Question 1

Fill in the blanks with suitable letters to continue the pattern in the sequence: a _ c _ abb _ a _ bc _ bc _ ab.

Accepted Answer

Introduction / Context: This is a letter pattern question where a long string made up of the letters a, b, and c is partially hidden by blanks. The options give six letters each, and these letters must be inserted into the blanks in order to complete the underlying pattern. Such problems check your ability to detect repeated blocks or cyclic structures within a sequence of characters, even when some positions are unknown. Given Data / Assumptions: Base string with blanks: a _ c _ abb _ a _ bc _ bc _ ab. There are exactly six blanks, to be filled in order from left to right. Each option gives six letters (separated for readability) that are to be plugged into those blanks sequentially. Only one choice will produce a neat, regular pattern of repeated blocks of a, b, and c. Concept / Approach: The core idea is to test each option by inserting its letters into the blanks and then examining the complete string. The correct choice will make the overall sequence look structured, with repeated small blocks like abc, abccab, or similar fragments. The wrong options will tend to produce awkward, irregular combinations that do not repeat or line up nicely. Because only three letters are involved, we look especially for a balance and regular cycling of a, b, and c across the whole structure. Step-by-Step Solution: Step 1: Represent the template more clearly as: a _ c _ abb _ a _ bc _ bc _ ab. Step 2: Choose option C, which provides the six letters b, c, c, a, a, c. Step 3: Fill the blanks in order from left to right. The resulting sequence becomes: a b c c abb c a a bc a bc c ab. Step 4: Remove spaces to see the continuous pattern: abccabbcaabcabccab. Step 5: Observe that this completed string can be segmented into overlapping repeating blocks such as abccab and bcab. The letters a, b, and c appear in a regular and balanced way, with no strange isolated clusters. Verification / Alternative check: Now test the other options in the same manner. Inserting option A (c b c a a a) yields uneven fragments where the distribution of a, b, and c is skewed, and no clean repeating sub pattern emerges. Option B (b c c c a b) and option D (a c b a b c) also produce long sequences with awkward letter groupings that do not show a convincing cyclic or repetitive structure. Among all options, only option C generates a smooth pattern that can be partitioned into repeating and symmetric segments, which is exactly what such exam questions generally aim for. Why Other Options Are Wrong: Each of the other options either produces too many identical consecutive letters or breaks possible repeating blocks. For instance, some combinations create runs like bbb or uneven transitions that do not match the rest of the string. Because pattern questions rely on intentionally designed, tidy repetitions, these irregular results indicate that those options are not intended to be correct. Common Pitfalls: Students often try to guess based on the first two or three blanks and do not construct the full completed string. This can easily lead to wrong choices, since many options might appear reasonable locally but fail to produce a global pattern. A better strategy is to fully substitute each candidate and then look at the overall sequence for repeated smaller blocks and a balanced distribution of letters. Final Answer: The sequence is completed most regularly by inserting the letters b c c a a c, so the correct option is b c c a a c (option C).

Question 2

Complete the next number in the given number series: 21, 56, 102, 160, 231, 316, ?

Accepted Answer

Introduction / Context: This series increases in a non linear way, which suggests that the differences between terms themselves may follow a pattern. When differences between consecutive terms are not constant, second differences often reveal a simple arithmetic rule. Questions of this type test your understanding of first and second differences in sequences, a common technique in advanced number series problems. Given Data / Assumptions: Series: 21, 56, 102, 160, 231, 316, ? Exactly one next term is missing. The pattern is expected to be systematic, likely involving changing differences between terms. Concept / Approach: First compute the differences between consecutive terms. If those differences do not form a constant sequence, compute the differences of the differences (second differences). A constant or steadily changing second difference sequence usually indicates that the original series is built from a quadratic type pattern. We can then extend the second difference pattern to get the next first difference and hence the missing term. Step-by-Step Solution: Step 1: Compute the first differences. 56 - 21 = 35. 102 - 56 = 46. 160 - 102 = 58. 231 - 160 = 71. 316 - 231 = 85. Step 2: Collect these differences: 35, 46, 58, 71, 85. Step 3: Compute the second differences (differences of the first differences). 46 - 35 = 11. 58 - 46 = 12. 71 - 58 = 13. 85 - 71 = 14. Step 4: Second differences follow the simple pattern 11, 12, 13, 14, so the next one should be 15. Step 5: The next first difference will therefore be 85 + 15 = 100. Step 6: Add this new first difference to the last known term: 316 + 100 = 416. Verification / Alternative check: Extend the series with the found term: 21, 56, 102, 160, 231, 316, 416. Recompute the first differences: 35, 46, 58, 71, 85, 100. Second differences then become 11, 12, 13, 14, 15, which is a perfectly regular sequence increasing by 1 each time. This confirms that the structure of the series is maintained and validates 416 as the correct missing number. Why Other Options Are Wrong: If we try 415, 414, or 413 as the final term, the last first difference and the corresponding second difference no longer follow the neat pattern. For example, if we used 415, the last difference would be 415 - 316 = 99, giving a second difference of 99 - 85 = 14, which repeats rather than increasing to 15. Since the question clearly follows an increasing second difference sequence, these alternative values cannot be correct. Common Pitfalls: Many students stop after examining only first differences and conclude that the series is irregular. In such cases, it is crucial to remember the concept of second differences, which often reveals a much simpler hidden pattern. Another mistake is to guess a number based on rough growth estimation instead of verifying it through systematic calculations. Final Answer: The next number that correctly completes the series is 416.

Question 3

Find the next number in the given series: 9, 7, 10, 6, 11, ?

