Question 1

In the following number series, select the missing number that will correctly complete the sequence: 58, 61, 65, 70, ?, 83.

Accepted Answer

Introduction / Context: This problem involves an increasing number series in which the differences between consecutive terms are themselves increasing. Recognizing this secondary pattern in the differences is key to solving the question. Such series are very common in competitive exams to assess logical and numerical reasoning skills. Given Data / Assumptions: Given series: 58, 61, 65, 70, ?, 83.The term between 70 and 83 is missing.We assume a smooth, consistent pattern in the differences between terms. Concept / Approach: We start by calculating the differences between known consecutive terms. If these differences form a clear pattern, such as a simple arithmetic progression, we can predict the next difference and then determine the missing term. Here, the numbers increase modestly, suggesting that the differences may themselves be small and steadily growing integers like 3, 4, 5, and so on. Step-by-Step Solution: Step 1: Compute 61 - 58 = 3.Step 2: Compute 65 - 61 = 4.Step 3: Compute 70 - 65 = 5.Step 4: The differences so far are 3, 4, 5, which strongly suggests that the next differences should be 6 and then 7.Step 5: Let the missing term be x. From 70 to x we should add 6, giving x = 70 + 6 = 76.Step 6: Verify the next step: from x to 83 we should add 7. Indeed, 76 + 7 = 83, exactly matching the last given term. Verification / Alternative check: Write the full series with the candidate value: 58, 61, 65, 70, 76, 83. The sequence of differences becomes 3, 4, 5, 6, 7, which is a simple and elegant pattern of consecutive integers. This is a typical structure used in exam questions, and the complete series aligns perfectly with it, providing strong confirmation that 76 is correct. Why Other Options Are Wrong: Option 77 would give a difference of 7 from 70 to 77, which skips the expected difference of 6 and makes the pattern of differences inconsistent.Option 78 yields differences 70 to 78 = 8 and 78 to 83 = 5, which do not fit the increasing sequence 3, 4, 5, 6, 7.Option 75 provides differences 5 and 8, again failing to form any simple sequence of steadily increasing differences. Common Pitfalls: Some learners might try to average neighbouring terms or look for multiplicative relationships, which are not appropriate here. Another pitfall is to miscalculate one of the differences and thus miss the neat pattern of 3, 4, 5, 6, 7. Always compute each difference carefully and check whether the sequence of differences itself follows a recognizable progression. Final Answer: The missing number that completes the series is 76.

Question 2

A letter series using Roman numeral symbols is given with one term missing. Choose the correct alternative from the options that will complete the series: XIIIII, IXIIII, IIXIII, IIIXII, IIIIXI, ?

Accepted Answer

Introduction / Context: This verbal reasoning question uses the Roman numeral symbols I and X arranged in a pattern. The task is to identify how the arrangement changes from term to term and then determine which option continues that pattern. The focus is on positional changes of a specific character rather than on calculating actual Roman numeral values. Given Data / Assumptions: Given series: XIIIII, IXIIII, IIXIII, IIIXII, IIIIXI, ?Each term contains exactly one X and multiple I symbols.We assume that the position of X follows a consistent movement across the series. Concept / Approach: The main idea is to track the position of X from left to right within each term. The total number of letters remains constant, but the X appears to be shifting one place to the right in every successive term. By examining each term character by character, we can verify this movement and then predict the final position of X in the next term. We are not required to interpret the numeral values; only the arrangement matters here. Step-by-Step Solution: Step 1: Write the first term as a sequence of six characters: X I I I I I (X at position 1).Step 2: Second term: I X I I I I (X at position 2).Step 3: Third term: I I X I I I (X at position 3).Step 4: Fourth term: I I I X I I (X at position 4).Step 5: Fifth term: I I I I X I (X at position 5).Step 6: The pattern clearly shows that X shifts one place to the right in each term, so in the next term X must move to position 6.Step 7: A term with X at position 6 and I in all earlier positions is I I I I I X, written as IIIIIX. Verification / Alternative check: List the positions of X across the given terms: 1, 2, 3, 4, 5. This forms a simple sequence increasing by 1 each time. The logical continuation is position 6. Among the options, only IIIIIX has X in the sixth and final position. All other letters remain I, keeping the total number of characters and their types unchanged. This fully matches the observed rule, confirming that IIIIIX is the correct next term. Why Other Options Are Wrong: Option IIIIXII has X in the middle with a total of seven letters, which breaks both the six-character length and the one-step shift pattern.Option IIIIIXI places X at the second last position and adds an extra I at the end, again giving seven characters and violating the fixed length.Option XIIIIX has X at both the first and last positions, introducing two X symbols and completely breaking the rule that there should be exactly one X. Common Pitfalls: One common error is to overthink the Roman numeral values and attempt arithmetic operations, which are not relevant here. Others may ignore character counts and only consider visual similarity, missing the consistent shift of X by one position. Carefully counting positions and maintaining the constant length is essential to avoid these mistakes. Final Answer: The term that correctly completes the letter pattern series is IIIIIX.

Question 3

A number series of perfect squares is given with one term missing. Choose the correct alternative from the options that will complete the series: 49, 64, ?, 100, 121.

Accepted Answer

Introduction / Context: This question presents a number series made of perfect squares. The task is to identify which square is missing and select it from the options. Recognizing perfect squares and their corresponding integer roots is a fundamental number skill used often in aptitude and reasoning questions. Given Data / Assumptions: Given series: 49, 64, ?, 100, 121.We must find the missing third term.We assume the numbers are consecutive squares of natural numbers in increasing order. Concept / Approach: Perfect squares are numbers of the form n^2, where n is an integer. To solve this question, we identify the integer roots of the known terms and check whether they follow a consecutive sequence. Once we see which integer is missing in that sequence, we square it to obtain the missing term. This method is simple and reliable for square-based series. Step-by-Step Solution: Step 1: Express 49 as a square: 49 = 7^2.Step 2: Express 64 as a square: 64 = 8^2.Step 3: Express 100 as a square: 100 = 10^2.Step 4: Express 121 as a square: 121 = 11^2.Step 5: The sequence of roots is 7, 8, ?, 10, 11. It is clear that 9 is missing between 8 and 10.Step 6: Square the missing root: 9^2 = 81, so the missing term is 81. Verification / Alternative check: Write the completed series of squares: 49 (7^2), 64 (8^2), 81 (9^2), 100 (10^2), 121 (11^2). The roots form a clean sequence of consecutive integers from 7 to 11. This is a typical exam pattern and confirms that the series is indeed built from consecutive square numbers. Since 81 is the only value that completes this structure, it must be the correct answer. Why Other Options Are Wrong: Option 74 is not a perfect square and does not correspond to any integer root.Option 80 is also not a perfect square; its square root is not an integer.Option 75 is similarly non-square and would break the pattern of consecutive perfect squares. Common Pitfalls: Some learners may attempt to look at differences between terms rather than recognizing the square pattern, which can be misleading here. Another mistake is confusing near-square numbers such as 80 or 75 with actual squares. Memorizing squares of numbers from 1 to at least 20 is extremely helpful for quickly identifying such patterns in exams. Final Answer: The missing term that completes the series of perfect squares is 81.

