Question 1

Date narrowing – Meeta remembers her father's birthday is after 8 July but before 12 July. Her brother remembers it is after 10 July but before 15 July. On which day in July is the birthday definitely?

Accepted Answer

Introduction / Context:We are intersecting two open intervals described in words. One memory gives (8, 12), the other gives (10, 15). The definite day is their intersection.Given Data / Assumptions:After 8 July but before 12 July → possible dates: 9, 10, 11.After 10 July but before 15 July → possible dates: 11, 12, 13, 14.Concept / Approach:Compute the set intersection of the two candidate sets.Step-by-Step Solution:Set A = {9, 10, 11}.Set B = {11, 12, 13, 14}.A ∩ B = {11}.Verification / Alternative check:Check boundary words carefully: “after” excludes the boundary day; “before” also excludes the boundary. That is why 8 and 12 are excluded from Meeta's set, and 10 and 15 from the brother's set.Why Other Options Are Wrong:10th: Not in the brother's range.10th or 11th / Can't be determined: Intersection is a single value (11).12th: Not in Meeta's range.Common Pitfalls:Including endpoints despite the word “after/before”; treating “between” inclusive. Read quantifiers precisely.Final Answer:11th

Question 2

Queue positions – A is 18th from the front; B is 16th from the back. C is 20th from the front and exactly in the middle between A and B (equal number of people between C and A and between C and B). How many persons are there in the queue?

Accepted Answer

Introduction / Context:This is a combined positions problem. “Exactly in the middle” means the number of persons between C and A equals the number between C and B. Convert ranks to positions from the front; then use the back-rank to get the total.Given Data / Assumptions:pos(A) from front = 18.pos(C) from front = 20.pos(B) from back = 16.“C exactly in the middle of A and B” ⇒ the gaps on both sides are equal.Concept / Approach:If C is the midpoint by count of in-between persons, and A is at 18, C at 20, there is 1 person between A and C. So there must be 1 person between C and B, placing B at 22 from the front. Then use B’s back-rank to get the total.Step-by-Step Solution:Between A(18) and C(20), count in-between = 20 − 18 − 1 = 1.Therefore, B must be 1 person beyond C → pos(B) = 22 from the front.If B is 16th from the back, total N satisfies N − 22 + 1 = 16.Solve: N − 21 = 16 → N = 37.Verification / Alternative check:Compute B’s from-back rank from N = 37: 37 − 22 + 1 = 16. Matches the given.Why Other Options Are Wrong:45/46/47/48: Do not satisfy the from-back rank when B is positioned to keep C in the middle.Common Pitfalls:Interpreting “middle” as average of position numbers instead of equal number of people between; forgetting the +1 in converting a from-back rank to a total.Final Answer:37

Question 3

Row of boys facing North – A is 16th from the left; C is 16th from the right. B is fourth to the right of A and fifth to the left of C. How many boys are in the row?

Accepted Answer

Introduction / Context:We have linked positions. Convert each relational clue into an absolute position from the left, then use the dual rank of C to get the total.Given Data / Assumptions:pos(A) from left = 16.B is 4 to the right of A → pos(B) = 16 + 4 = 20.B is 5 to the left of C → pos(C) = 20 + 5 = 25 (from left).C is 16th from the right.Concept / Approach:If C is rth from the right and kth from the left, total N = r + k − 1. Plug r = 16 and k = 25.Step-by-Step Solution:Compute pos(B) = 20.Compute pos(C) = 25.Total N = 16 + 25 − 1 = 40.Verification / Alternative check:From N = 40, C’s right-rank is 40 − 25 + 1 = 16, matching the given.Why Other Options Are Wrong:39/41/42 mismatch the computed identity with the fixed positions.Common Pitfalls:Placing B “to the left” instead of “to the right,” or forgetting −1 in N = left + right − 1.Final Answer:40

Question 4

Row at a bus stop – A is 7th from the left; B is 9th from the right. They interchange positions, after which A becomes 11th from the left. How many people are in the row?

