Question 1

A number series is given with one term missing. Choose the correct alternative from the given options that will complete the series. ?, 9, 19, 39, 79

Accepted Answer

Introduction / Context: In this number series, the missing term appears at the beginning. The pattern is based on differences that grow by a constant factor. The learner must work backward using the same rule that governs the forward movement of the series. This builds skill in both forward and backward reasoning with numerical patterns. Given Data / Assumptions: - Series: ?, 9, 19, 39, 79. - The first term is missing. - Differences between known terms suggest a pattern. Concept / Approach: The approach is to compute the differences between consecutive known terms and observe how those differences change. If the differences follow a consistent rule such as doubling, that rule can be applied backward to determine the initial term. Because the first term is missing, analysis begins from the second term onward. Step-by-Step Solution: Step 1: Find differences between known terms. 9 to 19: difference = 10. 19 to 39: difference = 20. 39 to 79: difference = 40. Step 2: The differences are 10, 20, and 40, which clearly double each time. Step 3: If the pattern extends backward, then the difference between the missing first term and 9 should be 5, half of 10. Step 4: Therefore, 9 minus 5 must equal the missing first term. Step 5: Calculate 9 - 5 = 4. Verification / Alternative check: Rebuild the full series using the discovered rule: start with 4, add 5 to get 9, then add 10 to get 19, add 20 to get 39, and finally add 40 to get 79. This generates 4, 9, 19, 39, 79, which matches the pattern perfectly and confirms that 4 is the correct starting term. Why Other Options Are Wrong: - Option 9 would make the first two terms equal and break the doubling differences pattern. - Option 7 would give a difference of 2 between the first two terms, which does not fit with the later differences of 10, 20, and 40. - Option 6 would lead to a difference of 3 between the first two terms, again inconsistent with the doubling pattern. Common Pitfalls: Learners may try to apply a direct formula to the terms instead of first examining the differences. Another error is to assume arbitrary starting values without checking consistency across all steps. Always verify that the same rule explains every transition in the series, both forward and backward. Final Answer: The missing first term is 4, so the correct option is 4.

Question 2

A number series is given with one term missing. Choose the correct alternative from the given options that will complete the series. 0.5, 2, 3.5, ?, 6.5

Accepted Answer

Introduction / Context: This question focuses on a simple arithmetic progression with decimal values where each term increases by a fixed amount. The learner must identify the common difference and use it to find the missing middle term. Such questions are basic but important for building confidence with decimal arithmetic in series. Given Data / Assumptions: - Series: 0.5, 2, 3.5, ?, 6.5. - The fourth term is missing. - The pattern is expected to involve equal increments. Concept / Approach: In an arithmetic progression, each term differs from the previous term by a constant amount. By calculating the difference between successive known terms and checking for consistency, the common difference can be discovered. The missing term is then obtained by adding this difference to the preceding term or subtracting it from the following term. Step-by-Step Solution: Step 1: Compute the difference between the first and second terms: 2 - 0.5 = 1.5. Step 2: Compute the difference between the second and third terms: 3.5 - 2 = 1.5. Step 3: The common difference is therefore 1.5. Step 4: Use this difference to find the fourth term: 3.5 + 1.5 = 5.0. Step 5: Confirm with the last term: 5.0 + 1.5 = 6.5, which matches the given final term. Verification / Alternative check: You can also check by using the first and fifth terms. The total change from 0.5 to 6.5 is 6.0, spread over four equal steps. Each step must then be 6.0 / 4 = 1.5. Using this value to fill in the series yields 0.5, 2.0, 3.5, 5.0, 6.5, which confirms the missing term is 5. Why Other Options Are Wrong: - Option 4.5 would give a difference of 1.0 from 3.5, which does not match the 1.5 step seen elsewhere. - Option 4 would give a difference of 0.5 from 3.5 and 2.5 to reach 6.5, breaking the equal-step condition. - Option 6 would skip over one increment size and would not fit the constant difference pattern. Common Pitfalls: Some learners average the wrong pair of terms or perform incorrect decimal subtraction. Others forget to verify the pattern against all known terms. Always test the discovered difference both forward and backward through the series to avoid hidden mistakes. Final Answer: The missing term in the series is 5, so the correct option is 5.

Question 3

A number series is given with one term missing. Choose the correct alternative from the given options that will complete the series. 60, 80, 95, 105, ?

Accepted Answer

Introduction / Context: This series presents increasing numbers where the increments themselves decrease in a regular manner. The learner must observe not only the terms but also how the differences shrink, which is a frequent pattern in aptitude style questions. Recognising the pattern in the differences allows precise prediction of the next term. Given Data / Assumptions: - Series: 60, 80, 95, 105, ? - The fifth term is missing. - The series increases but at a slowing rate. Concept / Approach: The approach is to compute the differences between consecutive terms and then see how these differences change. When the differences change in a simple way, for example by a constant amount, we can extend that pattern to the next difference and thus to the next term. This is essentially a second level arithmetic progression on the differences. Step-by-Step Solution: Step 1: Compute differences. 80 - 60 = 20. 95 - 80 = 15. 105 - 95 = 10. Step 2: The differences are 20, 15, and 10, each decreasing by 5. Step 3: The next difference should be 10 - 5 = 5. Step 4: Add this difference to the last known term to get the missing value: 105 + 5 = 110. Verification / Alternative check: An alternative check is to extend the difference sequence: 20, 15, 10, 5. If you add these differences cumulatively starting from 60, you obtain 80, 95, 105, and 110. This reconstructs the series consistently and confirms that the missing term must be 110. Why Other Options Are Wrong: - Option 190 would require an increase of 85 from 105, which clearly does not match the gently decreasing differences. - Option 150 would require a jump of 45, again inconsistent with the pattern of decreasing increments. - Option 250 requires an even larger difference that completely ignores the observed structure. Common Pitfalls: Learners may try to force a single formula on the terms instead of first examining simple first and second differences. Another mistake is to miscalculate one of the differences and miss the clear minus five pattern, which leads to incorrect extension of the series. Final Answer: The missing term is 110, so the correct option is 110.