Question 4

A number series is given with one term missing. Choose the correct alternative from the given options that will complete the series: 1, 7, 42, 210, 840, ?

Accepted Answer

Introduction / Context: This is a multiplicative number series where each term is obtained by multiplying the previous term by a whole number. Interestingly, the multipliers themselves follow a decreasing pattern. Such questions test the ability to recognize factorial-like or product-based structures in sequences, which are common in logical reasoning and quantitative aptitude exams. Given Data / Assumptions: Given series: 1, 7, 42, 210, 840, ?We need to find the next term after 840.We assume that each term is a product of the previous term and a systematically changing multiplier. Concept / Approach: The strategy is to find the ratio between each pair of consecutive terms. If these ratios form a recognizable pattern, such as descending integers, we can extend that pattern to determine the next ratio and thus compute the missing term. This method is especially effective when the series grows quickly, indicating a multiplicative rather than additive structure. Step-by-Step Solution: Step 1: Compute the ratio 7 / 1 = 7.Step 2: Compute the ratio 42 / 7 = 6.Step 3: Compute the ratio 210 / 42 = 5.Step 4: Compute the ratio 840 / 210 = 4.Step 5: The multipliers are 7, 6, 5, 4, which form a descending sequence of integers.Step 6: The next multiplier should therefore be 3.Step 7: Multiply 840 by 3 to get the next term: 840 * 3 = 2520. Verification / Alternative check: Write the extended series with the candidate term: 1, 7, 42, 210, 840, 2520. Now list the multipliers: 1 * 7 = 7, 7 * 6 = 42, 42 * 5 = 210, 210 * 4 = 840, and 840 * 3 = 2520. The pattern of decreasing multipliers 7, 6, 5, 4, 3 is consistent and natural, confirming the correctness of 2520 as the next term. This structure is reminiscent of partial factorial patterns often used in exam questions. Why Other Options Are Wrong: Option 1240 does not equal 840 multiplied by any integer in the descending sequence and breaks the smooth product pattern.Option 2640 corresponds to 840 * 3.1428..., which is not a simple integer multiplier and does not fit the pattern of descending whole number factors.Option 1680 equals 840 * 2, which would continue with a multiplier of 2 instead of the next logical multiplier 3 in the descending sequence 7, 6, 5, 4, 3. Common Pitfalls: Some learners initially try to use addition or subtraction, which becomes impractical as the numbers grow rapidly. Others may miscalculate the ratios or overlook the descending nature of the multipliers. Always compute the ratios carefully and look for simple integer sequences such as 7, 6, 5, 4 that describe how the series evolves. Final Answer: The missing term that completes the multiplicative series is 2520.

Question 5

A number series is given with one term missing. Choose the correct alternative from the options that will complete the series: 1, 5, 30, 210, 1680, ?

Accepted Answer

Introduction / Context: This number series again uses a multiplicative pattern in which each term is produced by multiplying the previous one by a growing integer. The task is to identify the changing multipliers and extend that pattern to find the missing next term. Such structures are often inspired by factorial-like growth and are common in competitive reasoning exams. Given Data / Assumptions: Given series: 1, 5, 30, 210, 1680, ?We must determine the term that follows 1680.We assume a consistent pattern in the integer multipliers between consecutive terms. Concept / Approach: To solve this, we examine the ratio between each pair of adjacent terms. If these ratios follow a recognizable pattern, such as increasing consecutive integers, we can use that to find the next ratio and compute the missing term. When numbers increase very quickly, multiplication by larger and larger integers is usually involved rather than simple addition. Step-by-Step Solution: Step 1: Compute 5 / 1 = 5.Step 2: Compute 30 / 5 = 6.Step 3: Compute 210 / 30 = 7.Step 4: Compute 1680 / 210 = 8.Step 5: The multipliers are 5, 6, 7, 8, forming an increasing sequence of consecutive integers.Step 6: The next logical multiplier is 9.Step 7: Multiply 1680 by 9: 1680 * 9 = 15120, which gives the missing term. Verification / Alternative check: Write the extended series including the candidate term: 1, 5, 30, 210, 1680, 15120. Now check the multipliers: 1 * 5 = 5, 5 * 6 = 30, 30 * 7 = 210, 210 * 8 = 1680, 1680 * 9 = 15120. The pattern of multipliers 5, 6, 7, 8, 9 is perfectly consistent and typical of exam questions that build on consecutive integer factors. This confirms 15120 as the correct answer. Why Other Options Are Wrong: Option 13440 corresponds to 1680 * 8, which repeats the previous multiplier and breaks the increasing pattern.Option 11760 equals 1680 * 7, which would reverse the direction of the multipliers instead of continuing them forward.Option 8400 equals 1680 * 5, discarding the established pattern of steadily increasing multipliers from 5 to 9. Common Pitfalls: Some candidates try to approximate pattern recognition by averaging or by using arbitrary factors. Others may miscalculate products involving large numbers, such as 1680 * 9. It is important to systematically compute ratios, identify the clear integer sequence in the multipliers, and then perform the multiplication accurately to avoid such mistakes. Final Answer: The missing term that completes the product-based number series is 15120.

Question 6

A number series is given with one term missing. Choose the correct alternative from the options that will complete the series: 206, 309, 412, ?, 618, 721.