Accepted Answer

Introduction / Context: This is a compact number series that uses alternating addition and subtraction with steadily increasing magnitudes. The goal is to identify this alternating pattern and then use it to predict the next term. Questions of this kind help develop your ability to track signs and magnitudes of changes in a sequence rather than just looking at raw values. Given Data / Assumptions: Series: 9, 7, 10, 6, 11, ? Exactly one term is missing at the end. The changes between consecutive terms appear to alternate between increases and decreases. Concept / Approach: We focus on the differences between consecutive terms and look for two patterns at once: the sign of the change (positive or negative) and the size of the change. Many exam series alternate between adding and subtracting numbers whose magnitudes grow in a regular way such as 2, 3, 4, 5, and so on. Once the pattern is identified, extending the sequence is straightforward. Step-by-Step Solution: Step 1: Compute the differences between consecutive terms. 7 - 9 = -2. 10 - 7 = +3. 6 - 10 = -4. 11 - 6 = +5. Step 2: Observe that the signs alternate: minus, plus, minus, plus. Step 3: Observe the magnitudes: 2, 3, 4, 5. Each step increases by 1. Step 4: Following this pattern, the next difference should be negative again (to continue the alternation) and its magnitude should be 6 (the next integer after 5). Step 5: So the next difference is -6. Step 6: Apply this to the last known term: 11 + (-6) = 5. Verification / Alternative check: Now write the extended sequence: 9, 7, 10, 6, 11, 5. Recompute all differences: -2, +3, -4, +5, -6. The signs alternate perfectly and the absolute values form a simple increasing sequence 2, 3, 4, 5, 6. This double pattern provides a strong confirmation that 5 is the correct next term. Why Other Options Are Wrong: If we choose 4, 13, or 15, the final difference becomes -7, +2, or +4 respectively, none of which fit the combined rule of alternating signs with stepwise increasing magnitudes. For example, choosing 13 would give a last difference of +2, which breaks both the expected negative sign and the required magnitude of 6. Therefore these options do not match the clearly observed structure of the series. Common Pitfalls: Some candidates look only at values that go up and down and guess randomly, missing the exact numeric pattern of the differences. Others may identify the alternating signs but fail to notice that the sizes of the jumps increase steadily. Always examine both the sign and the magnitude of changes in alternating series problems. Final Answer: The next number that correctly completes the series is 5.

Question 4

Select the missing number from the given alternatives in the sequence: 12, 8, 4, 8, 4, 12, 4, 12, 8, 100, 44, ?

Accepted Answer

Introduction / Context: This question mixes a simple repeating set of three numbers with an additional set of terms generated by a product based rule. It tests whether you can see not only the repetition of small blocks but also how groups of three numbers can be combined to generate new numbers later in the series. Such sliding window product plus patterns are common in reasoning questions. Given Data / Assumptions: Long series: 12, 8, 4, 8, 4, 12, 4, 12, 8, 100, 44, ? The first nine numbers show recurring values 12, 8, and 4 in different orders. The last three numbers, 100, 44, and the missing term, are related to the previous triplets. Concept / Approach: Notice that 12, 8, 4 appears as a triple, then 8, 4, 12, then 4, 12, 8. These are rotations of the same three values. The numbers 100 and 44 can be compared against the preceding triplets to see if there is a relationship that uses multiplication and addition. A neat pattern is often of the form first * second + third for each group of three consecutive numbers. Step-by-Step Solution: Step 1: Take the first three numbers 12, 8, 4 and compute 12 * 8 + 4. 12 * 8 = 96, and 96 + 4 = 100, which matches the tenth term in the series. Step 2: Take the next three numbers 8, 4, 12 and compute 8 * 4 + 12. 8 * 4 = 32, and 32 + 12 = 44, which matches the eleventh term in the series. Step 3: Take the next three numbers 4, 12, 8 and compute 4 * 12 + 8. 4 * 12 = 48, and 48 + 8 = 56. Step 4: Therefore, by applying the same rule first * second + third, the missing twelfth term must be 56. Verification / Alternative check: Summarise the pattern using a sliding window of size three: (12, 8, 4) generate 100; (8, 4, 12) generate 44; (4, 12, 8) generate 56. The rule applied consistently is first * second + third. Since all three computations match the actual or required terms, this strongly confirms that 56 is the correct missing number derived from the last visible triplet before the question mark. Why Other Options Are Wrong: Options 80, 48, and 36 do not equal 4 * 12 + 8. Using any of these values would break the consistent rule that ties each group of three numbers to a resulting number later in the chain. Since both 100 and 44 align perfectly with the formula, the last result must also follow it for the series to remain logically constructed. Common Pitfalls: Some students focus only on the first nine terms and try to guess a direct pattern among them, missing the link between the three number blocks and the later values. Others may attempt to use simple differences, which do not reveal the multiplicative structure here. When groups of three or more repeat, always consider sliding window style operations such as products and sums across each group. Final Answer: The missing number that completes the series according to the rule first * second + third is 56.

Question 5

In the following question, select the missing number from the given decreasing series: 146, 137, 128, ?, 110, 101.

Accepted Answer

Introduction / Context: This question presents a simple decreasing number series where each term is obtained by subtracting a constant amount from the previous term. The aim is to identify that constant difference and use it to find the missing value. Such uniform decrement series are among the most basic patterns in number series questions and are often used to check quick observation skills. Given Data / Assumptions: Series: 146, 137, 128, ?, 110, 101. One middle term is missing. The sequence appears to be decreasing steadily by a fixed number. Concept / Approach: For a series that appears to decline smoothly, the natural first step is to compute the difference between easily visible consecutive terms. If that difference is constant, the entire sequence is likely an arithmetic progression. In this case, we can then insert the missing term by subtracting the same constant difference for each step, both before and after the blank. Step-by-Step Solution: Step 1: Calculate the difference between the first and second terms. 137 - 146 = -9, so the series goes down by 9 from 146 to 137. Step 2: Calculate the difference between the second and third terms. 128 - 137 = -9, again a decrease of 9. Step 3: Check a later visible step to see if the same difference holds. 110 - 119 would be -9, and 101 - 110 = -9, so it is reasonable to assume that each step is a decrease by 9. Step 4: To find the missing term, subtract 9 from 128. 128 - 9 = 119, so the blank should be 119. Verification / Alternative check: Write the completed sequence with the missing term filled in: 146, 137, 128, 119, 110, 101. Now check every difference: 137 - 146 = -9, 128 - 137 = -9, 119 - 128 = -9, 110 - 119 = -9, and 101 - 110 = -9. The constant difference of -9 is maintained across the entire series, confirming that 119 is completely consistent with the pattern. Why Other Options Are Wrong: If we choose 123, 121, or 117, at least one of the differences between consecutive terms will not equal -9. For example, if the missing term were 121, then 128 - 137 = -9 but 121 - 128 = -7, breaking the uniform step size. Since the question clearly follows a constant decrement rule, any option that produces a different difference is incorrect. Common Pitfalls: Students sometimes overcomplicate simple series by looking for multiplicative or mixed operations when a constant addition or subtraction is enough. Another mistake is to compute only a single difference and assume a pattern without verifying it across the whole sequence. Always validate a suspected constant difference at multiple points before finalising your answer. Final Answer: The missing number in the series is 119.