Question 4

In the following arithmetic expression, apply the correct order of operations and determine the value that should replace the question mark (?). 452 + 312 ÷ 13 = 34 × ?

Accepted Answer

Introduction / Context: This question tests application of the order of operations, commonly known as BODMAS or PEMDAS, in an equation that relates an arithmetic expression to a product involving an unknown multiplier. The learner must correctly evaluate the left hand side and then solve for the missing value on the right hand side. Given Data / Assumptions: - Expression: 452 + 312 ÷ 13 = 34 × ? - Division must be carried out before addition. - The symbol × denotes multiplication. Concept / Approach: According to the order of operations, division is performed before addition, and multiplication is handled once both sides of the equation are simplified. After evaluating the left side completely, the result is equated to 34 times the unknown number. Solving this simple linear equation gives the required value of the question mark. Step-by-Step Solution: Step 1: Evaluate the division on the left side: 312 ÷ 13. Step 2: Perform the division: 312 ÷ 13 = 24. Step 3: Add this result to 452: 452 + 24 = 476. Step 4: Now the equation becomes 476 = 34 × ?. Step 5: Solve for the unknown: ? = 476 ÷ 34. Step 6: Compute 476 ÷ 34 = 14. Verification / Alternative check: To verify, substitute 14 back into the equation. Compute 34 × 14, which equals 476. The left side is also 452 + (312 ÷ 13) = 452 + 24 = 476. Since both sides give the same result, the value 14 correctly satisfies the equation. Why Other Options Are Wrong: - Option 12 would give 34 × 12 = 408, which does not match the left side value 476. - Option 16 would give 34 × 16 = 544, larger than the left side result. - Option 18 would produce 34 × 18 = 612, which is again not equal to 476. Common Pitfalls: Some learners mistakenly add first and divide later, which gives an incorrect value for the left side. Others may perform the division but then miscalculate the final division when solving for the unknown. Careful, stepwise use of the order of operations is crucial in such problems. Final Answer: The value of the question mark is 14, so the correct option is 14.

Question 5

What will come in place of the question mark (?) in the following calculation involving percentages and basic arithmetic? 1.5% of 4600 + 2.8% of 2000 - 109 = ?

Accepted Answer

Introduction / Context: This problem checks the ability to handle percentage calculations combined with addition and subtraction. It mirrors the type of quick arithmetic required in banking, finance, and government examinations. The learner must convert percentages to actual values and then perform basic operations carefully. Given Data / Assumptions: - Expression: 1.5% of 4600 + 2.8% of 2000 - 109. - The symbol % means percent, or parts per hundred. - Standard order of operations applies. Concept / Approach: Percent calculations follow the rule x% of y = (x / 100) * y. After finding each percentage value, those results are combined using normal arithmetic. The final number is then compared with the given options. Accuracy in multiplication and subtraction is essential, since small errors change the answer completely. Step-by-Step Solution: Step 1: Compute 1.5% of 4600: (1.5 / 100) * 4600 = 0.015 * 4600 = 69. Step 2: Compute 2.8% of 2000: (2.8 / 100) * 2000 = 0.028 * 2000 = 56. Step 3: Add these two results: 69 + 56 = 125. Step 4: Subtract 109 from this sum: 125 - 109 = 16. Step 5: Therefore, the required value of the expression is 16. Verification / Alternative check: You can approximate to confirm the reasonableness of the answer. One and a half percent of 4600 is a bit less than 2% of 4600 (which is 92), and 2.8% of 2000 is a bit more than 2% of 2000 (which is 40). So their sum is expected somewhere around 69 plus 56, close to 125. Subtracting about 100 gives a result slightly above 20. The exact computation gives 16, which is consistent with this rough estimate when we consider the exact values. Why Other Options Are Wrong: - Option 32 would require 125 - 109 to equal 32, which is arithmetically incorrect. - Option 28 also does not match the correct subtraction result. - Option 12 would correspond to a different subtraction such as 121 - 109, not the value obtained here. Common Pitfalls: Common mistakes include misplacing the decimal point during percent conversion, such as using 1.5 instead of 0.015, and subtracting 109 from only one of the two percentage components instead of from their sum. Another error is performing operations in a different order, which distorts the result. Final Answer: The value of the expression is 16, so the correct option is 16.