Accepted Answer

Introduction / Context: This question presents what is effectively an arithmetic series, where a constant difference is added to each term to obtain the next one. The task is to identify that difference and use it to find the missing term in the middle of the sequence. Such constant-difference patterns are fundamental in number series questions. Given Data / Assumptions: Given series: 206, 309, 412, ?, 618, 721.The fourth term is missing between 412 and 618.We assume that the difference between consecutive terms is constant. Concept / Approach: We begin by calculating the difference between the first two and next two known consecutive terms. If these differences are equal, it indicates an arithmetic progression. With the common difference established, we can compute the missing term by either adding or subtracting that difference from the nearest known term. This method is straightforward and reliable for linear patterns. Step-by-Step Solution: Step 1: Compute 309 - 206 = 103.Step 2: Compute 412 - 309 = 103.Step 3: The common difference between the first three terms is therefore 103, indicating an arithmetic series.Step 4: Let the missing term be x. It should be obtained by adding 103 to 412: x = 412 + 103 = 515.Step 5: Verify the later terms: 515 + 103 = 618, and 618 + 103 = 721.Step 6: Since the difference 103 holds throughout, 515 is the correct missing term. Verification / Alternative check: Write the full series with the candidate term: 206, 309, 412, 515, 618, 721. Now compute all differences: 309 - 206 = 103, 412 - 309 = 103, 515 - 412 = 103, 618 - 515 = 103, and 721 - 618 = 103. The constant difference of 103 remains unchanged, confirming a simple arithmetic progression and validating 515 as the correct answer. Why Other Options Are Wrong: Option 751 does not maintain the constant difference; 751 - 412 = 339 and 618 - 751 = -133, breaking the pattern entirely.Option 749 also yields inconsistent differences and does not allow 618 and 721 to be produced by repeatedly adding the same number.Option 514 would give 514 - 412 = 102, and 618 - 514 = 104, so the difference is not constant and fails to form a proper arithmetic series. Common Pitfalls: One common error is miscalculating the difference, especially with three-digit numbers. Another is assuming a more complex pattern than necessary when a simple arithmetic series with a constant difference is sufficient. Always verify differences between multiple consecutive terms before deciding on the pattern and computing the missing value. Final Answer: The missing number that completes the arithmetic series is 515.

Question 7

A series of ordered pairs is given with one pair missing. Choose the correct alternative from the given options that will complete the series: (3, 5), (5, 7), ( ? ), (11, 13).

Accepted Answer

Introduction / Context: This question uses ordered pairs of numbers arranged in a sequence. The task is to identify the pattern that connects consecutive pairs and then determine which missing pair fits that pattern. Here the pattern is based on prime numbers and their positions in the sequence, testing number sense and recognition of prime progressions. Given Data / Assumptions: Given pairs: (3, 5), (5, 7), ( ? ), (11, 13).We must find the missing third pair.We assume that the pairs follow a logical progression involving prime numbers. Concept / Approach: The key idea is to examine the first and second elements of each pair separately. We observe that all visible numbers 3, 5, 7, 11, and 13 are primes. The pairs appear to link consecutive primes in an overlapping way: the second element of one pair often becomes the first element of the next. By listing primes in order, we can map how the sequence of pairs is constructed and insert the missing pair accordingly. Step-by-Step Solution: Step 1: List primes in order: 2, 3, 5, 7, 11, 13, and so on.Step 2: Observe that (3, 5) contains the primes 3 and 5, and (5, 7) contains 5 and 7. These are consecutive primes: (3rd, 4th) and (4th, 5th) primes if we index from 2.Step 3: The last given pair (11, 13) contains 11 and 13, which are again consecutive primes later in the list.Step 4: To continue the overlapping pattern, after (5, 7) we expect a pair formed by the next two consecutive primes after 7, which are 7 and 11.Step 5: Therefore, the missing pair is (7, 11). Verification / Alternative check: Write the sequence of pairs using consecutive primes in a sliding window: (3, 5), (5, 7), (7, 11), (11, 13). Each pair consists of two consecutive primes and the second prime of one pair becomes the first of the next pair, except where the sequence jumps from 7 to 11 due to the absence of 9, which is composite. This structure is consistent and natural, confirming that (7, 11) is the correct missing pair. Why Other Options Are Wrong: Option (7, 9) introduces 9, which is not a prime number, breaking the prime-based pattern.Option (9, 11) again includes 9, a composite number, so it does not fit the strict prime sequence.Option (9, 13) contains 9 and also skips 11 in the second element, disrupting both primality and the idea of consecutive primes. Common Pitfalls: Some learners focus only on numerical differences between elements of each pair and overlook the key property that all valid numbers must be prime. Another common mistake is to treat 9 as a prime simply because it is odd. Always verify primality by checking divisibility, especially for smaller numbers like 9 which are frequently used as traps in exam questions. Final Answer: The missing ordered pair that completes the prime-based sequence is (7, 11).

Question 8

A number series is given with one term missing. Choose the correct alternative from the options that will complete the series: 10, 29, 66, 127, ?

Accepted Answer

Introduction / Context: This question involves a number series where the differences between consecutive terms are not constant but increase according to a secondary pattern. To solve such problems, we often need to examine not only the first differences but also the second differences. This tests deeper numerical reasoning skills beyond simple arithmetic sequences. Given Data / Assumptions: Given series: 10, 29, 66, 127, ?The fifth term is missing.We assume a consistent and simple pattern exists in the first and possibly second differences. Concept / Approach: The approach is to compute the differences between consecutive terms and then check whether those differences themselves follow an arithmetic pattern. If the first differences increase by a constant amount, we have constant second differences, which is a hallmark of quadratic-type number patterns often used in reasoning questions. Once we identify the second difference, we can predict the next first difference and find the missing term. Step-by-Step Solution: Step 1: Compute first differences: 29 - 10 = 19.Step 2: Next difference: 66 - 29 = 37.Step 3: Next difference: 127 - 66 = 61.Step 4: Now compute second differences: 37 - 19 = 18 and 61 - 37 = 24.Step 5: The second differences, 18 and 24, increase by 6. We expect the next second difference to be 30.Step 6: Add this expected second difference to the last first difference: 61 + 30 = 91.Step 7: Add this new first difference to the last term to get the missing term: 127 + 91 = 218. Verification / Alternative check: Insert the candidate term to get the complete series: 10, 29, 66, 127, 218. Recalculate first differences: 19, 37, 61, 91. Now calculate second differences: 37 - 19 = 18, 61 - 37 = 24, 91 - 61 = 30. These second differences form an arithmetic sequence 18, 24, 30, with a common difference of 6, confirming that the pattern is consistent and that 218 fits perfectly. Why Other Options Are Wrong: Option 330 would yield first differences that do not maintain the increasing second-difference pattern of plus 6.Option 115 would make the series decrease from 127 to 115, breaking the overall increasing trend and the computed difference structure.Option 273 would produce very large differences that are inconsistent with the smooth progression of second differences established earlier. Common Pitfalls: Some students stop after checking for a constant first difference and, failing to find one, may guess randomly. Others may miscalculate second differences or fail to notice that they increase by a constant amount. A systematic approach of computing both first and second differences and observing their patterns is crucial for reliably solving such questions. Final Answer: The missing term that correctly completes the series is 218.

