Question 1

Work-rate/cutting logic: Calculate how many rolls are cut in the allotted time.  Context: Each roll is cut into 10 equal pieces (thus 9 cuts per roll). Cutting speed = 45 cuts per minute. Time allowed = 24 minutes.  Choose the correct number of roll…

Accepted Answer

Given data Pieces per roll = 10 ⇒ Cuts per roll = pieces − 1 = 9 Cutting rate = 45 cuts/min Time = 24 min Step-by-Step calculation Total cuts = 45 × 24 = 1080 cuts Rolls completed = Total cuts ÷ Cuts per roll = 1080 ÷ 9 = 120 rolls Verification 120 rolls × 9 cuts/roll = 1080 cuts (matches total). Common pitfalls Using 10 cuts per roll (forgetting that n pieces require n−1 cuts). Final Answer 120 rolls

Question 2

Perimeter counting on a square fence: Compute total poles when corners are shared.  Context: Square plot with 27 fence poles on each side. Corner poles are common to two sides and must not be double-counted.  Choose the correct total number of poles…

Accepted Answer

Given data & concept Each side lists 27 poles, which includes both corner poles for that side. Naively summing gives 4 × 27 = 108 counts, but the four corner poles are double-counted. Step-by-Step calculation Total (naive) = 4 × 27 = 108 Adjust for 4 corners counted twice: 108 − 4 = 104 Common pitfalls Forgetting to subtract the 4 overcounts at the corners. Final Answer 104

Question 3

Age word problem: Translate the statement into an equation and solve for Varun's present age.  Statement: “One year from today, he will be twice as old as he was 12 years ago.”  Choose the correct present age of Varun.

Accepted Answer

Let the present age be x years Translate the condition One year from now ⇒ x + 1 Twelve years ago ⇒ x − 12 Equation: x + 1 = 2(x − 12) Solve x + 1 = 2x − 24 25 = x Verification Now: 25 ⇒ In a year: 26; 12 years ago: 13; 26 = 2 × 13 ✔ Final Answer 25 years

Question 4

Class composition problem: Deduce total students and compute number of girls.  Context: 18 boys over 160 cm are three-fourths of all boys. Boys constitute two-thirds of the total students in the class.  Find: Number of girls in the class. Choose the…

Accepted Answer

Given data 18 boys = (3/4) of total boys ⇒ Total boys = 18 ÷ (3/4) = 18 × (4/3) = 24 Boys = (2/3) of total students ⇒ Total students = 24 ÷ (2/3) = 24 × (3/2) = 36 Compute girls Girls = Total students − Boys = 36 − 24 = 12 Common pitfalls Dividing by 3/4 as 24 × 3/4 instead of 24 ÷ 3/4 = 24 × 4/3.

Question 5

Percentages and ratios — festival participation: Find the fraction of all students who took part.  In an institute fete, 1/5 of the girls and 1/8 of the boys participated. Determine the overall fraction of the total student body that participated. C…

Accepted Answer

Given data Fraction of girls who participated = 1/5 of all girls. Fraction of boys who participated = 1/8 of all boys. Concept/ApproachLet the numbers of girls and boys be G and B. Then participants are G/5 + B/8 and the total students are G + B. The overall fraction is (G/5 + B/8) / (G + B), which depends on the (unknown) ratio G:B. Step-by-step reasoningOverall fraction = (G/5 + B/8) ÷ (G + B) = (8G + 5B) / (40(G + B)).This varies with G and B (e.g., if G = B, fraction = 13/80; if G = 2B, it becomes 21/120 = 7/40). ConclusionThe exact fraction cannot be uniquely determined without the girl-to-boy ratio. Final AnswerData inadequate

Question 6

Linear value allocation — cash plus perk: Determine the monetary value of the free holiday.  Mr. Johnson was to earn £300 and a free holiday for seven weeks' work. He worked only 4 weeks and received £30 and the same free holiday. Find the value (in…

Accepted Answer

Given data Total package for 7 weeks = £300 cash + holiday (value = H). Total received for 4 weeks = £30 cash + holiday (same H). Concept/ApproachAssume compensation scales linearly with time: the 4-week package is 4/7 of the 7-week package. Step-by-step calculation(4/7) × (300 + H) = 30 + HMultiply by 7: 4(300 + H) = 7(30 + H)1200 + 4H = 210 + 7H1200 − 210 = 7H − 4H990 = 3H ⇒ H = 330 Verification7-week total = 300 + 330 = 630. 4/7 of 630 = 360, which equals 30 + 330. Final Answer£ 330