Question 6

What will come in place of the question mark (?) in the following equation involving percentages on both sides? 120% of 750 ÷ 25 - 16 = ?% of 1240 ÷ 31

Accepted Answer

Introduction / Context: This problem involves an equation where both sides contain percentage based expressions. The task is to simplify each side using the order of operations, then solve for the unknown percentage on the right side. Such questions blend arithmetic, percent calculations, and basic algebra. Given Data / Assumptions: - Left side: 120% of 750 ÷ 25 - 16. - Right side: ?% of 1240 ÷ 31. - The goal is to find the value of the unknown percent that makes both sides equal. Concept / Approach: The expression x% of y is equal to (x / 100) * y. The left side must be simplified step by step: first the percent, then the division, then the subtraction. On the right side, we express ?% as an unknown variable multiplied by 1240 and divided by 31. Equating both sides results in a simple equation in one variable. Step-by-Step Solution: Step 1: Compute 120% of 750: (120 / 100) * 750 = 1.2 * 750 = 900. Step 2: Divide this by 25: 900 ÷ 25 = 36. Step 3: Subtract 16: 36 - 16 = 20. The left side equals 20. Step 4: Let the unknown percent be x. Then x% of 1240 ÷ 31 equals (x / 100) * 1240 ÷ 31. Step 5: Simplify the right side: (x / 100) * 1240 ÷ 31 = x * 1240 / (100 * 31). Step 6: Set this equal to 20 and solve: x * 1240 / 3100 = 20. Step 7: Multiply both sides by 3100: x * 1240 = 20 * 3100 = 62000. Step 8: Divide both sides by 1240: x = 62000 ÷ 1240 = 50. Verification / Alternative check: Substitute x = 50 back into the right side. Compute 50% of 1240 as (50 / 100) * 1240 = 620. Then divide by 31: 620 ÷ 31 = 20. This matches the already simplified left side value 20, so x = 50 is confirmed as correct. Why Other Options Are Wrong: - Option 40 would give 40% of 1240 as 496, and 496 ÷ 31 equals 16, which is not equal to 20. - Option 45 gives 558 ÷ 31, which equals 18, different from 20. - Option 55 leads to 682 ÷ 31, which is about 22, again not equal to 20. Common Pitfalls: A common mistake is to divide 750 by 25 before applying the 120%, which changes the value. Another error is to forget to divide by 31 on the right side or to mismanage the fractions when solving for x. Keeping each step clear and maintaining the correct order avoids these issues. Final Answer: The unknown percent is 50, so the correct option is 50.

Question 7

A number series is given with one term missing. Choose the correct alternative from the given options that will complete the series. 12, 60, 240, 720, ?

Accepted Answer

Introduction / Context: This number series grows rapidly by multiplication with a changing multiplier. The learner must identify how each term is obtained from the previous term by using progressively smaller integer factors. Such patterns often appear in competitive exam series questions to test observation and multiplication skills. Given Data / Assumptions: - Series: 12, 60, 240, 720, ? - One term is missing in the fifth position. - The terms increase significantly, suggesting multiplication. Concept / Approach: To solve, compute the ratio between consecutive terms and inspect how this ratio changes. Here, the series seems to multiply by 5, then 4, then 3, and then likely by 2. This descending multiplier pattern is common and leads directly to the missing term. Step-by-Step Solution: Step 1: Compute ratios between consecutive terms. 60 ÷ 12 = 5. 240 ÷ 60 = 4. 720 ÷ 240 = 3. Step 2: The multipliers are 5, 4, and 3, decreasing by 1 each time. Step 3: The next logical multiplier is 2. Step 4: Multiply 720 by 2 to get the missing term: 720 * 2 = 1440. Verification / Alternative check: Rebuild the pattern from the start: 12 * 5 = 60, 60 * 4 = 240, 240 * 3 = 720, 720 * 2 = 1440. This confirms the descending sequence of multipliers and verifies that 1440 is correct. Why Other Options Are Wrong: - Option 1420 does not equal 720 multiplied by any neat integer that fits the pattern. - Option 1400 also fails the simple multiplier rule and would break the systematic sequence. - Option 1460 is similarly inconsistent with the neat multiplication pattern. Common Pitfalls: Learners may try to treat the growth as a fixed ratio or may miscalculate one of the products. Another error is to ignore the clear pattern in the multipliers and guess a value that seems close but does not actually follow the rule. Confirming ratios carefully prevents such mistakes. Final Answer: The missing term in the series is 1440, so the correct option is 1440.

Question 8

What should come in place of the question mark (?) in the following calculation, if you apply the correct order of operations? 600 + 300 ÷ 15 = ? × 31

Accepted Answer

Introduction / Context: This question tests understanding of the order of operations in an equation that links an arithmetic expression on the left to a product on the right. The learner must simplify the left hand side correctly and then solve for the unknown multiplier that appears on the right side. Given Data / Assumptions: - Equation: 600 + 300 ÷ 15 = ? × 31. - Division is done before addition. - Multiplication by 31 happens after the left side is simplified. Concept / Approach: According to the order of operations, division precedes addition. Thus we first divide 300 by 15, then add the result to 600. Once the left side is fully evaluated, we equate it to 31 times the unknown number and solve a simple linear equation to find that number. Step-by-Step Solution: Step 1: Evaluate 300 ÷ 15 = 20. Step 2: Add this result to 600: 600 + 20 = 620. Step 3: The equation becomes 620 = ? × 31. Step 4: Solve for the unknown: ? = 620 ÷ 31. Step 5: Compute 620 ÷ 31 = 20. Verification / Alternative check: Substitute 20 back into the right side to verify: 20 × 31 = 620. This matches the simplified left side value 620. Since both sides are equal, the value 20 satisfies the equation and is therefore correct. Why Other Options Are Wrong: - Option 18 gives 18 × 31 = 558, which is less than 620. - Option 25 gives 25 × 31 = 775, which is greater than 620. - Option 40 gives 40 × 31 = 1240, which also does not equal 620. Common Pitfalls: A typical mistake is to add first and divide later, which would change the left side value. Another error is miscalculating 300 ÷ 15 or the final division by 31. Sticking closely to the order of operations and checking each step avoids these mistakes. Final Answer: The value that satisfies the equation is 20, so the correct option is 20.