Question 9

A number series is given with one term missing. Choose the correct alternative from the options that will complete the series: 79, 159, 199, 219, ?

Accepted Answer

Introduction / Context: This question involves a number series where the differences between consecutive terms form a pattern related to halving. Recognizing that the increments themselves shrink in a structured way is essential. Such patterns test the ability to observe changes in differences rather than just in the original numbers. Given Data / Assumptions: Given series: 79, 159, 199, 219, ?We must find the next term after 219.We assume that the differences between terms follow a simple, repeating, or steadily changing rule. Concept / Approach: We start by calculating the differences between consecutive terms. If these differences themselves follow a pattern, such as halving or doubling, we extend that pattern to obtain the next difference and thus the missing term. This technique is standard when the primary sequence appears irregular at first glance but the steps between terms show more regularity. Step-by-Step Solution: Step 1: Compute the difference 159 - 79 = 80.Step 2: Compute the difference 199 - 159 = 40.Step 3: Compute the difference 219 - 199 = 20.Step 4: The differences are 80, 40, 20, forming a sequence where each difference is half of the previous one.Step 5: Continuing this pattern, the next difference should be 10, which is half of 20.Step 6: Add this difference to the last term: 219 + 10 = 229. Verification / Alternative check: Write the series including the candidate term: 79, 159, 199, 219, 229. Now compute all differences: 159 - 79 = 80, 199 - 159 = 40, 219 - 199 = 20, and 229 - 219 = 10. The pattern of differences 80, 40, 20, 10 consistently halves each time, confirming that 229 is the correct next term in the sequence. Why Other Options Are Wrong: Option 234 would give a difference of 15 from 219, which does not match the halving pattern of 80, 40, 20, 10.Option 239 would produce a difference of 20, repeating the previous difference instead of halving it, and thereby breaking the established pattern.Option 222 would yield a difference of 3, which fits no simple relationship with the earlier differences of 80, 40, and 20. Common Pitfalls: Students sometimes search for a direct rule among the original numbers and overlook the more obvious pattern in the differences. Another frequent mistake is failing to compute differences correctly, especially when several values are involved in a chain. Always calculate differences systematically and check whether they follow a simple structure like halving or doubling. Final Answer: The missing term that continues the halving-difference pattern is 229.

Question 10

A number series is given with one term missing. Choose the correct alternative from the options that will complete the series: 200, 100, 50, 25, 12.5, 6.25, ?

Accepted Answer

Introduction / Context: This question presents a decreasing number series involving decimals. The pattern appears to involve repeated halving of each term. Such series are useful for testing understanding of fractional operations and comfort with decimal arithmetic in reasoning problems. Given Data / Assumptions: Given series: 200, 100, 50, 25, 12.5, 6.25, ?We must determine the next term after 6.25.We assume that each term is related to the previous term by a consistent operation, likely division by 2. Concept / Approach: When numbers are steadily halved, the pattern is multiplicative with a ratio of 1 / 2 between consecutive terms. Recognizing this allows us to apply simple division repeatedly. The presence of decimals like 12.5 and 6.25 supports the idea that halving continues beyond whole numbers. We therefore check whether each term is exactly half of the previous one and then extend this process. Step-by-Step Solution: Step 1: Check 100 as half of 200: 200 / 2 = 100.Step 2: Check 50 as half of 100: 100 / 2 = 50.Step 3: Check 25 as half of 50: 50 / 2 = 25.Step 4: Check 12.5 as half of 25: 25 / 2 = 12.5.Step 5: Check 6.25 as half of 12.5: 12.5 / 2 = 6.25.Step 6: Continue the pattern by halving 6.25: 6.25 / 2 = 3.125.Step 7: Therefore, the missing term is 3.125. Verification / Alternative check: Write the fully extended series including the candidate term: 200, 100, 50, 25, 12.5, 6.25, 3.125. Each step is generated by dividing the previous term by 2. This steady halving is simple, consistent, and exactly matches all transitions in the series, confirming that 3.125 is the correct answer. Why Other Options Are Wrong: Option 2.125 does not equal 6.25 divided by 2 and would represent a ratio of approximately 0.34 instead of 0.5.Option 3.025 is not an exact half of 6.25 and suggests no clear fractionally consistent pattern.Option 2.025 is even further from half of 6.25 and completely breaks the halving rule that governs the series. Common Pitfalls: Some learners may be uncomfortable with decimals and therefore miscalculate the halving step after 6.25. Others might incorrectly round intermediate values, which can distort the pattern. It is important to perform exact halving, remembering that 6.25 is 6 and one quarter, so half of it is 3 and one eighth, which is 3.125 in decimal form. Final Answer: The missing number that continues the halving pattern is 3.125.

Question 11

A number series is given with one term missing. Choose the correct alternative from the options that will complete the series: 30, 60, 360, 3600, ?