Question 6

In the following question, select the missing number from the given series: 2, 4, 13, 41, 106, ?

Accepted Answer

Introduction / Context: This series grows quite rapidly, and the step sizes between consecutive terms increase in a non linear way. Problems like this often hide a pattern in the differences between terms, where those differences follow a rule related to squares or cubes. In this question, the differences are based on cubes of natural numbers plus one, which is a nice example of using an auxiliary sequence to control the growth of the main series. Given Data / Assumptions: Series: 2, 4, 13, 41, 106, ? Exactly one next term is missing. The differences between terms increase and are unlikely to be constant. Concept / Approach: Calculate the differences between consecutive terms and then see if these differences themselves form a recognisable pattern. Here, each difference turns out to be one more than a perfect cube. Once we recognise that the differences are 1^3 + 1, 2^3 + 1, 3^3 + 1, and so on, we can immediately compute the next difference and hence the missing term in the series. Step-by-Step Solution: Step 1: Compute the first differences. 4 - 2 = 2. 13 - 4 = 9. 41 - 13 = 28. 106 - 41 = 65. Step 2: Observe these differences: 2, 9, 28, 65. Step 3: Express each difference in terms of cubes. 2 = 1^3 + 1. 9 = 2^3 + 1. 28 = 3^3 + 1. 65 = 4^3 + 1. Step 4: The pattern is difference(n) = n^3 + 1 for n = 1, 2, 3, 4, ... Step 5: The next difference should be 5^3 + 1 = 125 + 1 = 126. Step 6: Add this to the last known term 106: 106 + 126 = 232. Verification / Alternative check: Extend the series with the computed term: 2, 4, 13, 41, 106, 232. Now recompute the differences: 2, 9, 28, 65, 126. These match exactly 1^3 + 1, 2^3 + 1, 3^3 + 1, 4^3 + 1, 5^3 + 1. The pattern is therefore perfectly consistent, confirming that 232 is the correct missing term and that the underlying structure of the series is based on cubes plus one. Why Other Options Are Wrong: Values 172, 191, and 219 do not produce a final difference that equals 126. For example, 191 - 106 = 85, which is not equal to 5^3 + 1. Using any of these alternatives would break the clean sequence of differences being exact cube plus one values, making the series inconsistent with the discovered rule. Common Pitfalls: It is tempting to try proportional or multiplicative relationships directly on the main terms, which quickly becomes messy here. Another common error is to look for square based differences rather than cube based ones, since squares are more familiar. The key is to systematically test small powers and see which ones fit, rather than guessing. Recognising 2, 9, 28, 65 as cubes plus one is the decisive step in solving this problem. Final Answer: The next number in the series is 232.

Question 7

In the following question, select the missing number from the given series: 3, 8, 5, 27, 8, 64, 12, 125, 17, ?

Accepted Answer

Introduction / Context: This series can be better understood by grouping the numbers into pairs. Each pair consists of a smaller first term and a much larger second term. A common pattern in such cases is that the second term of each pair is a cube, while the first terms follow a separate additive rule. Recognising the two interwoven sequences is the key to solving this question correctly. Given Data / Assumptions: Series: 3, 8, 5, 27, 8, 64, 12, 125, 17, ? Consider the series as pairs: (3, 8), (5, 27), (8, 64), (12, 125), (17, ?). The second elements look like perfect cubes. Concept / Approach: Split the series into two subsequences. One subsequence uses the first number of each pair, and the other uses the second number of each pair. Often the second numbers form powers like cubes or squares, while the first numbers form a simple additive progression. Once we identify both patterns, we can fill in the missing value in the final pair. Step-by-Step Solution: Step 1: Form pairs: (3, 8), (5, 27), (8, 64), (12, 125), (17, ?). Step 2: Examine the second elements: 8, 27, 64, 125. These are 2^3, 3^3, 4^3, and 5^3 respectively. Step 3: This suggests that the series of second elements is cubes of consecutive integers: 2^3, 3^3, 4^3, 5^3, 6^3. Step 4: The next cube should be 6^3 = 216. Step 5: Now examine the first elements of each pair: 3, 5, 8, 12, 17. Differences between these first elements are: 5 - 3 = 2, 8 - 5 = 3, 12 - 8 = 4, 17 - 12 = 5. Step 6: The first elements increase by 2, then 3, then 4, then 5, which is a simple pattern of adding consecutive integers. This confirms the design of the pairs. Verification / Alternative check: Write the final paired sequence explicitly: (3, 8), (5, 27), (8, 64), (12, 125), (17, 216). The first term in each pair follows the progression 3, 5, 8, 12, 17, where the increments are 2, 3, 4, 5. The second term in each pair follows 2^3, 3^3, 4^3, 5^3, 6^3. This double structure is very clean and exactly matches all given values, so 216 is fully consistent as the missing term. Why Other Options Are Wrong: 361, 625, and 441 are all perfect squares (19^2, 25^2, and 21^2 respectively) but the series of second terms is clearly following perfect cubes, not squares. Also, moving from 125 to any of these numbers does not maintain the pattern of cubes of consecutive integers. Therefore none of these alternatives can be correct under the discovered rule. Common Pitfalls: Some candidates try to treat the entire ten term series as one single sequence, which makes the pattern look very complex. The crucial step is to recognise the pair structure and analyse first and second elements separately. Another mistake is to spot only the cubes and ignore the subtle but simple pattern in the first elements, which can lead to uncertainty about whether the cube pattern truly extends to 6^3. Final Answer: The missing number in the series is the next cube, which is 216.

Question 8

What will come in place of the question mark in the following number series: 14, 18, 9, 25, 0, ?

