Section A
Sec A MCQs — 15 Questions
(+4)
1
counting
easy
Count the number of blocks in the following picture.
A
15
B
18
C
20
D
21
E
24
Show answer
Answer: D
Each of the three identical block pictures is a stepped stack: 4 blocks in the lower layer, 2 blocks in the second layer, and 1 block in the top layer, giving 4 + 2 + 1 = 7 blocks per picture (some blocks are hidden behind others in the isometric drawing but are still part of the stack). Since there are 3 identical pictures shown, the total number of blocks is 7 × 3 = 21.
2
counting
medium
Count the number of triangles in the picture.
A
5
B
6
C
4
D
3
E
9
Show answer
Answer: A
The figure is a wide tent-shaped triangle with a rectangular box straddling its right side; a diagonal line inside the box crosses the tent's own slanted edge. There are 2 large triangles (the full outer tent triangle, and the large triangle formed by the box's diagonal together with the tent's base and right slope) and 3 smaller triangles created where the box's vertical edges and internal diagonal cut across the tent's slanted edge. In total, 2 big + 3 small = 5 triangles.
3
logic
medium
Suzy has five kids. Amy is older than Beth but younger than Carla. David is older than Erwin but younger than Beth. Who is the eldest child?
A
Amy
B
Beth
C
Carla
D
David
E
Erwin
Show answer
Answer: C
From 'Amy is older than Beth but younger than Carla': Carla > Amy > Beth. From 'David is older than Erwin but younger than Beth': Beth > David > Erwin. Chaining these together: Carla > Amy > Beth > David > Erwin. The eldest child is Carla.
4
time
medium
Sarah's birthday falls on the 6th of September each year. Today is 27th July and a Sunday. What day will be Sarah's birthday this year?
A
Thursday
B
Saturday
C
Sunday
D
Monday
E
Friday
Show answer
Answer: B
Count the days from 27th July to 6th September: 4 remaining days in July (28th-31st), all 31 days of August, and 6 days into September (1st-6th), giving 4 + 31 + 6 = 41 days later. Since every 7 days returns to the same day of the week, 41 ÷ 7 = 5 remainder 6, so the birthday falls 6 days after a Sunday. Counting forward 6 days from Sunday (Mon, Tue, Wed, Thu, Fri, Sat) lands on Saturday.
5
arithmetic
easy
On the number table of 1-100, we finally reached 50 after we added 72 and subtracted 36 from the original number. What is the original number?
A
86
B
14
C
48
D
50
E
84
Show answer
Answer: B
Let the original number be x. Then x + 72 − 36 = 50, so x + 36 = 50, giving x = 50 − 36 = 14. (Working backwards from 50: undo the subtraction of 36 by adding it back, then undo the addition of 72 by subtracting it: 50 + 36 − 72 = 14.)
6
number-theory
medium
How many whole numbers are there which are less than 300 and their digits add up to 5?
A
18
B
10
C
12
D
15
E
14
Show answer
Answer: D
One-digit numbers with digit sum 5: just 5 itself (1 number). Two-digit numbers with digit sum 5: 14, 23, 32, 41, 50 (5 numbers). Three-digit numbers below 300 with digit sum 5: with hundreds digit 1, the remaining two digits must sum to 4, giving 104, 113, 122, 131, 140 (5 numbers); with hundreds digit 2, the remaining two digits must sum to 3, giving 203, 212, 221, 230 (4 numbers) — 9 three-digit numbers in total. Altogether: 1 + 5 + 9 = 15.
7
arithmetic
easy
Roy walks 10 m to his school and then continues the remaining three-fourths of the whole journey by bus. How far is Roy's school from his house?
A
134 m
B
100 m
C
30 m
D
40 m
E
400 m
Show answer
Answer: D
Walking 10 m covers the remaining one-fourth of the journey that is not covered by bus (since three-fourths is by bus, one-fourth is on foot). So 1 unit (one-fourth of the trip) = 10 m, and the whole journey is 4 units = 4 × 10 = 40 m.
8
geometry
easy
ABCD is a square with an area of 72 m². It is further divided into 9 smaller squares with equal areas. Find the area of 5 such smaller squares, in m².
The source PDF prints only 4 options for this question (no fifth option); labels here are A-D, following the exact on-page top-to-bottom order. This is a benign page-layout quirk — the correct value (40) is still among the 4 printed choices, so it does not affect scoring.