Accepted Answer

Introduction / Context: This question features a rapidly increasing number series driven by multiplication. The multipliers themselves follow a pattern, and correctly identifying that pattern is the key to determining the missing term. Such problems test the ability to understand higher-order patterns in products rather than simple addition or subtraction. Given Data / Assumptions: Given series: 30, 60, 360, 3600, ?We must find the term that follows 3600.We assume that each term is obtained from the previous one by multiplying it with a systematically changing integer. Concept / Approach: When numbers grow very large very quickly, a multiplicative pattern is usually at work. The strategy is to compute the ratio between each pair of consecutive terms and check whether these ratios follow their own numeric pattern, often an arithmetic progression. Once that pattern is clear, we extend it to find the next multiplier and thus compute the missing term. Step-by-Step Solution: Step 1: Compute 60 / 30 = 2, so the second term is 30 multiplied by 2.Step 2: Compute 360 / 60 = 6, so the third term is 60 multiplied by 6.Step 3: Compute 3600 / 360 = 10, so the fourth term is 360 multiplied by 10.Step 4: The multipliers are 2, 6, 10, which form an arithmetic sequence with a common difference of 4.Step 5: The next multiplier should be 14, obtained by adding 4 to 10.Step 6: Multiply 3600 by 14: 3600 * 14 = 50400. Verification / Alternative check: Extend the series with the candidate term: 30, 60, 360, 3600, 50400. List the multipliers again: 30 * 2 = 60, 60 * 6 = 360, 360 * 10 = 3600, 3600 * 14 = 50400. The multipliers 2, 6, 10, 14 themselves form a clean arithmetic progression with difference 4. This confirms that 50400 follows naturally in the sequence and is the correct missing term. Why Other Options Are Wrong: Option 48500 does not equal 3600 multiplied by any member of the pattern 2, 6, 10, 14 and breaks the arithmetic progression in the multipliers.Option 50500 similarly fails to be 3600 times a multiplier that fits the established pattern, and introduces an inconsistent ratio.Option 40800 equals 3600 * 11.333..., which is not part of the integer multiplier sequence and does not align with the +4 step in the multipliers. Common Pitfalls: Some learners may mistakenly look for a constant multiplier, which is not present, or miscalculate products involving large numbers. Another common error is to confuse the pattern of the main terms with that of the multipliers. Focusing on the ratio between successive terms and then observing the progression of those ratios is the most reliable method here. Final Answer: The missing term that completes the multiplicative series is 50400.

Question 12

A number series is given with one term missing. Choose the correct alternative from the options that will complete the series: 13, 25, 49, 85, ?

Accepted Answer

Introduction / Context: This question presents an increasing number series where the differences between terms gradually grow in a structured way. By examining those differences, we can identify a pattern of increasing increments and use it to determine the missing term. This type of series evaluates the ability to track and extend non-constant differences. Given Data / Assumptions: Given series: 13, 25, 49, 85, ?The fifth term is missing.We assume a simple pattern in the differences between consecutive terms, likely involving multiples of a basic value. Concept / Approach: The method is to calculate the differences between consecutive terms and observe how these differences themselves change. If the differences increase by a constant amount, then the second differences are constant, indicating a quadratic-like pattern. Once we identify that the differences form a sequence such as 12, 24, 36, and so on, we can predict the next difference and hence the missing term. Step-by-Step Solution: Step 1: Compute 25 - 13 = 12.Step 2: Compute 49 - 25 = 24.Step 3: Compute 85 - 49 = 36.Step 4: The differences are 12, 24, 36, which are multiples of 12: 1 * 12, 2 * 12, 3 * 12.Step 5: The next difference should naturally be 4 * 12 = 48.Step 6: Add this difference to the last known term: 85 + 48 = 133.Step 7: Therefore, the missing term is 133. Verification / Alternative check: Insert the candidate term: 13, 25, 49, 85, 133. Recalculate the differences: 25 - 13 = 12, 49 - 25 = 24, 85 - 49 = 36, and 133 - 85 = 48. These differences form a clear sequence of 12, 24, 36, 48, which increases by 12 each time. This confirms that the series follows a pattern of adding successive multiples of 12, and 133 fits perfectly as the next term. Why Other Options Are Wrong: Option 331 would create a jump of 246 from 85, which does not match the controlled increase seen in the earlier differences.Option 132 produces a difference of 47, which breaks the multiple-of-12 pattern and the constant increase of 12 in the differences.Option 381 results in a very large and unstructured jump that is completely inconsistent with the earlier pattern. Common Pitfalls: Some learners may try to find multiplicative relationships among the original numbers, which can be misleading when the true pattern lies in the differences. Others might miscalculate one of the intermediate differences, which obscures the neat sequence of multiples of 12. A careful and systematic calculation of differences is essential to correctly identify and extend the underlying pattern. Final Answer: The missing number that completes the series is 133.

Question 13

In the following verbal reasoning number series, one term is missing. Carefully observe the pattern in the series 15, 32, 99, 400, ? and choose the correct alternative from the given options that will complete the sequence.

Accepted Answer

Introduction / Context: This question belongs to the verbal reasoning and number series category. The task is to recognise the hidden pattern in the given sequence 15, 32, 99, 400, ? and then select the correct missing term from the options. Such questions test a candidate's ability to observe numerical relationships and apply them consistently, which is very important for competitive exams and aptitude tests. Given Data / Assumptions: The given series is: 15, 32, 99, 400, ? We assume that there is a single consistent rule that links each term to the next. The next term must follow the same pattern as the previous steps. Only one of the options should satisfy the discovered rule when extended to the missing position. Concept / Approach: For number series questions, a good starting point is to examine how each term is obtained from the previous one. Here, differences alone look irregular, so we try operations involving multiplication and addition together. The observation is that each term seems to be generated from the previous term by multiplying with an increasing integer and then adding the same integer. This produces a pattern of the form: next term = current term * n + n, where n increases step by step (2, 3, 4, 5, and so on). Step-by-Step Solution: From 15 to 32: 15 * 2 + 2 = 30 + 2 = 32. From 32 to 99: 32 * 3 + 3 = 96 + 3 = 99. From 99 to 400: 99 * 4 + 4 = 396 + 4 = 400. The multiplier and addend increase by 1 each time (2, 3, 4, ...), so the next step should use 5. From 400 to the missing term: 400 * 5 + 5 = 2000 + 5 = 2005. Thus, the missing number that continues the pattern correctly is 2005. Verification / Alternative check: We can verify the rule by checking every step. Each time we multiply the previous term by an integer n and then add the same integer n. The sequence of n values is 2, 3, 4, and then 5. The calculated terms exactly match the existing series up to 400, and extending the rule gives 2005. No other option, when inserted, preserves such a smooth and consistent pattern. This confirms that the logic is correct and that 2005 is the only suitable continuation. Why Other Options Are Wrong: Option A: 2001 does not fit the rule current term * 5 + 5, since 400 * 5 + 5 is not 2001. Option B: 2004 is also inconsistent with the same pattern and breaks the multiplier plus addend logic. Option D: 1994 similarly fails the rule and would require a completely different and irregular pattern. Option E: 2010 does not come from any simple extension of the established operation and is therefore not valid. Common Pitfalls: A common mistake is to focus only on the differences between terms (17, 67, 301) and assume that the pattern is too irregular, causing candidates to guess. Another pitfall is to search only for simple arithmetic or geometric progressions instead of exploring combined operations like multiply then add. In many exam questions, the key is to notice that both the multiplier and the number added increase in a regular fashion, which is easy to miss under time pressure. Final Answer: The number that correctly completes the series is 2005, so the correct option is 2005.