Accepted Answer

Introduction / Context: This series alternates between increases and decreases, and the magnitudes of these changes are perfect squares. The question tests whether you can observe both the sign of the change and the fact that the differences are 2^2, 3^2, 4^2, 5^2, and so on. Such alternating square difference patterns are a favourite type of number series in competitive exams. Given Data / Assumptions: Series: 14, 18, 9, 25, 0, ? Exactly one term is missing at the end. The terms both increase and decrease, suggesting an alternating pattern. Concept / Approach: Compute the differences between consecutive terms and examine both their signs (positive or negative) and magnitudes. If you notice that the magnitudes are 4, 9, 16, 25, which are the squares of 2, 3, 4, 5, and the signs alternate plus, minus, plus, minus, then you can predict the next difference as the next square with the opposite sign. This approach makes it easy to find the missing term. Step-by-Step Solution: Step 1: Compute the differences between consecutive terms. 18 - 14 = +4. 9 - 18 = -9. 25 - 9 = +16. 0 - 25 = -25. Step 2: Observe the absolute values of these differences: 4, 9, 16, 25. Step 3: Recognise that 4 = 2^2, 9 = 3^2, 16 = 4^2, and 25 = 5^2. Step 4: Note the sign pattern of the differences: +, -, +, -. Step 5: Therefore, the next difference should follow the same rule: it should be positive (continuing the alternation) and have magnitude 6^2 = 36. Step 6: Apply this to the last known term: 0 + 36 = 36. Verification / Alternative check: Write the full extended series with the computed term: 14, 18, 9, 25, 0, 36. Differences are then +4, -9, +16, -25, +36, whose magnitudes are 2^2, 3^2, 4^2, 5^2, 6^2 and whose signs alternate +, -, +, -, +. This shows a perfectly regular pattern in both magnitude and sign, confirming that 36 is the only value that fits naturally at the end of the series. Why Other Options Are Wrong: If we choose 11, 23, or 20 instead, the last difference will either not be a perfect square or will not have the correct sign. For instance, 20 - 0 = 20, which is not equal to 36 and is not the square of an integer in this sequence. As a result, the series would break the observed rule of alternating differences with magnitudes 2^2, 3^2, 4^2, 5^2, 6^2. Therefore these options cannot be correct. Common Pitfalls: Some learners pay attention only to whether the numbers are increasing or decreasing and miss the structure in the magnitudes of the jumps. Others may see that 4, 9, 16 are squares but fail to notice that 25 is also a square and that the signs alternate. In questions where the series oscillates up and down, it is especially important to track both the absolute values and the signs of the differences. Final Answer: The correct term to fill the blank and continue the pattern is 36.

Question 9

In the following question, select the missing number from the given series: 3, 7, 16, 35, ?

Accepted Answer

Introduction / Context: This series involves numbers that increase more rapidly than a simple arithmetic progression. The differences between consecutive terms grow in a structured way, and second differences reveal the true pattern. Recognising how second differences behave is a key reasoning skill for solving advanced number series questions of this type. Given Data / Assumptions: Series: 3, 7, 16, 35, ? Exactly one term is missing at the end. The increases between terms are not constant. Concept / Approach: We first compute the differences between consecutive terms and then compute the differences between those differences (second differences). If the second differences follow a simple pattern, for example doubling each time, we can extend this pattern to obtain the next first difference and hence the next term in the original series. This is essentially using the idea of a quadratic like growth in the sequence. Step-by-Step Solution: Step 1: Compute the first differences. 7 - 3 = 4. 16 - 7 = 9. 35 - 16 = 19. Step 2: Collect these: 4, 9, 19. Step 3: Compute the second differences (differences of the first differences). 9 - 4 = 5. 19 - 9 = 10. Step 4: The second differences 5 and 10 show a doubling pattern: each step multiplies by 2. Step 5: Continuing this, the next second difference should be 20. Step 6: Add this to the last first difference: 19 + 20 = 39. Step 7: Now add this new first difference to the last term of the original series: 35 + 39 = 74. Verification / Alternative check: Rewrite the series including the missing term: 3, 7, 16, 35, 74. The first differences are 4, 9, 19, 39. The second differences are 9 - 4 = 5, 19 - 9 = 10, 39 - 19 = 20. These second differences clearly double each time, forming 5, 10, 20, which is a consistent and simple rule. This confirms that 74 is the correct next term maintaining the structure of the series. Why Other Options Are Wrong: If we choose 73, 78, or 82, the first and second differences no longer follow the exact doubling rule. For example, using 78 would give a last first difference of 78 - 35 = 43, and the second differences would not form a neat pattern of 5, 10, 20. Because the given steps clearly indicate a doubling behaviour at the level of second differences, any number that spoils this regularity cannot be the correct answer. Common Pitfalls: Some learners stop after checking that the first differences are increasing but do not investigate how they are increasing. Others try to force the numbers into linear or simple multiplicative patterns, which do not fit well. Whenever first differences appear to grow in a non uniform way, always consider second differences as a tool to uncover a hidden but simple rule. Final Answer: The missing number that correctly completes the series is 74.

Question 10

A series is given with one number missing. Choose the correct alternative from the given ones that will complete the series: -7.25, -5.75, -4.25, -2.75, ?, 0.25.

Accepted Answer

Introduction / Context: This is an arithmetic sequence involving negative decimals where each term increases by the same fixed amount. The task is to find the missing term in the middle. Such questions test basic understanding of arithmetic progressions and comfort with decimal addition and subtraction, particularly involving negative values. Given Data / Assumptions: Series: -7.25, -5.75, -4.25, -2.75, ?, 0.25. One term is missing between -2.75 and 0.25. The numbers appear to increase by a constant decimal step. Concept / Approach: In an arithmetic progression, each term differs from the previous one by a constant value known as the common difference. Here, we calculate the difference between any two consecutive known terms to determine that common difference. Once we know the step size, we can move forward or backward to fill in the missing term. Working carefully with decimals is important to avoid small arithmetic mistakes. Step-by-Step Solution: Step 1: Compute the difference between the first two terms. -5.75 - (-7.25) = -5.75 + 7.25 = 1.5. Step 2: Compute the next difference to confirm it is constant. -4.25 - (-5.75) = -4.25 + 5.75 = 1.5. Step 3: Check once more. -2.75 - (-4.25) = -2.75 + 4.25 = 1.5. Step 4: Therefore, the common difference of the arithmetic sequence is +1.5. Step 5: To find the missing term after -2.75, add 1.5. -2.75 + 1.5 = -1.25. Verification / Alternative check: Now include the missing term and check the entire progression: -7.25, -5.75, -4.25, -2.75, -1.25, 0.25. Compute all differences: each step gives +1.5. That is, -5.75 - (-7.25) = 1.5, -4.25 - (-5.75) = 1.5, -2.75 - (-4.25) = 1.5, -1.25 - (-2.75) = 1.5, and 0.25 - (-1.25) = 1.5. This confirms that the entire series is a regular arithmetic progression with common difference 1.5. Why Other Options Are Wrong: Values 1.25 and 1.5 are positive and would place the missing term on the wrong side of zero, breaking the constant step between -2.75 and 0.25. Value -1.5 would create a difference of +1.25 from -2.75 instead of +1.5, again ruining the constant difference property. Only -1.25 preserves the same increment of 1.5 that we observe between all other consecutive terms. Common Pitfalls: Some students mishandle the negative signs and decimals, especially when subtracting a negative number. Others may guess based on approximate spacing without actually computing the exact difference. The safest method is always to calculate the difference between terms explicitly, paying attention to signs and decimal places, and then check that the same difference works throughout the series. Final Answer: The missing number that completes the arithmetic sequence is -1.25.