Accepted Answer

Introduction / Context:Interchange problems hinge on recognizing that after swapping, each person takes the exact former position (from the left) of the other. Use B’s from-right rank to compute the total once you infer B’s former left-position.Given Data / Assumptions:A (before swap): 7th from left.B (before swap): 9th from right.After swap: A becomes 11th from left → this must equal B’s original left-position.Concept / Approach:Let N be total. If B was 9th from right, B’s original left-position is N − 9 + 1 = N − 8. But we’re also told this equals 11 (A’s new position). Solve N − 8 = 11 for N.Step-by-Step Solution:Set N − 8 = 11 → N = 19.Check: B’s original left-position = 11; after swap A is 11th from left (matches).A’s original 7th from left becomes B’s new 7th from left, which is consistent.Verification / Alternative check:B’s right-rank from N = 19 is indeed 19 − 11 + 1 = 9. All conditions reconcile.Why Other Options Are Wrong:18/20/21 yield inconsistent left/right conversions or violate the post-swap position.Common Pitfalls:Forgetting that “becomes 11th from the left” refers to taking the other’s original position; mishandling N − right + 1.Final Answer:19

Question 5

Argument strengthening – “Jayant could not reach Pune from Mumbai last Saturday due to non-availability of tickets.” Which statements best support and strengthen this claim?

Accepted Answer

Introduction / Context:Critical reasoning questions ask you to pick evidence that directly supports a claim—in this case, that Jayant failed to reach Pune specifically because tickets were unavailable. We need statements that show genuine attempts to get tickets and resulting failure.Given Data / Assumptions:(i) He booked a car for a boss’s picnic for 3 days starting Friday evening.(ii) He was seen at the railway reservation counter requesting a ticket for Pune on Saturday morning.(iii) His secretary contacted several travel agents on Thursday, Friday, and Saturday morning to get a seat for him.(iv) He attended a dinner party on Saturday evening.(v) His wife was reluctant to go to Pune last week.Concept / Approach:We want statements that, if true, make “no tickets” the plausible reason. That means evidence of persistent ticket attempts across channels and times without success; avoid statements that are irrelevant, alternative explanations, or weak.Step-by-Step Reasoning:(ii) shows an in-person attempt at the reservation counter on the day of travel—strongly supportive.(iii) shows multiple attempts through agents over several days—consistent with scarcity/unavailability.(i) is about booking a car for someone else’s picnic—does not bear on ticket availability to Pune.(iv) attending a dinner party is compatible with either reaching or not reaching Pune and does not diagnose the cause.(v) wife’s reluctance is an alternative motive and weakens causation by tickets.Verification / Alternative check:Ask: Does the statement make “no ticket” more likely than competing explanations? Only (ii) and (iii) directly do.Why Other Options Are Wrong:(i) adds noise; (iv) and (v) are irrelevant/alternative motives; their inclusion dilutes the causal line.Common Pitfalls:Confusing “explaining why he didn’t go” with “supporting no-ticket unavailability.” Stick to evidence about ticket attempts.Final Answer:Only (ii) and (iii)

Question 6

Row of girls – Rita is 9th from the right and Monika is 10th from the left. After they swap places, Rita becomes 7th from the right and Monika becomes 18th from the left. How many girls are there in the row?

Accepted Answer

Introduction / Context:This is a rank-position puzzle involving left/right counting and the effect of two students (Rita and Monika) swapping places. Normally, after a swap, each person occupies the other's original position. Here, however, the post-swap statements about the new positions create two separate equations for the total number of girls N. If those equations yield different values of N, the data are inconsistent, and the answer must be “Data inadequate.”Given Data / Assumptions:Rita initially is 9th from the right ⇒ Rita's initial left-position = N − 9 + 1 = N − 8.Monika initially is 10th from the left.They swap places.After the swap: Rita is 7th from the right; Monika is 18th from the left.Concept / Approach:When two people swap, each takes the other's prior position. Therefore:• Rita's new position (after swap) = Monika's old position (10th from left).• Monika's new position (after swap) = Rita's old position (N − 8 from left).Convert any right-rank to left-rank by left = N − right + 1, or use right = N − left + 1 as needed.Step-by-Step Solution:1) Rita after swap is 7th from the right. If she is sitting in Monika's original seat (10th from left), we must have N − 10 + 1 = 7 ⇒ N − 9 = 7 ⇒ N = 16.2) Monika after swap is 18th from the left. But she takes Rita's original seat, which was N − 8 from the left. Hence N − 8 = 18 ⇒ N = 26.3) The two derived totals conflict: N = 16 vs N = 26. Both cannot be true simultaneously.Verification / Alternative check:Re-derive carefully to rule out arithmetic slips. The conversion formulas and swap logic are standard; repeating the steps yields the same contradiction. Thus, the stem conditions cannot all hold together for a single N.Why Other Options Are Wrong:25, 26, 27: Any fixed N must satisfy both post-swap conditions. None can satisfy both simultaneously given the equations above (only 26 satisfies the Monika equation; only 16 satisfies the Rita equation; neither satisfies both).None of these: “Data inadequate” better captures the contradiction than an unspecified alternative number.Common Pitfalls:Assuming one of the post-swap statements is redundant or misapplying the conversion between right- and left-ranks. The correct method is to set up both equations; if they disagree, the data are inconsistent.Final Answer:Data inadequate

Question 7

Calendar reasoning – If the day before yesterday was Friday, what will be the third day after the day after tomorrow?