Question 14

In this verbal reasoning number series question, one term is missing. Carefully study the series 30, 62, 189, 760, ? and choose the correct alternative from the options that best completes the sequence.

Accepted Answer

Introduction / Context: This is another number series question from verbal reasoning where one term is missing. The series given is 30, 62, 189, 760, ? and the task is to detect the underlying rule and use it to find the next term. Such questions are very popular in competitive exams because they test observation, logical thinking, and the ability to recognise numerical patterns quickly and accurately. Given Data / Assumptions: Given series: 30, 62, 189, 760, ? Exactly one consistent pattern links each term to the next. The same pattern must be applied step by step throughout the series. Only one of the provided options will satisfy the pattern for the missing term. Concept / Approach: As with many non-trivial series, simple differences do not give a clear pattern here. Instead, we test operations where each term is generated from the previous term using multiplication combined with addition. If we attempt the pattern previous term * n + n (with n increasing gradually), we notice that it works perfectly: 30 * 2 + 2, 62 * 3 + 3, 189 * 4 + 4, and so on. The integers 2, 3, 4, 5 form a clear increasing sequence for the multipliers and addends. Step-by-Step Solution: From 30 to 62: 30 * 2 + 2 = 60 + 2 = 62. From 62 to 189: 62 * 3 + 3 = 186 + 3 = 189. From 189 to 760: 189 * 4 + 4 = 756 + 4 = 760. The pattern clearly uses multipliers 2, 3, and 4, each time adding the same integer as well. Next, we should use 5 as both multiplier and addend: 760 * 5 + 5 = 3800 + 5 = 3805. So, the missing term must be 3805. Verification / Alternative check: We verify by rechecking each transition. The formula previous term * n + n is valid for all known steps. The sequence of n as 2, 3, 4, and 5 is simple and logical. Substituting n = 5 produces 3805, which matches exactly one option. No other option maintains such a smooth progression, so the pattern is robust and not forced. This confirms that 3805 is the correct continuation of the series. Why Other Options Are Wrong: Option A: 3306 cannot be written as 760 * 5 + 5 or any simple extension of the earlier rule. Option B: 1157 is far too small compared with the explosive growth of the series and does not satisfy the pattern. Option C: 2185 also fails the multiplier plus addend logic observed earlier. Option E: 1521 is unrelated to the established structure and would require a completely new and inconsistent rule. Common Pitfalls: Many candidates only check differences: 32, 127, 571, which look irregular and confusing. This may tempt them to guess. Another pitfall is assuming only one type of operation (pure multiplication or pure addition). In higher level exams, exam setters often combine multiplication with addition or subtraction, and the increment in the multiplier itself follows a simple sequence that must be noticed. Ignoring this can lead to wrong answers even when the pattern is actually very systematic. Final Answer: The missing number that correctly completes the series is 3805, so the correct option is 3805.

Question 15

A number series is given with one term missing. Study the pattern in 0, 3, 8, ?, 24, 35 and choose the correct alternative that will complete the series.

Accepted Answer

Introduction / Context: This problem is a classic number series question where one middle term is missing. The given series is 0, 3, 8, ?, 24, 35. The aim is to identify the pattern that generates each term and then use it to find the missing value. Such questions assess the candidate's numerical reasoning skills and familiarity with common series types such as squares, cubes, and other polynomial patterns. Given Data / Assumptions: Given series: 0, 3, 8, ?, 24, 35. Exactly one term is missing between 8 and 24. We assume that the same rule is used consistently for all terms. The correct answer must be one of the provided options and must fit the pattern perfectly. Concept / Approach: A useful approach with small, steadily increasing series is to check whether terms relate to perfect squares or cubes with a fixed adjustment. Observing the numbers, we notice that they can be expressed as n^2 minus 1 for consecutive values of n. That is, 1^2 minus 1, 2^2 minus 1, 3^2 minus 1, and so on. This suggests a simple formula-driven pattern rather than a random difference pattern. Step-by-Step Solution: For n = 1: 1^2 - 1 = 1 - 1 = 0 (first term). For n = 2: 2^2 - 1 = 4 - 1 = 3 (second term). For n = 3: 3^2 - 1 = 9 - 1 = 8 (third term). For n = 4: 4^2 - 1 = 16 - 1 = 15 (this must be the missing term). For n = 5: 5^2 - 1 = 25 - 1 = 24 (matches the given fifth term). For n = 6: 6^2 - 1 = 36 - 1 = 35 (matches the last term). Thus, the missing number is 15. Verification / Alternative check: We verify the pattern across all known positions. Each term fits the formula term = n^2 - 1 for n = 1 to 6. The given numbers at positions 1, 2, 3, 5, and 6 all align exactly with the formula. The only value that makes the fourth term consistent is 15, since 4^2 - 1 equals 15. Therefore the pattern is robust and uniquely determines the missing value. Why Other Options Are Wrong: Option B: 16 would correspond to 4^2, not 4^2 - 1, and would break the consistent use of minus 1. Option C: 18 does not fit any simple square minus 1 sequence for the positions in this series. Option D: 9 would be equal to 3^2, which already appears in adjusted form at position three, so it is inconsistent here. Option E: 21 also does not correspond to n^2 - 1 for any integer n between 1 and 6 in this context. Common Pitfalls: Many students focus only on differences between terms (3, 5, ?, ?, 11) and do not realise that the series comes from squares. Differences alone look irregular and may lead to guessing. Another common mistake is to check cubes or mixed patterns before testing the simplest possible square-based pattern. Remember that exam questions frequently use small adjustments such as plus or minus 1 applied to basic powers of integers. Final Answer: The only value that maintains the pattern n^2 minus 1 is 15, so the correct option is 15.

Question 16

A number series involving fractions and decimals is given with one term missing. Observe the pattern in 1.5, 9/4, 3, ?, 4.5, 21/4 and choose the correct alternative that completes the series.