Question 11

Bhavin has his birthday on Monday, 29th May. In the same year, on what day of the week will Rachit's birthday fall if Rachit was born on 17th November?

Accepted Answer

Introduction / Context: This is a calendar and day of the week problem. You are told that Bhavin's birthday on 29 May falls on a Monday, and you must determine the day of the week on which Rachit's birthday on 17 November of the same year falls. Questions like this test your understanding of how days shift as you move forward through the calendar, taking into account the number of days in each month. Because both dates are in the same year and after February, leap year complications do not affect the difference between these two dates. Given Data / Assumptions: Bhavin's birthday: 29th May, which is a Monday. Rachit's birthday: 17th November of the same year. We assume the usual Gregorian calendar with month lengths: May 31, June 30, July 31, August 31, September 30, October 31, November 30. We only need the offset in days between 29 May and 17 November modulo 7. Concept / Approach: The key idea is to count the total number of days between the two given dates and then take this total modulo 7, because the days of the week repeat every 7 days. If we know that a certain day is Monday and we move forward by a certain number of days, dividing that number by 7 and taking the remainder tells us how many steps forward we move in the weekly cycle. A positive remainder r means the day advances by r positions from Monday. Step-by-Step Solution: Step 1: Count the days remaining in May after 29th. May has 31 days. From 30 May to 31 May there are 2 days. Step 2: Count the days in each full month from June to October. June: 30 days. July: 31 days. August: 31 days. September: 30 days. October: 31 days. Step 3: Count the days in November up to and including 17th. From 1 November to 17 November is 17 days. Step 4: Add all these day counts to get the total number of days from 29 May to 17 November. Total = 2 (May) + 30 (June) + 31 (July) + 31 (August) + 30 (September) + 31 (October) + 17 (November). Now compute: 2 + 30 = 32, 32 + 31 = 63, 63 + 31 = 94, 94 + 30 = 124, 124 + 31 = 155, 155 + 17 = 172. So there are 172 days from 29 May to 17 November. Step 5: Reduce 172 modulo 7. 7 * 24 = 168, and 172 - 168 = 4, so 172 ≡ 4 (mod 7). Step 6: Starting from Monday, move forward 4 days in the week. Monday + 1 day = Tuesday. Monday + 2 days = Wednesday. Monday + 3 days = Thursday. Monday + 4 days = Friday. Verification / Alternative check: You can verify by smaller blocks. After 7 days from 29 May, the day again becomes Monday. After 14, 21, and so on, it repeats. Only the remainder after dividing by 7 shifts the weekday. Because 172 divided by 7 leaves a remainder of 4, the weekday must move ahead by exactly 4 positions. This is independent of whether the year is a leap year, because both dates fall after February and the extra day in February would affect both dates equally in terms of relative distance from the start of the year. Why Other Options Are Wrong: Options Saturday, Wednesday, and Sunday correspond to advances of 5, 2, and 6 days from Monday respectively. None of these agree with the actual remainder of 4 when 172 is divided by 7. Only Friday matches the calculated offset, so the other options contradict the strict arithmetic of the calendar difference and must be rejected. Common Pitfalls: Common mistakes include miscounting the days in one of the months, especially June or September, or counting from 29 May incorrectly by including or excluding a boundary day in the wrong way. Another pitfall is to attempt to handle the problem month by month without converting everything into an exact total of days. Using a clear, step by step day count and then reducing modulo 7 is the most reliable approach. Final Answer: Rachit's birthday on 17th November in the same year falls on Friday.

Question 12

A series is given with one term missing. Choose the correct alternative from the given ones that will complete the series: 14, 22, 33, 47, 64, ?

Accepted Answer

Introduction / Context: This number series increases with non constant steps, but the increases themselves follow a simple pattern. In particular, the differences between consecutive terms form an arithmetic sequence. Identifying and extending that sequence of differences allows you to determine the missing next term efficiently. Given Data / Assumptions: Series: 14, 22, 33, 47, 64, ? Exactly one next term is missing. The term to term increments appear to grow gradually. Concept / Approach: Compute first differences between consecutive terms. If these differences form their own arithmetic progression, we can extend that progression to find the next difference. Adding this new difference to the last term of the original series yields the missing term. This method leverages the idea of a sequence built from another simpler sequence of step sizes. Step-by-Step Solution: Step 1: Compute the differences between consecutive terms. 22 - 14 = 8. 33 - 22 = 11. 47 - 33 = 14. 64 - 47 = 17. Step 2: Collect these differences: 8, 11, 14, 17. Step 3: Note that the differences form an arithmetic sequence, increasing by 3 each time: 8, 11, 14, 17. Step 4: The next difference should therefore be 17 + 3 = 20. Step 5: Add this next difference to the last known term of the series: 64 + 20 = 84. Verification / Alternative check: Extend the series with the computed number: 14, 22, 33, 47, 64, 84. Recalculate the differences: 8, 11, 14, 17, 20. These differences clearly form an arithmetic progression with common difference 3. This confirms that the underlying structure of the series is consistent and that 84 is the correct missing term. Why Other Options Are Wrong: If we choose 81, 92, or 94, the last difference will not be 20 and will break the +3 pattern in the difference sequence. For instance, if the next term were 81, the final difference would be 81 - 64 = 17, repeating rather than increasing, which contradicts the observed progression 8, 11, 14, 17. Therefore those alternatives are incompatible with the established rule. Common Pitfalls: Some candidates attempt to guess the next term by approximate growth without fully checking the differences. Others may look for multiplicative patterns among the main terms, which are not present here. The most reliable approach is to calculate all consecutive differences and examine them carefully for simple sequences like constant increments or decrements. Final Answer: The number that correctly completes the series is 84.