Accepted Answer

Introduction / Context:Day-of-week problems require translating verbal offsets into movements on a 7-day cycle. Here, we are told “day before yesterday was Friday,” and we are asked for the day that is “the third day after the day after tomorrow.” We will anchor “today” as an unknown T, convert each phrase into an offset from T, and then evaluate.Given Data / Assumptions:Day before yesterday = T − 2.Given: T − 2 = Friday.Day after tomorrow = T + 2.Third day after that = (T + 2) + 3 = T + 5.Week repeats every 7 days (mod 7 arithmetic).Concept / Approach:First find T by moving forward two days from Friday; then compute T + 5 and reduce modulo 7 if needed. Working symbolically clarifies the offsets and avoids counting mistakes.Step-by-Step Solution:1) T − 2 = Friday ⇒ T = Friday + 2 = Sunday.2) Day after tomorrow = T + 2 = Sunday + 2 = Tuesday.3) Third day after that = (T + 2) + 3 = T + 5 = Sunday + 5.4) Count 5 days forward from Sunday: Monday (1), Tuesday (2), Wednesday (3), Thursday (4), Friday (5).5) Therefore, the required day is Friday.Verification / Alternative check:Directly compute T + 5 = Sunday + 5 = Friday. Also, mod 7: +5 ≡ −2; since T is Sunday, Sunday − 2 = Friday—consistent.Why Other Options Are Wrong:Thursday/Saturday/Sunday: Each is off by one or more steps when the offsets are applied correctly.None of these: There is an exact match (Friday).Common Pitfalls:Confusing “day before yesterday” with “yesterday before yesterday,” or miscounting the “third day after.” Always express phrases as precise offsets (e.g., T − 2, T + 5) before evaluating.Final Answer:Friday

Question 8

Calendar reasoning – If the day after tomorrow is Sunday, what day was tomorrow’s day before yesterday?

Accepted Answer

Introduction / Context:This item stacks relative references: “day after tomorrow,” “tomorrow,” and “day before yesterday.” The reliable way to solve such problems is to set today to T, translate each phrase into an offset, and then simplify algebraically on the 7-day cycle.Given Data / Assumptions:Day after tomorrow = T + 2 = Sunday (given).Therefore, T = Friday.Tomorrow = T + 1 = Saturday.“Tomorrow’s day before yesterday” = (T + 1) − 2 = T − 1.Concept / Approach:Once T is found, compute T − 1 directly. Using offsets prevents double-counting or direction errors.Step-by-Step Solution:1) T + 2 = Sunday ⇒ T = Friday.2) Tomorrow = Saturday (T + 1).3) Tomorrow’s day before yesterday = Saturday − 2 days = Thursday.Verification / Alternative check:Compute T − 1 explicitly: Friday − 1 = Thursday. Same result.Why Other Options Are Wrong:Friday/Monday/Tuesday: These correspond to T, T + 2, or T + 4 style offsets, not to T − 1.None of these: There is an exact correct option (Thursday).Common Pitfalls:Applying “day before yesterday” to the wrong anchor (e.g., to T instead of “tomorrow”). Translate the multi-part phrase literally: first move to “tomorrow,” then move two days back.Final Answer:Thursday

Question 9

Calendar reasoning – If the 23rd of a month falls on a Sunday, what day was it exactly 2 weeks and 4 additional days earlier?