A
36
B
40
C
50
D
52
Show answer
Answer: B
Since the square's total area of 72 m² is divided evenly into 9 smaller squares, each smaller square has area 72 ÷ 9 = 8 m². The area of 5 such smaller squares is 5 × 8 = 40 m².
9
measurement
easy
A 1-litre bottle was filled up using a 150-ml and a 50-ml jug. Both jugs were poured thrice into the empty 1-litre bottle. How much more liquid can be poured into the bottle to fill it to the brim?
A
600 ml
B
650 ml
C
450 ml
D
400 ml
E
500 ml
Show answer
Answer: D
Pouring the 150-ml jug three times adds 150 × 3 = 450 ml. Pouring the 50-ml jug three times adds 50 × 3 = 150 ml. Together, 450 + 150 = 600 ml has been poured into the 1000-ml (1-litre) bottle. The amount still needed to fill it to the brim is 1000 − 600 = 400 ml.
10
number-theory
medium
If all alphabets are represented by a number starting with A = 1, B = 2, C = 3, and so on, find the sum of the digits represented by the word SMART.
(Note: DOG is written as 4157)
A
20
B
24
C
26
D
28
E
30
Show answer
Answer: C
Using A=1, B=2, …, Z=26 (matching the given check: D=4, O=15, G=7, concatenated as '4'+'15'+'7' = '4157', exactly as stated): S=19, M=13, A=1, R=18, T=20. Concatenating these values in order gives the number 191311820 (19, 13, 1, 18, 20 written one after another). Summing its digits: 1+9+1+3+1+1+8+2+0 = 26.
11
time
hard
How many times do the hour and minute hands cross an even number on the clock from 1 a.m. to 1 p.m.?
A
70
B
72
C
78
D
76
E
80
Show answer
Answer: C
From 1 a.m. to 1 p.m. is exactly 12 hours. The hour hand makes exactly one full revolution around the clock face in these 12 hours, so it passes each of the 6 even numbers (2, 4, 6, 8, 10, 12) exactly once, crossing an even number 6 times in total. The minute hand makes one full revolution every hour, passing all 12 numbers, of which 6 are even, so it crosses an even number 6 times per hour; over 12 hours that is 6 × 12 = 72 times. Combining both hands: 6 + 72 = 78.
12
arithmetic
easy
Find the sum: 4 + 16 + 24 + 36 + 44 + 56
The source PDF prints only 4 options for this question on its page (160, 170, 190, 200 — kept here as options A, B, D, E in their original printed order), omitting the correct value entirely. The correct sum is 180, confirmed independently and by the source's own Solutions section, which explicitly computes (4+16)+(24+36)+(44+56) = 20+60+100 = 180 — matching the source's own compact Answers-table value of 180 for this question. The four printed choices read as the natural run 160/170/(180 missing)/190/200, so the middle, correct entry appears to have been dropped by a print/layout error (the same class of defect responsible for Q8's missing 5th option, but here it happens to remove the correct choice itself). Since a multiple-choice question must offer its own correct answer as a selectable option, the missing value has been reconstructed and inserted here as option C = 180, disclosed transparently.
A
160
B
170
C
180
D
190
E
200
Show answer
Answer: C
Grouping the terms in pairs: (4+16) + (24+36) + (44+56) = 20 + 60 + 100 = 180.
13
arithmetic
easy
A fan has three blades. How many blades will there be in 150 such fans?
A
450
B
150
C
500
D
50
E
45
Show answer
Answer: A
Each fan has 3 blades, so 150 fans have 150 × 3 = 450 blades.
14
arithmetic
easy
The sum obtained after we add double of 25 to one-third of 21 is subtracted from 100. What is the final number in the end?
A
60
B
29
C
43
D
57
E
71
Show answer
Answer: C
Double of 25 is 50, and one-third of 21 is 7. Their sum is 50 + 7 = 57. Subtracting this sum from 100 gives 100 − 57 = 43.
15
number-theory
easy
What number has 2 hundreds, 5 more tens than 20 and 1 less than 7?
A
251
B
272
C
276
D
271
E
254
Show answer
Answer: C
2 hundreds = 200. '5 more tens than 20' means 5 tens (50) added to 20, giving 50 + 20 = 70. '1 less than 7' is 7 − 1 = 6. Adding all three parts together: 200 + 70 + 6 = 276.
Section B
Sec B SAQs — 10 Questions
(+5)
16
algebra
medium
Harry scored 3 more marks than Alwin. Sophia scored the same as Harry. The sum of their scores was 51. How many marks did Alwin score?