Question 7

Card distribution logic puzzle — equations from statements: Find the number of cards with player B.  Players A, B, C, D, E are playing cards; total cards = 133. A to B: “If you give me 3 cards, you will have as many as E has; if I give you 3, you wi…

Accepted Answer

Given data (translate to equations) B − 3 = E ⇒ b = e + 3 B + 3 = D ⇒ d = b + 3 A + B = D + E + 10 ⇒ a + b = d + e + 10 B = C + 2 ⇒ b = c + 2 Total: a + b + c + d + e = 133 Step-by-step calculationFrom b = e + 3 ⇒ e = b − 3.From d = b + 3.a + b = (b + 3) + (b − 3) + 10 = 2b + 10 ⇒ a = b + 10.c = b − 2.Sum: a + b + c + d + e = (b + 10) + b + (b − 2) + (b + 3) + (b − 3) = 5b + 8.5b + 8 = 133 ⇒ 5b = 125 ⇒ b = 25. Final Answer25

Question 8

Proportional payments — dinner bill split: Find Veena's fraction of the total bill.  Amita paid 2/3 as much as Veena paid. Veena paid 1/2 as much as Tanya paid. What fraction of the total bill was paid by Veena? Choose the correct fraction.

Accepted Answer

Let Veena's share be V Amita A = (2/3)V Veena V = (1/2)T ⇒ Tanya T = 2V Compute totalTotal = A + V + T = (2/3)V + V + 2V = (2/3 + 3)V = (11/3)V Fraction paid by VeenaV / [(11/3)V] = 3/11 Final Answer3/11

Question 9

Geometry of planting grid — compute garden length: Use rows, columns, spacing, and side margins.  Trees are planted in 10 rows and 12 columns; spacing between adjacent trees = 2 m. A clear margin of 1 m is left on all four sides from the boundary. F…

Accepted Answer

Concept/ApproachThe span along a direction with n trees at spacing s is (n − 1) × s. With a border margin m on both ends, total outer dimension is (n − 1)s + 2m. Compute length (take 12 columns along length)Length = (12 − 1) × 2 + 2 × 1 = 11 × 2 + 2 = 22 + 2 = 24 m Final Answer24 m

Question 10

Number theory — class composition check: Determine which total is impossible.  In a class, the number of boys is 3 times the number of girls. Which of the following cannot be the total number of students? Choose the single impossible total.

Accepted Answer

Given Boys = 3 × Girls ⇒ Total = Boys + Girls = 4 × Girls. ApproachTotal must be a multiple of 4. Check options48 ✔ multiple of 444 ✔ multiple of 442 ✖ not a multiple of 440 ✔ multiple of 4 Final Answer42

Question 11

Percent breakdown — ownership counts: Identify the statement that is definitely true.  20% of members own only two cars each. Of the remaining members, 40% own three cars each; the rest own only one car each. Which statement is definitely true? Sele…

Accepted Answer

Work with 100 members (percent model) 20% → 20 members own 2 cars each. Remaining = 80 members. 40% of remaining → 0.4 × 80 = 32 members own 3 cars each. Remaining members → 80 − 32 = 48 own 1 car each. Evaluate statements Only 20% own three cars each → false (it is 32%). 48% own only one car each → true. 60% own at least two cars → 20% + 32% = 52% → false. 80% own at least one car → actually 100% own ≥1 → false as written. Final Answer48% of the total members own only one car each.

Question 12

Arithmetic word problem — shared dishes at a party: Compute the number of guests from combined dish counts.  Every 2 guests shared 1 bowl of rice; every 3 guests shared 1 bowl of dal; every 4 guests shared 1 bowl of meat. Altogether, the total numbe…

Accepted Answer

Let the number of guests be N Bowls of rice = N/2 Bowls of dal = N/3 Bowls of meat = N/4 Total dishes = 65 EquationN/2 + N/3 + N/4 = 65N × (1/2 + 1/3 + 1/4) = 651/2 + 1/3 + 1/4 = (6 + 4 + 3)/12 = 13/12N × (13/12) = 65 ⇒ N = 65 × 12 / 13 = 60 Final Answer60

Question 13

Counting digits — page numbering from 1 to 366: Find the total digits used.  A book has 366 pages numbered consecutively starting from page 1. How many numerical digits are printed in all page numbers? Choose the correct total.