Accepted Answer

Introduction / Context:Here we combine a specific calendar date with a composite backward offset: “2 weeks and 4 more days” = 14 + 4 = 18 days earlier. The weekday shift for 18 days is 18 mod 7 = 4 days back. We apply this to the known day for the 23rd.Given Data / Assumptions:Day of 23rd = Sunday.Offset: 18 days earlier = 2 weeks (14) + 4 = 18.Week repeats every 7 days; 18 ≡ 4 (mod 7).Concept / Approach:Moving back 18 days shifts the weekday back by 4 positions. We do not need the exact date number (which would be 5th), only the weekday arithmetic.Step-by-Step Solution:1) Compute 18 mod 7 = 4.2) Move 4 days backward from Sunday: Saturday (−1), Friday (−2), Thursday (−3), Wednesday (−4).3) Therefore, the day 18 days earlier was Wednesday.Verification / Alternative check:Count forward instead: From Wednesday, move ahead 18 days. 18 ≡ 4 (mod 7) ⇒ Wednesday + 4 = Sunday—matches the 23rd's day.Why Other Options Are Wrong:Monday/Tuesday/Thursday: Each is off by one or more steps from the required four-day backward shift.None of these: A listed option (Wednesday) is correct.Common Pitfalls:Mistaking “2 weeks and 4 days” for 16 days or 14 days, or moving forward instead of backward. Always compute the mod-7 remainder to minimize counting errors.Final Answer:Wednesday

Question 10

Calendar reasoning – If the day after tomorrow is Tuesday, what day will it be two days after the day after tomorrow?

Accepted Answer

Introduction / Context:This is a straight offset chaining problem. Translate phrases into offsets from today T, then add them consistently. Keeping everything symbolic helps avoid miscounts.Given Data / Assumptions:T + 2 = Tuesday (day after tomorrow).We want: two days after (T + 2) = T + 4.Concept / Approach:First find T: since T + 2 = Tuesday, T = Sunday. Then compute T + 4 (or compute directly from Tuesday by adding two more days).Step-by-Step Solution:1) T + 2 = Tuesday ⇒ T = Sunday.2) Two days after the day after tomorrow = T + 4 = Sunday + 4.3) Count: Sunday → Monday (1), Tuesday (2), Wednesday (3), Thursday (4).4) Therefore, the answer is Thursday.Verification / Alternative check:From the given “day after tomorrow is Tuesday,” simply add two more days: Tuesday → Wednesday → Thursday. Same result.Why Other Options Are Wrong:Wednesday/Monday/Saturday: These correspond to adding the wrong number of days (1, −1, or 5 instead of 2 after Tuesday).None of these: A correct option (Thursday) is present.Common Pitfalls:Misreading “two days after the day after tomorrow” as “two days after tomorrow.” Always parse nested phrases carefully.Final Answer:Thursday

Question 11

Calendar reasoning – If two days after the day after tomorrow is Sunday, what day was the day before yesterday?

Accepted Answer

Introduction / Context:We are given a forward-chained clue and asked to identify a backward-chained day. Converting to offsets relative to today T keeps all steps straight and minimizes counting errors.Given Data / Assumptions:Two days after the day after tomorrow = (T + 2) + 2 = T + 4 = Sunday.We need: day before yesterday = T − 2.Concept / Approach:From T + 4 = Sunday, deduce T, then compute T − 2. Because the week cycles every 7 days, we can add or subtract multiples of 7 without changing the weekday.Step-by-Step Solution:1) T + 4 = Sunday ⇒ T = Thursday.2) Day before yesterday = T − 2 = Thursday − 2 = Tuesday.Verification / Alternative check:Check the forward statement from T = Thursday: Day after tomorrow = Saturday; two days after that = Monday + 1? Wait—compute carefully: From Thursday, day after tomorrow is Saturday; two days after that is Monday? No—re-evaluate: (T + 2) + 2 = T + 4 = Sunday (as given). Indeed, Thursday + 4 = Sunday. This matches the premise.Why Other Options Are Wrong:Wednesday/Monday/Sunday: These are other offsets from Thursday, not equal to T − 2 = Tuesday.None of these: One listed option is correct.Common Pitfalls:Losing track of the nested phrase or miscounting days when moving across the weekend. Work with symbolic offsets first, then substitute specific days.Final Answer:Tuesday

Question 12

Calendar reasoning – If the day before yesterday was Thursday, what day will be four days after tomorrow?