Question 9

What should come in place of the question mark (?) in the following number series, where the pattern is based on changing differences? 1, 244, 163, 190, 181, ?,

Accepted Answer

Introduction / Context: This series involves terms that do not follow a simple linear rule but instead use differences that themselves form a geometric pattern. The learner must compute the differences between terms, recognise the structure of those differences, and then extend this structure to find the missing term. Given Data / Assumptions: - Series: 1, 244, 163, 190, 181, ? - The sixth term is missing. - The differences between consecutive terms are not constant but appear to follow a pattern. Concept / Approach: First, calculate the difference between each pair of consecutive terms. Then, examine these differences to see whether they follow a recognisable pattern. In this case, the differences form a geometric progression with a negative ratio. Once that pattern is clear, the next difference can be predicted, and the missing term in the original series can be computed. Step-by-Step Solution: Step 1: Compute differences. 244 - 1 = 243. 163 - 244 = -81. 190 - 163 = 27. 181 - 190 = -9. Step 2: The sequence of differences is 243, -81, 27, -9. Step 3: Observe that each difference is obtained by multiplying the previous difference by -1 / 3. Step 4: To find the next difference, multiply -9 by -1 / 3, which gives 3. Step 5: Add this next difference to the last known term: 181 + 3 = 184. Verification / Alternative check: Check the ratio between consecutive differences. -81 ÷ 243 = -1 / 3, 27 ÷ -81 = -1 / 3, and -9 ÷ 27 = -1 / 3. This confirms the geometric pattern with ratio -1 / 3. Extending this to the next difference gives 3, and therefore the next term 184, so the solution is consistent. Why Other Options Are Wrong: - Option 188 would require a difference of 7 from 181, which does not fit the geometric pattern. - Option 198 would require a difference of 17, again inconsistent with multiplying by -1 / 3. - Option 221 requires a much larger jump and clearly breaks the established structure. Common Pitfalls: Many learners only look for additive or subtractive patterns directly on the main series and may not think to inspect the differences themselves. Others may calculate one of the differences incorrectly, making the geometric pattern harder to see. Careful computation and a willingness to examine second level patterns are important. Final Answer: The missing term in the series is 184, so the correct option is 184.

Question 10

What should come in place of the question mark (?) in the following number series, which follows a multiply then subtract pattern? 8, 6, 9, 23, ?

Accepted Answer

Introduction / Context: This number series uses a compound pattern where each term is derived from the previous term by multiplying with an increasing integer and then subtracting the next integer. Such series test a higher level of pattern recognition, because both multiplication and subtraction change at each step. Given Data / Assumptions: - Series: 8, 6, 9, 23, ? - The fifth term is missing. - The pattern likely involves operations that depend on the term position. Concept / Approach: Instead of looking only at simple differences or ratios, consider how each term might be obtained from the previous term using position based operations. One common pattern is of the form: multiply by n and then subtract (n plus 1), where n increases step by step. By checking this idea against the given terms, the exact rule can be identified. Step-by-Step Solution: Step 1: Move from 8 to 6: 8 × 1 - 2 = 6. Here the multiplier is 1 and the subtracted value is 2. Step 2: Move from 6 to 9: 6 × 2 - 3 = 12 - 3 = 9. Now the multiplier is 2 and the subtracted value is 3. Step 3: Move from 9 to 23: 9 × 3 - 4 = 27 - 4 = 23. Here the multiplier is 3 and the subtracted value is 4. Step 4: The pattern is therefore: multiply by n and subtract (n plus 1), where n starts at 1 and increases by 1 each time. Step 5: For the next term, n becomes 4, so compute 23 × 4 - 5. Step 6: 23 × 4 = 92, and 92 - 5 = 87. Verification / Alternative check: Rebuild the series using this rule from the start. Begin with 8, then 8 × 1 - 2 = 6, 6 × 2 - 3 = 9, 9 × 3 - 4 = 23, and 23 × 4 - 5 = 87. The pattern works consistently at every step, confirming that 87 is the correct next term. Why Other Options Are Wrong: - Option 53 does not arise from 23 × 4 - 5 and therefore breaks the established multiply then subtract rule. - Option 75 would require 23 × 4 minus a different number, which is not consistent with subtracting n plus 1. - Option 110 is again inconsistent with the position based operation observed in earlier terms. Common Pitfalls: Learners often focus only on differences between terms and may miss patterns where both multiplication and subtraction change with each step. Another pitfall is to guess the next term using approximate growth rather than confirming a precise rule. For advanced series, always test potential rules rigorously against every transition. Final Answer: The missing term that follows the pattern is 87, so the correct option is 87.

Question 11

What should come in place of the question mark (?) in the following number series based on alternating division? 36, 18, 6, 3, 1, ?