Accepted Answer

Break into ranges Pages 1–9: 9 pages × 1 digit = 9 Pages 10–99: 90 pages × 2 digits = 180 Pages 100–366: 267 pages × 3 digits = 801 Total digits9 + 180 + 801 = 990 Final Answer990

Question 14

LCM of time intervals — synchronized bells: Count joint tolls in one hour (excluding the start).  Five bells toll together initially, then at intervals of 6, 5, 7, 10 and 12 seconds respectively. How many additional times do they toll together withi…

Accepted Answer

Concept/ApproachThey toll together every LCM of the intervals. Compute LCMLCM(6, 5, 7, 10, 12) = 2^2 × 3 × 5 × 7 = 420 seconds = 7 minutes. Occurrences in 1 hour3600 / 420 = 8.571… ⇒ 8 full additional meetings within 60 minutes.Times: 7, 14, 21, 28, 35, 42, 49, 56 minutes. Final Answer8 times

Question 15

Average and linear equations (sports scoring): Determine individual scores from linked conditions and the team average.  Batsmen A, B, C, D, and E have an average score of 36 runs (total = 5 × 36 = 180). Given: D scored 5 more than E; E scored 8 few…

Accepted Answer

Given data Average of five batsmen = 36 ⇒ Total runs = 5 × 36 = 180. D = E + 5. E = A − 8 (i.e., A = E + 8). B = D + E. B + C = 107 ⇒ C = 107 − B. Concept/Approach Form a single-variable equation in E by expressing A, B, C, D in terms of E and using the total 180. Step-by-step calculation A = E + 8 D = E + 5 B = D + E = (E + 5) + E = 2E + 5 C = 107 − B = 107 − (2E + 5) = 102 − 2E Sum: A + B + C + D + E = (E + 8) + (2E + 5) + (102 − 2E) + (E + 5) + E = 3E + 120 Set equal to total: 3E + 120 = 180 ⇒ 3E = 60 ⇒ E = 20 Verification E = 20, D = 25, A = 28, B = 45, C = 62; total = 20 + 25 + 28 + 45 + 62 = 180 ✔ Common pitfalls Forgetting that “E scored 8 fewer than A” means A = E + 8 (not E = A + 8).

Question 16

Family composition puzzle (brothers and sisters): Use simultaneous conditions for sons and daughters.  Each daughter has as many brothers as sisters. Each son has twice as many sisters as brothers. Find the number of sons in the family. Choose the c…

Accepted Answer

Let b = number of sons, g = number of daughters. Translate conditions For a daughter: brothers = b, sisters = g − 1 ⇒ b = g − 1. For a son: sisters = g, brothers = b − 1 ⇒ g = 2(b − 1). Solve From b = g − 1 ⇒ b − 1 = g − 2. Plug into g = 2(b − 1): g = 2(g − 2) ⇒ g = 2g − 4 ⇒ g = 4. Then b = g − 1 = 3. Final Answer 3 sons

Question 17

Age puzzle with reversed digits and ratio condition: Determine the woman's present age.  When the woman's age digits are reversed, the result is her husband's age. He is older than she is. The difference between their ages equals one-eleventh of the…

Accepted Answer

Let ages Woman = 10a + b, Husband = 10b + a, with b > a (husband older). Given ratio/difference condition Difference = (1/11) × Sum (10b + a) − (10a + b) = (1/11)[(10b + a) + (10a + b)] 9(b − a) = (1/11)·11(a + b) ⇒ 9(b − a) = a + b ⇒ 8b = 10a ⇒ 4b = 5a. Digit solutions Let a = 4k, b = 5k with digits 0–9 ⇒ k = 1 works: a = 4, b = 5. Woman = 10·4 + 5 = 45, Husband = 54 (older ✔).

Question 18

Sum of ages back in time: Adjust a current total to a past total.  Present total age of Amar, Akbar, and Anthony = 80 years. Find the total of their ages three years ago. Choose the correct value.

Accepted Answer

Concept Going back 3 years reduces each person's age by 3; with three people, the total reduces by 3 × 3 = 9. Calculation Past total = 80 − 9 = 71 years.

Question 19

Pigeonhole principle (socks in the dark): Guarantee a matching pair with two colors available.  Drawer contains 20 black socks and 20 brown socks. Socks are drawn in the dark (no color visibility). Minimum number of socks to guarantee at least one m…

Accepted Answer

Concept With only two colors, the worst-case first two socks are different. The third sock must match one of them. Conclusion 3 socks guarantee a matching pair.

Question 20

Number theory/product trick: Multiply all the numbers on a telephone dial and identify the correct value.  Telephone dial digits considered: 0 through 9. Find the product 0 × 1 × 2 × … × 9. Choose the correct value.

Accepted Answer

Observation The dial includes the digit 0. Calculation 0 × 1 × 2 × … × 9 = 0. Note Since 0 is not listed among the numeric choices, the appropriate option would be "None of these".

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