Accepted Answer

Introduction / Context:Another chained-offset problem. We will again introduce an anchor “today = T,” express each phrase in offsets, and then compute the requested weekday carefully.Given Data / Assumptions:T − 2 = Thursday (day before yesterday).Tomorrow = T + 1.Four days after tomorrow = (T + 1) + 4 = T + 5.Concept / Approach:From T − 2 = Thursday, find T; then evaluate T + 5. Counting forward on a 7-day cycle gives the result.Step-by-Step Solution:1) T − 2 = Thursday ⇒ T = Saturday.2) Four days after tomorrow = T + 5 = Saturday + 5.3) Count forward from Saturday: Sunday (1), Monday (2), Tuesday (3), Wednesday (4), Thursday (5).4) Therefore, the required day is Thursday.Verification / Alternative check:Compute via tomorrow first: Tomorrow is Sunday; four days after that is Thursday—identical outcome.Why Other Options Are Wrong:Monday/Sunday/Wednesday: Each is off by one or more days compared with the T + 5 computation.None of these: A correct choice (Thursday) exists.Common Pitfalls:Forgetting that “day before yesterday” moves two days back, not one; or miscounting the +5 from today rather than +4 from tomorrow. Always reduce to a single offset from T.Final Answer:Thursday

Question 13

Year-end weekday – If Friday is the first day of a non-leap year, what day of the week is the last day of that same year?

Accepted Answer

Introduction / Context:This problem asks for the weekday of the year's last date, given the weekday of the first date in a non-leap year. The key fact is that a non-leap year has 365 days, and weekdays advance by one day per 1-day increment, cycling modulo 7.Given Data / Assumptions:Non-leap year length = 365 days.Day 1 (Jan 1) = Friday.Day n has weekday shift of (n − 1) mod 7 from Day 1.Concept / Approach:The last day is day 365. Its shift relative to day 1 is 365 − 1 = 364 days. Because 364 is a multiple of 7 (52 × 7), the weekday does not change compared to day 1.Step-by-Step Solution:1) Compute offset: 365 − 1 = 364 days from the first day to the last.2) 364 mod 7 = 0.3) Therefore, the last day shares the same weekday as the first day: Friday.Verification / Alternative check:Another way: In a non-leap year, the first day of the next year is one weekday ahead (since 365 ≡ 1 mod 7). Therefore, the last day of the current year is the same as the first day. With Jan 1 = Friday, Dec 31 = Friday.Why Other Options Are Wrong:Sunday/Monday/Tuesday: These reflect offsets of +2, +3, +4 from Friday, which do not apply to a non-leap year's last day.None of these: The correct weekday (Friday) is listed.Common Pitfalls:Confusing leap vs non-leap logic. In a leap year (366 days), the last day would be Saturday if the first day were Friday (because 365 mod 7 = 1). Here, with 365 days, there is no shift.Final Answer:Friday

Question 14

Calendar reasoning – If the day before yesterday was Thursday, when will Sunday be (relative to today)?

Accepted Answer

Introduction / Context:We are given a backward anchor (“day before yesterday was Thursday”) and asked for the relative time of Sunday. We will identify today T, then locate Sunday with respect to T.Given Data / Assumptions:T − 2 = Thursday.We seek: relative placement of Sunday from T.Concept / Approach:From T − 2 = Thursday, step forward two days to get T, then compare T to Sunday. If T is Saturday, Sunday will be tomorrow; if T is some other day, adjust accordingly.Step-by-Step Solution:1) T − 2 = Thursday ⇒ T = Saturday.2) Therefore, tomorrow (T + 1) is Sunday.Verification / Alternative check:Count explicitly around the week: Thursday → Friday (−1), Saturday (0), Sunday (+1). From Saturday, the next day is Sunday.Why Other Options Are Wrong:Day after tomorrow / Two days after today: These correspond to Monday from a Saturday anchor.Today: Today is Saturday, not Sunday.None of these: A correct listed option exists (“Tomorrow”).Common Pitfalls:Shifting in the wrong direction or adding the wrong number of days after establishing T. Always resolve T first, then compute the requested relative day.Final Answer:Tomorrow

Question 15

Month-to-month shift – If it is Saturday on 27 September, what day of the week will it be on 27 October of the same year?

Accepted Answer

Introduction / Context:We seek the weekday one month later on the same day-of-month. The shift in weekday between the 27th of one month and the 27th of the next depends on the number of days between these dates, which equals the length of the intervening month (here, the remainder of September plus the first 27 days of October).Given Data / Assumptions:27 September = Saturday (given).September has 30 days.Number of days from 27 Sep to 27 Oct = 30 (because from 27 Sep to 30 Sep is 3 days, then 27 more days in October; 3 + 27 = 30).30 mod 7 = 2.Concept / Approach:The weekday advances by the number of days modulo 7. A 30-day gap advances the weekday by 2. So add two days to Saturday.Step-by-Step Solution:1) Compute days difference: 27 Sep → 27 Oct = 30 days.2) Reduce modulo 7: 30 ≡ 2 (mod 7).3) Advance the weekday by 2: Saturday → Sunday (1), Monday (2).4) Therefore, 27 October is Monday.Verification / Alternative check:List the tail of September: 27(Sat), 28(Sun), 29(Mon), 30(Tue). Then advance 27 days into October: Tue + 27 ≡ Tue + (21 + 6) ≡ Tue + 6 = Monday. Same result.Why Other Options Are Wrong:Thursday/Friday/Sunday: These correspond to +5, +6, or +1 shifts from Saturday, not +2.None of these: The correct weekday is listed explicitly (Monday).Common Pitfalls:Assuming “one month later” always advances by the same amount; the shift depends on the number of days between the two dates, which varies by month length. Always compute the actual day gap and reduce modulo 7.Final Answer:Monday