Accepted Answer

Introduction / Context: This series features a decreasing pattern where terms are obtained by dividing by different integers in an alternating way. The learner must recognise that the sequence alternates division by 2 and division by 3 to reduce the values. Such patterns are common in reasoning tests to check comfort with division and sequence rules. Given Data / Assumptions: - Series: 36, 18, 6, 3, 1, ? - The sixth term is missing. - The terms decrease in a non linear manner. Concept / Approach: Calculate the ratio between consecutive terms to see by what factor each term is obtained from the previous one. If the ratios follow a repeating pattern, such as dividing by 2, then by 3, and so on, this pattern can be extended to find the next term. The key is to track the operations rather than only differences. Step-by-Step Solution: Step 1: Compute ratios between terms. 18 ÷ 36 = 1 / 2, so the first step is divide by 2. 6 ÷ 18 = 1 / 3, so the second step is divide by 3. 3 ÷ 6 = 1 / 2, so the third step is again divide by 2. 1 ÷ 3 ≈ 1 / 3, so the fourth step is divide by 3. Step 2: The pattern alternates between dividing by 2 and dividing by 3. Step 3: After division by 3, the next step should be division by 2 again. Step 4: Therefore, the missing term is 1 ÷ 2 = 0.5. Verification / Alternative check: Reconstruct the operations in order: 36 ÷ 2 = 18, 18 ÷ 3 = 6, 6 ÷ 2 = 3, 3 ÷ 3 = 1, and finally 1 ÷ 2 = 0.5. This confirms that the alternating division pattern is consistent and leads to 0.5 as the next term. Why Other Options Are Wrong: - Option 0.25 would correspond to dividing 1 by 4, which does not fit the alternating 2 and 3 pattern. - Option 1.5 would increase the value instead of decreasing it and would ignore the division based structure. - Option 0.75 would require dividing by 4 / 3 rather than by 2, which again breaks the clear rule. Common Pitfalls: Learners sometimes focus on differences rather than ratios, which is less helpful in division based patterns. Another pitfall is to miscalculate fractions, especially when dividing by 3, leading to incorrect subsequent steps. Careful computation of each division prevents such errors. Final Answer: The missing term is 0.5, so the correct option is 0.5.

Question 12

What will come in place of the question mark (?) in the following number series, where the increments alternate between two values? 18, 29, 42, 53, ?, 77

Accepted Answer

Introduction / Context: This series increases by two alternating differences. The learner must identify that the increments switch repetitively between two specific values. Recognising alternating addition patterns is a vital skill in many number series questions. Given Data / Assumptions: - Series: 18, 29, 42, 53, ?, 77. - The fifth term is missing. - The differences between terms appear to repeat in a pattern. Concept / Approach: Compute the differences between consecutive terms and look for repetition. If two values alternate, then this alternation can be extended to determine the missing increment and therefore the missing term. Checking both the earlier and later parts of the series ensures that the pattern is correct. Step-by-Step Solution: Step 1: Compute differences. 29 - 18 = 11. 42 - 29 = 13. 53 - 42 = 11. Step 2: The differences observed so far are 11, 13, and 11. Step 3: This suggests an alternating pattern: +11, +13, +11, +13, and so on. Step 4: The next difference after 11 should therefore be 13. Step 5: Add 13 to 53 to find the missing term: 53 + 13 = 66. Step 6: Confirm with the final step: 77 - 66 = 11, which fits the alternation of 11 and 13. Verification / Alternative check: Write out the pattern of differences explicitly: 18 + 11 = 29, 29 + 13 = 42, 42 + 11 = 53, 53 + 13 = 66, 66 + 11 = 77. This reconstruction confirms the alternating sequence of +11 and +13 and shows that 66 is the only value that keeps the pattern intact. Why Other Options Are Wrong: - Option 64 would give a difference of 11 from 53 but then require 13 to reach 77, which would not match the established order. - Option 71 would yield a difference of 18 from 53 and then 6 to reach 77, which does not fit the consistent pattern. - Option 65 introduces a difference of 12 that is not part of the alternating 11 and 13 structure. Common Pitfalls: Learners may miscalculate one of the differences and then fail to see the alternating pattern. Others might focus only on the first few terms and not confirm the pattern with later terms. A full check across the entire series is essential to avoid incorrect conclusions. Final Answer: The missing term in the series is 66, so the correct option is 66.

Question 13

In the following question, select the missing number from the given series, which uses steadily increasing increments. 23, 28, 34, 41, 49, ?

Accepted Answer

Introduction / Context: This number series gradually increases, with the gaps between terms themselves growing in a simple pattern. The learner must compute the step between each term and recognise that these steps increase by a constant amount. This is a classic example of using second level differences to determine the next term. Given Data / Assumptions: - Series: 23, 28, 34, 41, 49, ? - The sixth term is missing. - The differences between terms appear to increase gradually. Concept / Approach: First compute the difference between each pair of consecutive terms. Then examine whether these differences follow their own pattern, such as increasing by 1 each time. Once this secondary pattern is known, it can be extended to find the next difference, which in turn gives the missing term. Step-by-Step Solution: Step 1: Compute differences. 28 - 23 = 5. 34 - 28 = 6. 41 - 34 = 7. 49 - 41 = 8. Step 2: The differences are 5, 6, 7, and 8, increasing by 1 each time. Step 3: The next difference in this sequence should be 9. Step 4: Add this difference to the last known term: 49 + 9 = 58. Verification / Alternative check: Reconstruct the series using the difference pattern: starting from 23, add 5, 6, 7, 8, and 9. This yields 28, 34, 41, 49, and 58. The pattern of increasing differences remains perfectly consistent, confirming 58 as the correct next term. Why Other Options Are Wrong: - Option 59 would require a difference of 10 from 49, which would skip the expected increase of 9. - Option 57 gives a difference of 8, repeating the last difference instead of increasing it by 1. - Option 56 gives a difference of 7 and clearly breaks the upward trend of the differences. Common Pitfalls: Some learners may only look for a constant difference and miss the gradually increasing nature of the increments. Others may miscalculate a difference and fail to see the clear pattern of plus 1 each time. Checking the sequence of differences carefully helps avoid such errors. Final Answer: The missing term in the series is 58, so the correct option is 58.

Question 14

In the following question, select the missing number from the given series, which decreases by a constant amount each time. 672, 666, 660, 654, ?