Question 13

A series is given with one term missing. Select the correct alternative from the given ones that will complete the series: 2, 7, 16, ?, 46, 67.

Accepted Answer

Introduction / Context: This number series increases with steps that become larger each time. The differences between consecutive terms themselves grow linearly. The question tests whether you can identify this sequence of differences and extend it to locate the missing term in the middle of the series. Given Data / Assumptions: Series: 2, 7, 16, ?, 46, 67. One middle term is missing. The increments between terms increase steadily. Concept / Approach: We first compute the differences between the known consecutive terms. Then we examine whether these differences form an arithmetic progression. If they do, we can insert the appropriate missing difference and reconstruct the missing term. This process uses the idea that the main sequence is built from a simpler sequence of step sizes. Step-by-Step Solution: Step 1: Compute known differences where possible. 7 - 2 = 5. 16 - 7 = 9. 46 - ? is unknown. 67 - 46 = 21. Step 2: Look at the pattern of known differences: 5, 9, ?, 21. Step 3: Notice that 5, 9, 13, 17, 21 would form an arithmetic progression with common difference 4. Step 4: Therefore, the missing differences are 13 and 17 between the central terms. Step 5: Use 13 as the next difference after 16. The missing term = 16 + 13 = 29. Step 6: Check the following step with 17: 29 + 17 = 46, which matches the given value. Verification / Alternative check: With the series completed as 2, 7, 16, 29, 46, 67, recalculate the differences: 7 - 2 = 5, 16 - 7 = 9, 29 - 16 = 13, 46 - 29 = 17, 67 - 46 = 21. These differences are 5, 9, 13, 17, 21, forming an arithmetic progression with common difference 4. This double check shows that the sequence of differences is perfectly regular and validates 29 as the correct missing term. Why Other Options Are Wrong: If we try 26, 27, or 31 as the missing term, the resulting differences fail to form the neat sequence 5, 9, 13, 17, 21. For example, if the missing term were 27, then 27 - 16 = 11 and 46 - 27 = 19, giving differences 5, 9, 11, 19, 21, which are irregular. Because the series is clearly built on a difference pattern with constant increment 4, any number that breaks this pattern cannot be correct. Common Pitfalls: Some learners look only at the main terms and guess based on rough spacing. Others notice that the differences are increasing but do not check whether they increase in a constant manner. The safest route is always to calculate all possible differences and then inspect them carefully for simple arithmetic sequences. Final Answer: The missing number in the series is 29.

Question 14

A series is given with one term missing. Select the correct alternative from the given ones that will complete the series: 80, 130, 190, 260, ?

Accepted Answer

Introduction / Context: This series grows in a controlled way where each step increases by a larger amount than the previous step. The differences between terms themselves form an arithmetic progression with a constant increment. Recognising this secondary progression allows us to find the missing term in the series easily. Given Data / Assumptions: Series: 80, 130, 190, 260, ? One next term is missing. The jump between terms is not constant but increases steadily. Concept / Approach: We begin by calculating the differences between consecutive terms. If these form an arithmetic progression, we can find the next difference by adding the common difference, and then add that to the last term to obtain the missing value. This method converts a slightly complex series into a simpler one at the level of first differences. Step-by-Step Solution: Step 1: Compute the first differences. 130 - 80 = 50. 190 - 130 = 60. 260 - 190 = 70. Step 2: Collect these differences: 50, 60, 70. Step 3: Observe that the differences themselves form an arithmetic sequence with a common difference of 10. Step 4: The next difference should therefore be 70 + 10 = 80. Step 5: Add this new difference to the last known term of the series: 260 + 80 = 340. Verification / Alternative check: Extend the series with the found value: 80, 130, 190, 260, 340. Recalculate differences: 50, 60, 70, 80. These differences clearly increase by 10 each time, which is a very simple and natural pattern. This confirms that 340 is the correct missing term and that the underlying structure of the series is consistent. Why Other Options Are Wrong: If we choose 350, 300, or 320, the last difference will not be 80, and the differences will not continue the 50, 60, 70, 80 pattern. For example, 350 would give a final difference of 90, breaking the constant increment of 10 in the difference sequence. Thus these options do not fit the clean arithmetic progression of first differences and must be rejected. Common Pitfalls: Some candidates see that the numbers are increasing quickly and try to impose a multiplicative pattern, which does not work here. Others may compute only the first couple of differences and stop too soon. It is important to compute all available differences and look for simple arithmetic progressions among them, especially when the main series shows steadily increasing step sizes. Final Answer: The missing number in the series is 340.

Question 15

A series is given, with one number missing. Choose the correct alternative from the given ones that will complete the series: 99, 90.7, 82.4, ?, 65.8, 57.5.

Accepted Answer

Introduction / Context: This is a decimal number series that decreases by the same amount at each step. Your task is to identify the constant decrement and then use it to compute the missing term in the middle. Decimal based arithmetic progressions like this are used to test precision in calculation and familiarity with decimal subtraction. Given Data / Assumptions: Series: 99, 90.7, 82.4, ?, 65.8, 57.5. One term is missing between 82.4 and 65.8. The series appears to decrease smoothly by a fixed decimal amount. Concept / Approach: To solve this, compute the difference between two consecutive known terms and check whether the same difference applies repeatedly. If the common difference is constant, the series is an arithmetic progression. We can then move forward or backward by adding or subtracting this difference to determine any missing term. Careful handling of decimals is required to avoid errors. Step-by-Step Solution: Step 1: Compute the difference between the first two terms. 90.7 - 99 = -8.3, so the series decreases by 8.3 from 99 to 90.7. Step 2: Compute the difference between the next two visible terms to confirm the pattern. 82.4 - 90.7 = -8.3. Step 3: We see a constant difference of -8.3 between these consecutive terms. Step 4: To find the term after 82.4, subtract 8.3 again. 82.4 - 8.3 = 74.1. Step 5: Check that this same difference continues to the later terms. 65.8 - 74.1 = -8.3, and 57.5 - 65.8 = -8.3, confirming the consistency. Verification / Alternative check: Insert the computed term into the series: 99, 90.7, 82.4, 74.1, 65.8, 57.5. Now verify all differences: 90.7 - 99 = -8.3, 82.4 - 90.7 = -8.3, 74.1 - 82.4 = -8.3, 65.8 - 74.1 = -8.3, and 57.5 - 65.8 = -8.3. Every step uses the same decrement, so the series is a perfect arithmetic progression with common difference -8.3, confirming that 74.1 is the correct missing term. Why Other Options Are Wrong: Options 73.3, 74.8, and 75.2 would each produce at least one difference that is not equal to -8.3. For example, if the missing term were 73.3, then 73.3 - 82.4 = -9.1, which does not match the observed pattern. Any deviation from the constant step of -8.3 would break the arithmetic progression, so these values cannot be correct. Common Pitfalls: Some learners approximate the decimal differences mentally and may incorrectly assume a slightly different step size, such as -8 or -9. Others may only check differences at the beginning of the series and not confirm them for all later terms. The safest approach is to compute all relevant differences accurately and ensure that the same value appears throughout the sequence. Final Answer: The number that correctly completes the decimal series is 74.1.