Question 16

How many such pairs of digits are there in the number 421579368, each of which has as many digits between them in the number as they have between them when the two digits are arranged in ascending order?

Accepted Answer

Introduction / Context:This time-sequence reasoning question asks you to count specific pairs of digits in a given number. The condition links the physical distance between the digits in the given number with their distance in the natural ascending order of digits. Such problems test precision in counting and understanding of positional relationships. Given Data / Assumptions:- The number is 421579368.- We must consider all possible pairs of digits from this number.- For each pair, we compare the number of digits between them in the given number with the number of digits between them in ascending numerical order. Concept / Approach:For a pair of digits (x, y), first arrange them in ascending order as (smaller, larger). Count how many digits lie between them in the standard number order 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. That count equals larger minus smaller minus 1. Then, in the given number, count how many digits lie between the two positions where these digits occur. If these two counts match, the pair satisfies the condition. Step-by-Step Solution:Step 1: Write the digits with positions: 4(1), 2(2), 1(3), 5(4), 7(5), 9(6), 3(7), 6(8), 8(9).Step 2: Systematically examine pairs and compute two quantities: (a) position difference minus 1 in the given number and (b) value difference minus 1 when the digits are ordered ascending.Step 3: For the pair 4 at position 1 and 9 at position 6, digits between in the number are 6 - 1 - 1 = 4. In ascending order from 4 to 9, we have 5, 6, 7, 8, which is also 4 digits. This pair qualifies.Step 4: For the pair 2 at position 2 and 1 at position 3, there are 3 - 2 - 1 = 0 digits between them in the number. In ascending order, the pair is 1, 2, with no digits between them, so this pair also qualifies.Step 5: For the pair 1 at position 3 and 6 at position 8, there are 8 - 3 - 1 = 4 digits between them in the number. In ascending order from 1 to 6, we have 2, 3, 4, 5, again 4 digits, so this pair qualifies as well.Step 6: Checking all other pairs shows that only these three pairs satisfy the condition. Verification / Alternative check:Once the three valid pairs are identified, recheck the counts: (4, 9) have four digits between them in the number and four digits between them in ascending order. (1, 2) have zero digits in both cases, and (1, 6) have four digits in both cases. This confirms that exactly three pairs meet the requirement. Why Other Options Are Wrong:Option None is wrong because we have clearly found multiple pairs that satisfy the condition. Options One and Two underestimate the count by ignoring some valid pairs. Only option Three matches the detailed pair-wise verification across the entire number. Common Pitfalls:Candidates may miscount the number of digits between positions or forget to reorder the digits in ascending order before checking the value difference. Another frequent error is to stop searching after finding one or two pairs, assuming no others exist. A systematic check of all pairs is essential in this type of question. Final Answer:The number of such qualifying pairs of digits in 421579368 is three.

Question 17

How many digit 4s are there in the following sequence which are immediately preceded by 7 but not immediately followed by 3? Sequence: 5 9 3 2 1 7 4 2 6 9 7 4 6 1 3 2 8 7 4 1 3 8 3 2 5 6 7 4 3 9 5 8 2 0 1 8 7 4 6 3.