Accepted Answer

Introduction / Context: This number series decreases steadily by the same amount at each step. The learner must recognise this constant difference and apply it to find the next term. Such linear decreasing sequences are foundational in number series practice. Given Data / Assumptions: - Series: 672, 666, 660, 654, ? - The fifth term is missing. - The series appears to be descending by equal steps. Concept / Approach: To identify a constant difference, compute the subtraction between each pair of consecutive terms. If the difference is the same, the series is an arithmetic progression with a negative common difference. The missing term is found by subtracting this difference from the last known value. Step-by-Step Solution: Step 1: Compute differences. 666 - 672 = -6. 660 - 666 = -6. 654 - 660 = -6. Step 2: The common difference is -6 at each step. Step 3: To find the next term, subtract 6 from 654. Step 4: 654 - 6 = 648. Verification / Alternative check: Rebuild the series starting from 672 and repeatedly subtract 6: 672, 666, 660, 654, 648. This matches the pattern of equal decrements and confirms that 648 is the correct missing term. Why Other Options Are Wrong: - Option 650 would imply a difference of -4 from 654, which breaks the constant step of -6. - Option 646 would require a difference of -8, again inconsistent with the pattern. - Option 652 gives a difference of -2, which also does not match the regular change. Common Pitfalls: Learners sometimes miscalculate one subtraction and then assume a different pattern. Others may try to overcomplicate a simple linear series. Always start with basic first differences before considering more complex structures. Final Answer: The missing term in the series is 648, so the correct option is 648.

Question 15

A number series is given with one term missing. Choose the correct alternative from the given options that will complete the pattern and identify the missing number in the sequence: 105, 130, 180, 255, ?

Accepted Answer

Introduction / Context: This question tests recognition of patterns in a numerical series. The sequence 105, 130, 180, 255, ? looks irregular at first glance, but the logic becomes clear when we focus on how each term changes. Such number series questions are common in banking, SSC, and other competitive exams and check a student's ability to detect consistent numerical operations between terms. Given Data / Assumptions: Series given: 105, 130, 180, 255, ? We must find the missing term. Options: 345, 365, 355, 335. Assume the pattern is consistent throughout the sequence. Concept / Approach: The usual approaches for such number series include checking differences between consecutive terms, second level differences, multiplication patterns, or combinations of addition and multiplication. Here, the numbers are increasing and the gaps are also increasing, which suggests an arithmetic pattern with increasing differences. Once we see how the differences grow, the missing term can be found easily. Step-by-Step Solution: Step 1: Compute first differences.130 - 105 = 25180 - 130 = 50255 - 180 = 75Step 2: Compare these differences.We have 25, 50, 75 which form an arithmetic progression with common difference 25.Step 3: Extend the pattern of differences.The next difference should be 75 + 25 = 100.Step 4: Add this difference to the last known term.Missing term = 255 + 100 = 355. Verification / Alternative check: List the sequence with the found term: 105, 130, 180, 255, 355. The consecutive differences are 25, 50, 75, 100. These differences clearly increase by 25 each time, which is a smooth and consistent pattern. There is no contradiction or sudden jump, so the answer 355 fits the series perfectly. Why Other Options Are Wrong: 345: Difference from 255 would be 90, which breaks the pattern of differences increasing by 25.365: Difference from 255 would be 110, which also does not follow the expected difference of 100.335: Difference from 255 would be 80, again inconsistent with the step of 25 in the differences. Common Pitfalls: Many candidates only check first differences but forget to see whether the differences themselves follow a pattern. Some may try multiplication based patterns or random trial and error, which wastes time. The correct way is to keep the approach systematic: first check differences, then second differences, and only then move to more complex ideas if needed. Final Answer: The missing term that continues the pattern of increasing differences by 25 is 355.

Question 16

Consider the digit sequence 6 6 8 5 5 3 7 3 7 2 5 8 8 7 8 1 5 5 3. Using this sequence, determine which two digit number among 83, 35, 27, and 81 does not belong to the group based on a consistent positional pattern of digits.

Accepted Answer

Introduction / Context: This is a reasoning question based on a long sequence of digits. From the sequence 6 6 8 5 5 3 7 3 7 2 5 8 8 7 8 1 5 5 3, we must decide which of the numbers 83, 35, 27, and 81 does not belong to the group. Such questions test pattern recognition at the digit level rather than direct numerical operations like addition or multiplication. Given Data / Assumptions: Digit sequence: 6 6 8 5 5 3 7 3 7 2 5 8 8 7 8 1 5 5 3. Candidate two digit numbers: 83, 35, 27, 81. We assume that a consistent positional rule links valid members of the group to this sequence. Concept / Approach: In many such puzzles, each valid two digit number XY must be formed by taking X and Y from the given digit sequence following a specific positional rule. One common type of rule is that the second digit appears a fixed number of positions to the right of the first digit. Here we look for a constant gap of two digits between the first and second digits of each valid pair when they are traced in the master sequence. Step-by-Step Solution: Step 1: Index the sequence positions.Positions: 1:6, 2:6, 3:8, 4:5, 5:5, 6:3, 7:7, 8:3, 9:7, 10:2, 11:5, 12:8, 13:8, 14:7, 15:8, 16:1, 17:5, 18:5, 19:3.Step 2: Check 83.Take 8 at position 3. If we skip exactly two digits (positions 4 and 5), we reach position 6 which holds 3. So 83 fits the pattern of second digit being third to the right of the first.Step 3: Check 35.Take 3 at position 8. Skipping positions 9 and 10 leads to position 11 which is 5. So 35 also follows this same gap of two digits.Step 4: Check 81.Take 8 at position 13. Skipping positions 14 and 15 leads to position 16 which is 1, so 81 matches the rule as well.Step 5: Check 27.Take 2 at position 10. Skipping positions 11 and 12 takes us to position 13 which is 8, not 7. There is no 7 exactly three positions to the right of any 2, so 27 breaks the rule. Verification / Alternative check: We can verify by scanning the sequence for all pairs that satisfy the rule "second digit is third to the right of the first digit." We find valid pairs such as 83, 35, and 81 by the method above, but 27 never appears under this exact spacing condition. Hence, 27 is structurally inconsistent with the pattern that connects the other three candidates to the base sequence. Why Other Options Are Wrong: 83: Follows the fixed gap rule and is therefore a valid member of the group.35: Also follows the same positional gap of two digits and belongs to the group.81: Again satisfies the rule, with 1 exactly three positions after 8.27: Fails the rule and hence does not belong to the group. Common Pitfalls: Candidates often try to build arithmetic relationships between the two digit numbers themselves and ignore the long digit sequence given in the stem. Others may look only for simple adjacency of digits rather than a fixed spacing rule. The key idea is to use the provided sequence and search for a structural positional rule that works consistently for three numbers but fails for one. Final Answer: The only number that does not follow the positional gap pattern in the digit sequence is 27.