Accepted Answer

Introduction / Context: This question presents a number series that mixes fractions and decimals. The sequence is 1.5, 9/4, 3, ?, 4.5, 21/4. The goal is to identify the underlying pattern and determine the missing term. Mixed-format series like this check whether a candidate can comfortably move between decimal and fractional representations while still spotting a simple arithmetic relationship. Given Data / Assumptions: Given series: 1.5, 9/4, 3, ?, 4.5, 21/4. We can freely convert between decimals and fractions for analysis. There is one consistent pattern governing the entire sequence. Exactly one option will fit the pattern for the missing position. Concept / Approach: A good strategy is to convert all terms to either pure decimals or pure fractions. Doing so often reveals a straightforward arithmetic progression. Converting the given numbers to decimals: 1.5, 2.25, 3.0, ?, 4.5, 5.25. This suggests that each term might be increasing by a constant difference. Checking quickly shows that the difference between successive terms is 0.75, which is equal to 3/4. Therefore the series is an arithmetic progression with common difference 0.75. Step-by-Step Solution: Convert 1.5 to decimal: 1.5. 9/4 as decimal is 2.25. 3 is already 3.00. Difference from 1.5 to 2.25 is 0.75, and from 2.25 to 3.00 is again 0.75. Add 0.75 to 3.00 to get the missing term: 3.00 + 0.75 = 3.75. 3.75 expressed as a fraction is 15/4. Next: 3.75 + 0.75 = 4.50, and 4.50 + 0.75 = 5.25, which matches 4.5 and 21/4. So the missing term must be 15/4. Verification / Alternative check: We verify the arithmetic progression: each step increases by 0.75. All known terms fit this rule perfectly when expressed as decimals. In fractional form, the common difference is 3/4. Converting 15/4 gives 3.75, which keeps the progression intact between 3 and 4.5. This shows that the found value is consistent with both the earlier and later terms in the sequence. Why Other Options Are Wrong: Option B: 7/2 is 3.5, which would use a step of only 0.5 from 3 and then a different step to reach 4.5, breaking the constant difference rule. Option C: 8 is far away from 3 and would destroy the smooth progression of small increments. Option D: 9 is even more unsuitable and does not reflect the gentle growth of the series. Option E: 13/4 gives 3.25, which does not maintain the 0.75 step size either. Common Pitfalls: One common mistake is to avoid converting fractions to decimals or vice versa and instead try to see a complicated pattern. Another pitfall is to assume that mixed-format series are always advanced, while here the relationship is just a simple arithmetic progression. Candidates should also be careful with fractional conversions, since calculation errors can lead to incorrect conclusions about the common difference. Final Answer: The missing term that preserves a constant increment of 0.75 is 15/4, so the correct option is 15/4.

Question 17

In the following number series with negative and positive fractional values, one term is missing. Carefully observe the pattern in -7/4, -1, -0.25, ?, 5/4, 2 and choose the correct alternative that completes the series.

Accepted Answer

Introduction / Context: This question presents a number series involving a smooth transition from negative fractions to positive values. The given series is -7/4, -1, -0.25, ?, 5/4, 2. The objective is to understand the pattern that governs these changes and then find the missing term. Such questions test a candidate's comfort with fractions, decimals, and arithmetic progressions, especially when signs change from negative to positive. Given Data / Assumptions: Given series: -7/4, -1, -0.25, ?, 5/4, 2. We can represent the numbers in decimal form for easier comparison. There should be a single consistent rule applied across the series. The missing value must fit between -0.25 and 5/4 without breaking the pattern. Concept / Approach: First, convert the fractions to decimals: -7/4 = -1.75, -1 remains -1.00, -0.25 is already in decimal form, 5/4 = 1.25, and 2 is 2.00. Now the series becomes -1.75, -1.00, -0.25, ?, 1.25, 2.00. Observing the differences suggests that the sequence might be an arithmetic progression with a constant increment. The difference from -1.75 to -1.00 is +0.75, and from -1.00 to -0.25 is again +0.75. This indicates a common difference of 0.75 throughout the series. Step-by-Step Solution: Write the series in decimals: -1.75, -1.00, -0.25, ?, 1.25, 2.00. Difference from -1.75 to -1.00 is +0.75. Difference from -1.00 to -0.25 is +0.75 again. Add 0.75 to -0.25 to obtain the missing term: -0.25 + 0.75 = 0.50. Next, 0.50 + 0.75 = 1.25 and 1.25 + 0.75 = 2.00, which match the given later terms. Thus, the missing term is 0.5. Verification / Alternative check: We can verify the pattern by checking each step. The constant increment is 0.75 from the first to the last term. Using this single rule reproduces all given numbers perfectly when we insert 0.5 in the missing slot. If we try any other candidate, the difference sequence will break, proving that 0.5 is the only value that maintains the arithmetic progression. Why Other Options Are Wrong: Option B: 0.75 would give a step of 1.00 between -0.25 and 0.75, which is inconsistent with earlier differences. Option C: 0.25 would create a difference of only 0.50 from -0.25, again breaking the constant increment of 0.75. Option D: 1.00 jumps too far and does not maintain the regular pattern around 1.25 and 2.00. Option E: 1.5 leads to an even more irregular jump and cannot form a consistent arithmetic sequence. Common Pitfalls: Students sometimes ignore decimal conversions and try to work directly with fractions, which can hide the simple arithmetic progression. Others may be distracted by the change from negative to positive and assume that the rule is complicated. In reality, the entire series follows a uniform step size. Recognising that a series can cross zero while still using a constant difference is important for correctly solving such problems. Final Answer: The number that completes the series while maintaining a constant step of 0.75 is 0.5, so the correct option is 0.5.

Question 18

In the following number series question from verbal reasoning, one term is missing. Observe the sequence 9, 13, 18, 24, 31, ? and choose the correct alternative that completes the series.