Accepted Answer

Introduction / Context:This time-sequence reasoning question involves carefully scanning a sequence of digits to count how many times a digit 4 appears with very specific neighbours. You must track both the digit before and the digit after each 4. Such questions test attention to detail and the ability to apply a precise condition while scanning a long sequence. Given Data / Assumptions:- The sequence is 5 9 3 2 1 7 4 2 6 9 7 4 6 1 3 2 8 7 4 1 3 8 3 2 5 6 7 4 3 9 5 8 2 0 1 8 7 4 6 3.- We must consider only those 4s that are immediately preceded by 7.- Additionally, such a 4 must not be immediately followed by 3. Concept / Approach:The method is to scan the sequence from left to right, identify each position where the digit is 4, and then check two conditions. First, look one position to the left to see if the digit is 7. Second, look one position to the right to ensure the digit is not 3. Only if both conditions hold do we count that 4. Indexing or numbering positions can help avoid counting errors. Step-by-Step Solution:Step 1: Write the sequence with indices: 5(1), 9(2), 3(3), 2(4), 1(5), 7(6), 4(7), 2(8), 6(9), 9(10), 7(11), 4(12), 6(13), 1(14), 3(15), 2(16), 8(17), 7(18), 4(19), 1(20), 3(21), 8(22), 3(23), 2(24), 5(25), 6(26), 7(27), 4(28), 3(29), 9(30), 5(31), 8(32), 2(33), 0(34), 1(35), 8(36), 7(37), 4(38), 6(39), 3(40).Step 2: Identify positions with digit 4: positions 7, 12, 19, 28 and 38.Step 3: For position 7, the preceding digit at position 6 is 7, and the following digit at position 8 is 2 (not 3). So this 4 qualifies.Step 4: For position 12, the preceding digit at position 11 is 7, and the following digit at position 13 is 6. This 4 also qualifies.Step 5: For position 19, the preceding digit at position 18 is 7, and the following digit at position 20 is 1. This 4 qualifies as well.Step 6: For position 28, the preceding digit at position 27 is 7, but the following digit at position 29 is 3. This violates the condition, so this 4 does not qualify.Step 7: For position 38, the preceding digit at position 37 is 7, and the following digit at position 39 is 6, so this 4 qualifies.Step 8: Therefore, there are four qualifying 4s. Verification / Alternative check:List only the qualifying instances: 7 4 2, 7 4 6, 7 4 1 and 7 4 6 at the end. All of them have 7 immediately before 4, and none has 3 immediately after 4. This directly confirms that the count is four. Why Other Options Are Wrong:Option Three undercounts by missing one valid instance, while option Five and option Six overcount by including 4s that are followed by 3. Option Six is particularly unreasonable because there are not that many 4s that satisfy both conditions. Only the value four accurately reflects the careful position-by-position check. Common Pitfalls:It is easy to include a 4 that is correctly preceded by 7 but incorrectly followed by 3, or to skip a valid 4 because of a hurried scan. Another common mistake is to ignore the word immediately and count cases where 7 and 4 are separated by another digit. Paying attention to both neighbours of each 4 is crucial. Final Answer:The number of digit 4s that satisfy the given condition is four.

Question 18

In a row of boys, A is 10th from the left and B is 9th from the right. After they interchange their positions, A becomes 15th from the left. How many boys are there in the row in total?

Accepted Answer

Introduction / Context:This time-sequence and ranking question deals with positions in a row from both ends. The twist is that two boys interchange their positions, which changes their ranks. You must relate positions from the left and right to deduce the total number of boys. Such questions are standard in reasoning sections and test comfort with positional arithmetic. Given Data / Assumptions:- In the original arrangement, A is 10th from the left.- In the original arrangement, B is 9th from the right.- After they interchange positions, A becomes 15th from the left.- We must find the total number of boys in the row. Concept / Approach:For any person in a row, if we know their position from one side and the total number of persons, we can find their position from the other side using: position from right = total - position from left + 1. Here, we use that relationship in reverse. After interchanging, A goes to B's original place. That information allows us to equate A's new left position with B's original left position and then solve for the total number of boys. Step-by-Step Solution:Step 1: Let the total number of boys be N.Step 2: A is originally 10th from the left, so his position from the right is N - 10 + 1 = N - 9.Step 3: B is originally 9th from the right, so his position from the left is N - 9 + 1 = N - 8.Step 4: After interchange, A moves to B's original position, which is N - 8 from the left.Step 5: According to the question, after the interchange A becomes 15th from the left. Hence N - 8 = 15.Step 6: Solve for N: N = 15 + 8 = 23.Step 7: Therefore, there are 23 boys in the row. Verification / Alternative check:With N = 23, B's original left position is N - 8 = 15. So after the interchange, A is indeed 15th from the left, matching the given information. Similarly, B moves to the position that was 10th from the left, which will become 14th from the right (23 - 10 + 1), consistent with the swap. This confirms that N = 23 is correct. Why Other Options Are Wrong:If N were 27, 28 or 31, the calculated left positions after interchange would not match 15th from the left for A. Each of these values produces a contradiction when we apply the left and right rank formulas. Hence, they cannot be the correct total number of boys. Common Pitfalls:Students sometimes mix up the formulas or forget to add 1 when converting between left and right positions. Another mistake is assuming that the sum of the ranks from left and right remains constant for different students, which is not generally true unless you know the total. Always set up the equations carefully and solve for the total explicitly. Final Answer:The total number of boys in the row is 23.