Question 17

A number series is given with one term missing. Select the correct alternative from the given options that will complete the pattern and determine the missing number in the sequence: 4, 13, 40, 121, ?

Accepted Answer

Introduction / Context: This question involves a non linear number series where each term is generated from the previous term using a consistent rule. The sequence 4, 13, 40, 121, ? increases rapidly, which suggests a combination of multiplication and addition rather than simple constant differences. Such patterns are very common in reasoning and aptitude exams. Given Data / Assumptions: Series: 4, 13, 40, 121, ? Options: 350, 360, 364, 362. We assume one fixed rule applies between every pair of consecutive terms. Concept / Approach: For fast growing series, it is natural to test multiplicative patterns such as "multiply by a constant and add or subtract a small number." If differences themselves grow in a nearly multiplicative way, that reinforces this idea. Here, testing the relation T(n+1) = 3 * T(n) + 1 quickly shows a perfect fit for the first three transitions, which can then be extended to find the missing term. Step-by-Step Solution: Step 1: Check relation from 4 to 13.3 * 4 + 1 = 12 + 1 = 13.Step 2: Check relation from 13 to 40.3 * 13 + 1 = 39 + 1 = 40.Step 3: Check relation from 40 to 121.3 * 40 + 1 = 120 + 1 = 121.Step 4: Apply the same pattern to 121.Next term = 3 * 121 + 1 = 363 + 1 = 364. Verification / Alternative check: Write the complete series using the found term: 4, 13, 40, 121, 364. Now verify every jump: 4 to 13, 13 to 40, 40 to 121, and 121 to 364 all follow the exact rule "multiply by 3 and then add 1." There is no break or inconsistency anywhere, which confirms that 364 fits perfectly. The rapid growth and uniform transformation at each step support this as the unique valid answer. Why Other Options Are Wrong: 350: This cannot be written as 3 * 121 + constant with the same constant as previous steps.360: Also does not satisfy T(n+1) = 3 * T(n) + 1 for n = 4th term.362: Fails the established relation and breaks the pattern. Common Pitfalls: Some candidates may look only at differences: 9, 27, 81 and guess that the next difference is 243, which coincidentally leads to the same answer 364. However, they may not articulate the underlying relation clearly. It is safer to express the core pattern directly as T(n+1) = 3 * T(n) + 1 so that the logic remains easy to verify and apply to similar problems. Final Answer: The missing term that follows the rule T(n+1) = 3 * T(n) + 1 is 364.

Question 18

A number series is given with one term missing. Choose the correct alternative from the given options that will complete the sequence and determine the missing number in the series: -1, 1, 4, 9, 16, ?

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Introduction / Context: At first glance this series looks similar to a sequence of perfect squares, but it starts with a negative value: -1, 1, 4, 9, 16, ?. Number series of this type often hide two related ideas: either the squares of integers or a pattern in the differences. Here the question tests familiarity with prime numbers as incremental steps in the series, which is a favourite pattern in competitive exams. Given Data / Assumptions: Given series: -1, 1, 4, 9, 16, ? Options: 24, 27, 26, 36. We assume one consistent rule throughout the series. Concept / Approach: Two complementary approaches work well here. The first is to look at the differences between consecutive terms. The second is to check whether there is any link with known important sequences such as prime numbers. If the differences themselves follow the sequence of prime numbers, that is a strong indication of the intended pattern. Let us compute and see. Step-by-Step Solution: Step 1: Compute differences between consecutive terms.From -1 to 1: difference = 2.From 1 to 4: difference = 3.From 4 to 9: difference = 5.From 9 to 16: difference = 7.Step 2: Observe the pattern in differences.The differences are 2, 3, 5, 7 which are the first four prime numbers.Step 3: Extend the prime sequence.The next prime after 7 is 11.Step 4: Add this next prime to the last term.Missing term = 16 + 11 = 27. Verification / Alternative check: We can write the series in terms of cumulative prime additions starting from -1. Starting term is -1. Add 2 to get 1. Add 3 to get 4. Add 5 to get 9. Add 7 to get 16. Add 11 to get 27. This confirms that the pattern is "add consecutive prime numbers" and that the result 27 is fully consistent with all known terms in the sequence. Why Other Options Are Wrong: 24: Would correspond to adding 8 to 16, but 8 is not the next prime number after 7.26: Would correspond to adding 10, again not prime and inconsistent with the observed pattern.36: Would require adding 20, which does not relate to the sequence of primes used earlier. Common Pitfalls: Because the sequence also resembles squares (1, 4, 9, 16), some students incorrectly jump to 25 or 36 based solely on square numbers and ignore the first term -1. The correct method is to consider all terms, including the starting one, and compute differences carefully. Recognising the prime sequence 2, 3, 5, 7, 11 is the key step here. Final Answer: The missing term obtained by adding the next prime number 11 to 16 is 27.