Question 16

A number series of perfect squares is given with one term missing. Choose the correct option that completes the sequence: 4, 9, 16, 25, 36, ?

Accepted Answer

Introduction / Context: This question tests the ability to recognize a simple pattern in a number series based on perfect squares of consecutive integers. Such questions are common in competitive examinations because they quickly reveal whether a candidate can identify basic numeric structures and extend them correctly. Understanding square numbers and how they grow as the base integer increases is an important foundation for many other quantitative topics. Given Data / Assumptions: The series given in the question is: 4, 9, 16, 25, 36, ? We must assume that there is a consistent rule generating each term from a simple mathematical concept, and we are expected to find the next number that follows the same rule. Concept / Approach: The concept involved is that of perfect squares. A perfect square is a number that can be written as n^2 for some integer n. When we look at the terms, each appears to be the square of a consecutive integer: 2^2, 3^2, 4^2, 5^2, and 6^2. Once we confirm that pattern, we can extend it by taking the next integer in order and squaring it. Step-by-Step Solution: Step 1: Express each term as a square of an integer.4 = 2^29 = 3^216 = 4^225 = 5^236 = 6^2Step 2: Observe that the bases are consecutive integers: 2, 3, 4, 5, 6.Step 3: The next integer after 6 is 7, so the next term should be 7^2.Step 4: Calculate 7^2.7^2 = 49. Verification / Alternative check: An alternative way to check is to look at the differences between the terms. The differences are 9 - 4 = 5, 16 - 9 = 7, 25 - 16 = 9, and 36 - 25 = 11. These differences themselves form a sequence of consecutive odd numbers. The difference between 36 and the next term should then be the next odd number, 13. Adding 13 to 36 also gives 49. This confirms the result from the square pattern. Why Other Options Are Wrong: 56 is not a perfect square and does not fit the odd difference pattern. 64 is a perfect square, but it would correspond to 8^2 and would skip 7^2, breaking the sequence of consecutive squares. 21 and 94 are neither perfect squares nor consistent with the difference pattern, so they cannot be correct. Common Pitfalls: Candidates sometimes look only at differences and may miscalculate them, or they may incorrectly jump to 64 because it is a well known square without checking that 49 is the correct next step. Another mistake is to assume a linear pattern when the growth clearly matches the pattern of n^2. Always verify the pattern across all terms, not just the last two. Final Answer: The missing term in the series 4, 9, 16, 25, 36, ? is 49.

Question 17

In the following sequence of numbers based on perfect squares, identify which one term is wrong and does not fit the pattern: 49, 36, 25, 18, 9, 4.

Accepted Answer

Introduction / Context: This problem asks you to find the wrong term in a series that is otherwise built from perfect squares. Detecting the odd term out in number series requires you to recognize a common mathematical pattern that most terms follow and then identify which number breaks that rule. This is a typical reasoning question in many examinations. Given Data / Assumptions: The series is: 49, 36, 25, 18, 9, 4 We assume that the designer of the question intended a consistent mathematical pattern and that exactly one term has been altered or misprinted. Our goal is to find that inconsistent term. Concept / Approach: The key idea here is perfect squares of integers in descending order. Perfect squares are numbers of the form n^2. Looking at the sequence, several terms obviously match well known squares: 49 = 7^2, 36 = 6^2, 25 = 5^2, 9 = 3^2, and 4 = 2^2. We should check whether all terms can be expressed as consecutive squares, and if one number cannot, that number is the wrong term. Step-by-Step Solution: Step 1: Rewrite each term as a square where possible.49 = 7^236 = 6^225 = 5^29 = 3^24 = 2^2Step 2: Observe the pattern. The squares correspond to descending integers: 7, 6, 5, (4 should appear here), 3, 2.Step 3: The correct descending sequence of squares should be 49, 36, 25, 16, 9, 4.Step 4: Notice that 18 appears where 16 (which is 4^2) should be. Therefore, 18 does not follow the square pattern. Verification / Alternative check: Check the differences between consecutive squares. For 7^2 to 6^2, 49 - 36 = 13; 36 - 25 = 11; 25 - 16 = 9; 16 - 9 = 7; 9 - 4 = 5. These are consecutive odd numbers in reverse order. If we compare 25 and 18, 25 - 18 = 7, which does not align with the expected difference of 9. This confirms that 18 breaks the established pattern. Why Other Options Are Wrong: 49, 36, 25, 9, and 4 are all perfect squares of consecutive integers 7, 6, 5, 3, and 2. They form a consistent descending sequence when combined with the missing 4^2. Therefore, these numbers follow the intended pattern and cannot be the wrong term. Common Pitfalls: Some learners may check only whether numbers are perfect squares without considering whether they are in consecutive order. Others might focus on differences between terms and get confused by non constant gaps. The robust method is to map each number to its square root and see if this sequence of roots is consistent and consecutive. Final Answer: The only term that does not fit the descending series of perfect squares is 18.

Question 18

A number series is given with one term missing. Using the observed pattern, choose the correct option to complete the series: 18, 25, 34, 45, ?