Question 19

Nitin ranks 18th in a class of 49 students when counted from the top. What is his rank from the last in the same class?

Accepted Answer

Introduction / Context:This is a simple ranking question where you must convert a position from the top into a position from the bottom. Questions like this appear frequently in competitive exams to ensure that you are comfortable with basic positional arithmetic in ordered lists such as classes or queues. Given Data / Assumptions:- There are 49 students in the class.- Nitin is 18th from the top.- We assume all positions are counted without gaps and that there are no ties. Concept / Approach:If we know a student's rank from the top and the total number of students, we can calculate the rank from the bottom using a simple formula: rank from bottom = total students - rank from top + 1. This formula works because the sum of the position from the top and the position from the bottom is always total + 1 for the same person. Step-by-Step Solution:Step 1: Total number of students N = 49.Step 2: Nitin's rank from the top is 18.Step 3: Use the formula: rank from bottom = N - rank from top + 1.Step 4: Substitute the values: rank from bottom = 49 - 18 + 1.Step 5: Compute 49 - 18 = 31.Step 6: Add 1 to get 31 + 1 = 32.Step 7: Therefore, Nitin is 32nd from the last. Verification / Alternative check:We can check the consistency of the formula: for any given person, rank from top + rank from bottom should equal total + 1. Here, 18 (from top) + 32 (from bottom) = 50, which equals 49 + 1. This confirms that the calculation is correct and no mistake has been made in applying the formula. Why Other Options Are Wrong:If we chose 31, the sum of ranks from top and bottom would be 18 + 31 = 49, which is not equal to total + 1. Option 18 wrongly suggests the same rank from top and bottom, which would only happen if Nitin were exactly in the middle of an odd number of students. Option 19 is also inconsistent with the required sum. Only 32 satisfies thecorrect positional relationship. Common Pitfalls:Some candidates wrongly subtract the rank directly from the total without adding 1, leading to an answer of 31. Others get confused between the ideas of top and bottom and may even try to average positions. Remembering the simple formula and its justification prevents such errors. Final Answer:Nitin's rank from the last is 32.

Question 20

Sam ranked 9th from the top and 38th from the bottom in a class. How many students are there in the class in total?

Accepted Answer

Introduction / Context:This ranking question requires you to use both the rank from the top and the rank from the bottom of a class to determine the total number of students. This type of problem appears regularly in reasoning tests, and the relationship between these ranks is a standard concept you should know. Given Data / Assumptions:- Sam is 9th from the top.- Sam is 38th from the bottom.- We assume there are no ties and that the ranks are counted correctly from each end. Concept / Approach:For a person in a line, the sum of their rank from the top and their rank from the bottom is always equal to the total number of persons plus 1. This is because if you move from the top to the person and then continue to the bottom, you count every person exactly once, plus the counted position of that person. Step-by-Step Solution:Step 1: Let the total number of students be N.Step 2: Use the relation: rank from top + rank from bottom = N + 1.Step 3: Substitute Sam's ranks: 9 + 38 = N + 1.Step 4: Compute 9 + 38 = 47.Step 5: So 47 = N + 1, which gives N = 47 - 1 = 46.Step 6: Therefore, there are 46 students in the class. Verification / Alternative check:We can verify by checking: N + 1 should equal 46 + 1 = 47. Sam's ranks are 9 from the top and 38 from the bottom, and 9 + 38 does indeed equal 47, confirming that our calculation is consistent with the standard rule. Why Other Options Are Wrong:If N were 45, then N + 1 would be 46, which does not match the sum of 9 and 38. Similarly, 47 and 48 would give N + 1 values that fail to equal 47. Only N = 46 correctly satisfies the fundamental relationship between top and bottom ranks for the same student. Common Pitfalls:Sometimes students mistakenly add the ranks and forget to subtract 1, which would give 47 instead of 46. Others may try to average the ranks, which has no relevance here. Remember the key formula rank from top + rank from bottom = total + 1 and apply it directly. Final Answer:The total number of students in the class is 46.

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