Question 19

A number series is given with one term missing. Choose the correct alternative from the given options that will complete the pattern and identify the missing number in the sequence: 5, 10, 13, 52, 57, ?

Accepted Answer

Introduction / Context: This question presents a mixed operation number series. The terms 5, 10, 13, 52, 57, ? alternate between moderate jumps and very large jumps, hinting that the pattern uses both multiplication and addition in a repeating cycle. Such alternating operation series are common in reasoning tests because they require careful observation over several steps. Given Data / Assumptions: Series: 5, 10, 13, 52, 57, ? Options: 285, 225, 342, 390. We assume that the same alternating pattern continues throughout the series. Concept / Approach: When terms increase sharply at every second step, a common pattern is "multiply by a certain number, then add another number" in an alternating way. Here we check transitions in order and see if the multipliers and addends form a simple arithmetic or geometric pattern, such as 2, 4, 6 or 3, 5, 7 and so on. Once found, we extend that pattern to compute the missing term. Step-by-Step Solution: Step 1: Examine transitions closely.From 5 to 10: 5 * 2 = 10.From 10 to 13: 10 + 3 = 13.From 13 to 52: 13 * 4 = 52.From 52 to 57: 52 + 5 = 57.Step 2: Recognise the pattern.Operations alternate as multiply, add, multiply, add and so on.Multipliers: 2, then 4, then next should be 6.Addends: 3, then 5, which are consecutive odd numbers, so the next addend would be 7 in future steps.Step 3: Apply the next operation to find the missing term.After 57, the next operation in the established pattern is multiply by 6.Missing term = 57 * 6 = 342. Verification / Alternative check: Write the series together with the operations: 5 * 2 = 10, 10 + 3 = 13, 13 * 4 = 52, 52 + 5 = 57, 57 * 6 = 342. We can also predict the next step for confirmation: 342 + 7 = 349 if the series continued. The pattern is therefore multiply by an even number (2, 4, 6, ...) and then add the next odd number (3, 5, 7, ...), alternating these operations. This confirms that 342 is consistent. Why Other Options Are Wrong: 285: Not equal to 57 multiplied by any simple continuation of the multiplier pattern, and does not fit an add operation either.225: Similarly fails the multiply by 6 or add 7 expectation and breaks the structure.390: Would correspond to 57 * something that does not continue the simple even number sequence 2, 4, 6. Common Pitfalls: Many candidates try to find one single operation linking every step, such as adding increasing differences only. However, because the series alternates operations, focusing on just differences can become confusing. A better method is to inspect each pair of terms, hypothesise a candidate operation, and then check whether that operation alternates regularly through the series. Final Answer: The missing number, obtained by multiplying 57 by 6, is 342.

Question 20

In the following question, a number series is given with one term missing. Select the missing number from the given series that correctly continues the pattern: 6, 9, 15, 24, 39, 63, ?

Accepted Answer

Introduction / Context: This is a classic example of a Fibonacci style number series, where each term after the first two is obtained by combining the previous two terms. Recognising such patterns is important in verbal reasoning and quantitative aptitude exams. The series given is 6, 9, 15, 24, 39, 63, ?, and we must find the missing term at the end. Given Data / Assumptions: Series: 6, 9, 15, 24, 39, 63, ? Options: 97, 102, 115, 127. We assume a single consistent rule drives the progression of terms. Concept / Approach: For series where each term looks roughly like the sum of the previous two, a Fibonacci type pattern is suspected. Instead of focusing on fixed differences, we check whether from some point onward each term equals the sum of the previous two terms. If this holds from the third term onward, we can safely extend it to find the next term. Step-by-Step Solution: Step 1: Test the relation T(n) = T(n-1) + T(n-2).Check 15: 6 + 9 = 15. This matches.Check 24: 9 + 15 = 24. This matches.Check 39: 15 + 24 = 39. This matches.Check 63: 24 + 39 = 63. This also matches.Step 2: Use the same rule for the missing term.Next term = 39 + 63 = 102. Verification / Alternative check: Write the complete series including the found term: 6, 9, 15, 24, 39, 63, 102. From the third term onward each term is exactly the sum of the two preceding terms. This is precisely how a Fibonacci type sequence behaves, and no term violates the rule. Therefore, 102 fits perfectly and ensures the structure of the series remains intact. Why Other Options Are Wrong: 97: 39 + 63 is not 97, so it cannot be the next term in a Fibonacci style pattern.115: Also does not equal 39 + 63, hence inconsistent with the established rule.127: Again does not match the required sum of 102. Common Pitfalls: Some students incorrectly focus on differences between consecutive terms: 3, 6, 9, 15, 24 and then attempt to find a second level pattern in those differences. While a pattern exists there too, it is more complicated than simply noticing that the main series is formed by summing the previous two terms. Always check for Fibonacci type patterns early when the numbers grow in this manner. Final Answer: The missing term that continues the Fibonacci style sequence is 102.

Number Series Questions