Accepted Answer

Introduction / Context: This question is a classic example of a number series based on increasing differences. Instead of directly applying a formula to the terms, we look at how each term changes relative to the previous one. Many reasoning questions rely on such difference patterns, so it is important to become comfortable with spotting them quickly. Given Data / Assumptions: The series provided is: 18, 25, 34, 45, ? We assume that there is a consistent pattern in the differences between consecutive terms, and we must extend this pattern to find the missing number. Concept / Approach: The main idea is to compute the difference between consecutive terms and see if these differences themselves form a recognizable pattern. Often these differences increase or decrease in a simple manner, such as adding a constant amount or following their own arithmetic progression. Step-by-Step Solution: Step 1: Compute the first differences between consecutive terms.25 - 18 = 734 - 25 = 945 - 34 = 11Step 2: Observe the pattern in the differences: 7, 9, 11. These are consecutive odd numbers.Step 3: The next difference should continue this pattern of odd numbers. After 7, 9, and 11, the next odd number is 13.Step 4: Add this next difference to the last known term.45 + 13 = 58. Verification / Alternative check: We can quickly verify by reconstructing the series from 18 using the observed pattern of odd differences: 18 + 7 = 25, 25 + 9 = 34, 34 + 11 = 45, and 45 + 13 = 58. Everything is consistent, confirming that the missing term must be 58 if the series is to preserve the pattern of increasing odd differences. Why Other Options Are Wrong: 60, 59, 65, and 52 do not maintain the odd difference progression 7, 9, 11, 13. For example, if we chose 60, the final difference would be 15, which jumps ahead, and the sequence of differences becomes 7, 9, 11, 15, breaking the neat pattern. The other options distort the difference sequence even more noticeably. Common Pitfalls: Students sometimes search for multiplicative or more complex rules when a simple difference pattern is sufficient. Another mistake is miscalculating one of the differences, which then leads to an incorrect next term. Always compute the differences carefully and check whether they follow a simple and consistent pattern before deciding on the answer. Final Answer: The missing term that correctly completes the series is 58.

Question 19

In the following number series, one term is missing. Identify the correct number that completes the pattern: 4, 7, 11, 18, 29, ?

Accepted Answer

Introduction / Context: This question presents a number series where each term after the first few is formed by combining information from earlier terms. Such series are slightly more advanced than simple difference based ones because you need to observe relationships between multiple preceding terms rather than only comparing neighbors. Given Data / Assumptions: The series is: 4, 7, 11, 18, 29, ? We assume that the series follows a consistent rule, likely involving sums of previous numbers, and we must extend the series by finding the next term. Concept / Approach: The guiding idea is that many series are Fibonacci like, where each term is the sum of the previous two terms. We check if that applies here by testing whether each term from the third term onwards equals the sum of the two terms immediately before it. If this holds for successive terms, we can confidently extend the pattern. Step-by-Step Solution: Step 1: Check whether the third term equals the sum of the first two.4 + 7 = 11, which matches the third term.Step 2: Check the fourth term.7 + 11 = 18, which matches the fourth term.Step 3: Check the fifth term.11 + 18 = 29, which matches the fifth term.Step 4: Since the pattern holds, compute the next term as the sum of the previous two terms.18 + 29 = 47. Verification / Alternative check: Another way to confirm is to reconstruct the series starting from 4 and 7 while imposing the rule that every new term equals the sum of the previous two. This gives: 4, 7, 11, 18, 29, 47, and so on. No contradictions appear, so 47 is a consistent and unique extension of the series. No other candidate preserves this simple rule of formation. Why Other Options Are Wrong: Values such as 45, 30, 32, or 41 do not equal 18 + 29. Choosing any of them would break the established rule that each term after the second is the sum of the preceding two terms. For instance, if we used 45, the sum 18 + 29 would no longer match the next term, and the series would lose its internal consistency. Common Pitfalls: Students may mistakenly search for a constant or increasing difference between terms and overlook the possibility that each term is a sum of earlier ones. Another common mistake is arithmetic error in adding the previous two terms. Carefully checking the pattern across several steps avoids such errors. Final Answer: The correct number that completes the series is 47.

Question 20

A number series is given with one term missing. Using the observed rule, select the correct number to complete the series: 10, 22, 46, ?

Accepted Answer

Introduction / Context: This question involves a number series that follows a simple multiplicative and additive rule. Many exam series questions use a combination of doubling, halving, or adding a constant to generate each next term. Quickly detecting such a pattern helps in solving these questions efficiently. Given Data / Assumptions: The series provided is: 10, 22, 46, ? We assume that each consecutive term is generated from the previous one by applying a consistent operation, most likely involving multiplication by a fixed factor and then addition or subtraction of a small constant. Concept / Approach: The natural first check is whether each term is approximately double the previous term. If so, we then examine whether a small correction, such as adding or subtracting a fixed number, is applied. This approach is common in reasoning questions where numbers grow relatively fast but not purely exponentially. Step-by-Step Solution: Step 1: Compare 10 and 22.10 multiplied by 2 gives 20, and then adding 2 gives 22. So, 10 * 2 + 2 = 22.Step 2: Compare 22 and 46.22 multiplied by 2 gives 44, and adding 2 gives 46. So, 22 * 2 + 2 = 46.Step 3: The pattern seems to be: new term = previous term * 2 + 2.Step 4: Apply the same rule to find the missing term.46 * 2 + 2 = 92 + 2 = 94. Verification / Alternative check: We can confirm by working backwards as well. If we take 94 and attempt the inverse operation, we subtract 2 and then divide by 2: (94 - 2) / 2 = 92 / 2 = 46, which matches the previous term. Applying this inverse logic again to 46 gives (46 - 2) / 2 = 22. This backward consistency supports our conclusion that the rule is correct. Why Other Options Are Wrong: Values like 90, 91, 95, and 88 do not satisfy the relation new term = previous term * 2 + 2. For example, 46 * 2 + 2 is not 90, 91, 95, or 88. Using any of them would break the precise pattern observed between earlier terms, which is not acceptable in a well formed series question. Common Pitfalls: One common error is to assume a constant difference between terms, which clearly does not hold here. Another is to approximate and think that because 22 is a little more than double 10 and 46 is a little more than double 22, any value around twice 46 is acceptable. However, the series relies on an exact recurrence, so minor deviations are not allowed. Final Answer: The missing number that correctly completes the series is 94.

Number Series Questions