four letters. The correct option should yield a repetition of ABBC, which is a common construction in such letter series questions. Step-by-Step Solution: Step 1: Mark the blanks at positions 2, 5, 9, and 12. Step 2: Choose option A, which provides the letters B A A C. Step 3: Fill the blanks to get: A B B C A B B C A B B C. Step 4: Group the final sequence as ABBC ABBC ABBC. Step 5: This clearly shows that ABBC is the repetitive unit, appearing three times in succession. Step 6: No part of the completed series conflicts with this structure, confirming that option A is consistent with a single repeating block. Verification / Alternative check: We can verify by checking that every group of four letters is exactly A B B C. Starting at position 1, the first four letters read ABBC. From position 5 to 8, we again see ABBC, and from position 9 to 12 we see ABBC one more time. There are no variations or mismatches. This perfect periodicity shows the series is completely determined by the ABBC block, which validates option A as the only correct choice. Why Other Options Are Wrong: Option B (BBBC) leads to a string where a B B B C sequence appears in places that break the ABBC structure, so all blocks do not match. Option C (BABA) produces a mixture of patterns with alternating A and B that cannot be grouped into a simple repeated four letter unit. Option D (ABBC) also disturbs the implied ABBC repetition at some positions and fails to give three identical consecutive blocks. In each of these cases, the completed series lacks the clear and uniform repetition found with option A. Common Pitfalls: A frequent mistake is to fill the blanks based on local impressions, for instance trying to ensure that no two similar letters touch, without checking whether the entire series forms equal length repeating blocks. Another pitfall is to ignore the importance of the last few characters, which must still conform to the same pattern. Careful grouping and explicit comparison of each block helps avoid such errors and reveals the underlying ABBC repetition reliably. Final Answer: The correct set of letters is option A, BAAC, giving the series ABBC repeated three times.

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