Accepted Answer

Introduction / Context: This question tests the ability to identify a simple pattern in a number series. The given sequence is 9, 13, 18, 24, 31, ?, and we need to determine the missing next term. Recognising patterns in incremental differences is a core skill in verbal reasoning and quantitative aptitude sections of many exams. Given Data / Assumptions: Series: 9, 13, 18, 24, 31, ? Exactly one term is missing at the end of the series. The same rule should apply consistently between every pair of consecutive terms. Only one of the provided options should fit the discovered pattern. Concept / Approach: The most natural way to tackle this series is to examine the differences between consecutive terms. If the differences themselves follow a clear pattern, we can extrapolate them. For many exam questions, differences increase or decrease regularly by 1, 2, or some small integer. We therefore compute each difference and see whether they form a familiar sequence such as consecutive integers. Step-by-Step Solution: Difference between 9 and 13: 13 - 9 = 4. Difference between 13 and 18: 18 - 13 = 5. Difference between 18 and 24: 24 - 18 = 6. Difference between 24 and 31: 31 - 24 = 7. The differences are 4, 5, 6, 7, which are consecutive integers. Next difference should be 8, so the missing term is 31 + 8 = 39. Therefore, the required number is 39. Verification / Alternative check: Checking the reconstructed sequence: 9, 13, 18, 24, 31, 39. The differences are 4, 5, 6, 7, 8, which form a smooth increasing sequence. None of the other options would create such a neat pattern of consecutive differences. This confirms that 39 is the only value that continues the logic in a consistent manner. Why Other Options Are Wrong: Option B: 35 gives a final difference of 4 (31 to 35), which breaks the increasing trend of 4, 5, 6, 7. Option C: 40 gives a difference of 9, jumping too far ahead and skipping 8 in the difference sequence. Option D: 37 gives a difference of 6, repeating an earlier difference instead of continuing the pattern. Option E: 45 produces a difference of 14, which is completely inconsistent with the smooth progression of small integers. Common Pitfalls: A frequent mistake is to look for multiplicative patterns where only simple addition is needed. Some students also overlook the idea that differences themselves can form a separate sequence with its own regularity. In competitive exams, many number series rely exactly on this principle: differences or second-level differences behave in a simple and predictable way. Final Answer: The number that correctly completes the series is 39, so the correct option is 39.

Question 19

Which number will complete the following verbal reasoning number series? Study the pattern in 6, 8, 17, 19, 28, 30, ? and choose the correct alternative from the options.

Accepted Answer

Introduction / Context: This number series problem involves an alternating pattern. The sequence provided is 6, 8, 17, 19, 28, 30, ?. The task is to discover the rule that generates each term and then use it to find the missing number. Many exam questions use two intertwined patterns, so recognising such alternation is a key reasoning skill. Given Data / Assumptions: Given series: 6, 8, 17, 19, 28, 30, ? The missing term comes after 30. There may be two related subsequences interwoven in alternate positions. Exactly one option will match a consistent pattern that extends the series. Concept / Approach: A good approach here is to split the series into two subsequences: terms at odd positions and terms at even positions. Often, one subsequence follows a particular rule (for example, adding a constant), while the other follows a similar or slightly different rule. This method is especially useful when the overall series seems to jump irregularly. Step-by-Step Solution: Write the terms with their positions: 1st: 6, 2nd: 8, 3rd: 17, 4th: 19, 5th: 28, 6th: 30, 7th: ?. Odd-position terms: 6 (1st), 17 (3rd), 28 (5th), ? (7th). Even-position terms: 8 (2nd), 19 (4th), 30 (6th). For odd positions: 6 to 17 is +11, 17 to 28 is +11, so the next should be 28 + 11 = 39. For even positions: 8 to 19 is +11, 19 to 30 is also +11, confirming the same rule. Thus, both subsequences increase by 11, and the missing term is 39. Verification / Alternative check: Combine the subsequences back: 6, 8, 17, 19, 28, 30, 39. Odd-position terms follow 6, 17, 28, 39 with a constant difference of 11; even-position terms follow 8, 19, 30, also with difference 11. This symmetrical structure confirms that the discovered rule is strong and consistent, leaving no doubt that 39 is the only suitable answer. Why Other Options Are Wrong: Option A: 32 does not follow the +11 rule from 28 and would break the odd-position subsequence pattern. Option B: 37 uses +9 instead of +11, which is inconsistent with all earlier jumps of 11. Option C: 38 uses +10, again breaking the uniform difference of 11. Option E: 35 is also not at a distance of 11 from 28 and does not match the observed structure. Common Pitfalls: Some candidates may only look at consecutive differences (2, 9, 2, 9, 2, ?) and fail to realise that two sequences are interwoven. Recognising alternating patterns is very important for solving a wide variety of number series questions quickly. Another pitfall is to assume a single arithmetic or geometric progression without exploring the possibility of multiple embedded patterns. Final Answer: The term that correctly completes the series is 39, so the correct option is 39.

Question 20

In the following number series, one term is missing. Observe the descending pattern in 219, 211, 204, 198, ?, 189 and choose the correct alternative that completes the series.

Accepted Answer

Introduction / Context: This question involves a decreasing number series. The given sequence is 219, 211, 204, 198, ?, 189. The challenge is to detect the rule governing the step-by-step decrease and then identify the missing term. Such questions test how well the candidate can work with differences and recognise simple patterns in subtraction. Given Data / Assumptions: Series: 219, 211, 204, 198, ?, 189. One term is missing between 198 and 189. The series is strictly decreasing overall. We assume that the same rule is used at each step to move from one term to the next. Concept / Approach: Because the series is decreasing, we start by calculating the differences between successive known terms. If these differences themselves follow a pattern, such as descending or ascending by 1, we can extend them to the missing position. This approach is standard in questions where the numbers fall steadily rather than grow. Step-by-Step Solution: First difference: 219 - 211 = 8. Second difference: 211 - 204 = 7. Third difference: 204 - 198 = 6. The differences so far are 8, 7, and 6, which are consecutive decreasing integers. Following this pattern, the next difference should be 5, and then 4. So from 198, subtract 5: 198 - 5 = 193 (this is the missing term). Then 193 - 4 = 189, which matches the last given number. Therefore, the missing term is 193. Verification / Alternative check: We reconstruct the full sequence: 219, 211, 204, 198, 193, 189. The differences become 8, 7, 6, 5, 4, forming a smooth decreasing sequence. This is a typical pattern used in competitive exam number series. No other candidate number will maintain this consistent drop in the differences, confirming that 193 is the correct value. Why Other Options Are Wrong: Option A: 189 repeats the last term too early and gives a difference of 9 from 198, which does not fit the pattern of 8, 7, 6. Option B: 192 creates a difference of 6 from 198, repeating the previous difference instead of continuing 5 and 4. Option D: 196 causes a difference of only 2, which breaks the descending sequence of differences. Option E: 195 gives a difference of 3, again inconsistent with the rule 8, 7, 6, 5, 4. Common Pitfalls: A common error is to focus on the values themselves without checking the differences systematically. Another mistake is to miscalculate a difference and then build an incorrect pattern from that error. It is always helpful to write out the differences clearly, observe how they change, and only then extend the pattern to deduce the missing term. Final Answer: The only number that maintains the decreasing differences 8, 7, 6, 5, 4 is 193, so the correct option is 193.

Number Series Questions