Show answer
Answer: 0015
Let Alwin's score be x. Then Harry's score is x + 3, and Sophia's score equals Harry's, x + 3. The sum is x + (x+3) + (x+3) = 3x + 6 = 51, so 3x = 45 and x = 15.
17
combinatorics
medium
Alice picked two cards from a 52-card deck such that the sum of the numbers on the two cards was 15. Find how many combinations she may have. (In the deck of cards, A = 1, J = 11, Q = 12, K = 13 while the remaining cards are numbers 2 to 10)
Show answer
Answer: 0006
The card values run from 1 to 13. We need two distinct values from 1-13 that add up to 15: (2,13), (3,12), (4,11), (5,10), (6,9), (7,8). That gives 6 possible value-combinations.
18
logic
medium
Five students entered a contest where they had to guess the number of candies in a box. Alan guessed 25 candies while Beth guessed 30. Charles guessed 27 and David guessed 35. Roma was declared the winner. One of the 4 students guessed 4 more than Roma's number while another student guessed 4 less than hers. What was the number guessed by Roma?
Show answer
Answer: 0031
Checking each of the 4 given guesses against +4/−4 of the others: Charles (27) + 4 = 31, and David (35) − 4 = 31 — both point to the same value, 31, which is not one of the 4 given guesses (consistent with Roma being the 5th, winning student). So Roma guessed 31.
19
arithmetic
medium
Ayer and Kumar tossed a coin. Ayer wins if it is a head while Kumar wins if it is a tail. The winner gets 3 marbles from the loser. Both had 20 marbles each in the beginning. They played 10 rounds and Ayer won 4 rounds. What is the total number of marbles Kumar had in the end?
Show answer
Answer: 0026
Kumar starts with 20 marbles. Ayer won 4 rounds, so Kumar lost 3 marbles to Ayer 4 times: 20 − 4×3 = 20 − 12 = 8. Kumar won the remaining 10 − 4 = 6 rounds, gaining 3 marbles each time from Ayer: 8 + 6×3 = 8 + 18 = 26.
20
combinatorics
hard
The place cards shown are folded along the dotted line so that only a number or letter is visible. Chrissy enters the room and sees all five place cards, with at least 2 number cards being shown. The sum of numbers that she sees is less than 8. How many different sets of numbers are there?
Show answer
Answer: 0010
Each of the 5 place cards shows either a letter (A-E) or its matching number (1-5, in the same left-to-right position), so any subset of the 5 positions can independently show a number instead of a letter. We need sets of at least 2 numbers, drawn from {1,2,3,4,5}, whose sum is less than 8. Sets of exactly 2 numbers summing under 8: {1,2}, {1,3}, {1,4}, {1,5}, {2,3}, {2,4}, {2,5}, {3,4} — 8 sets. Sets of exactly 3 numbers summing under 8: {1,2,3}(=6), {1,2,4}(=7) — 2 sets. No set of 4 or more numbers from {1,2,3,4,5} can sum below 8 (the smallest such sum, 1+2+3+4=10, already exceeds 7). In total: 8 + 2 = 10 different sets.
21
number-theory
medium
If the digits of a two-digit number are reversed to form a new number, the difference between the two numbers will be 45. How many different such pairs are there?
Show answer
Answer: 0005
Let the original number have tens digit A and ones digit B, so the number is 10A+B and its reversal is 10B+A. Their difference is (10A+B) − (10B+A) = 9(A−B) = 45, so A − B = 5. With A a digit from 1-9 and B = A−5 ≥ 0, the valid pairs are A=5,B=0; A=6,B=1; A=7,B=2; A=8,B=3; A=9,B=4 — giving the number pairs (50,05), (61,16), (72,27), (83,38), (94,49). That is 5 different pairs.
22
number-theory
medium
Harry wrote 1, 2, 3, 11, 22, 33, 111, 222, 333, … until he got 17 numbers. What is the sum of the digits of the last number he wrote?
Show answer
Answer: 0012
The numbers come in groups of 3: the k-th group consists of the three k-digit repunit-style numbers made of digits 1, 2, and 3 (e.g. group 1 = 1,2,3; group 2 = 11,22,33; group 3 = 111,222,333; and so on). Since 17 ÷ 3 = 5 remainder 2, the 17th number is the 2nd number of the 6th group. The 6th group consists of 6-digit numbers 111111, 222222, 333333, so the 2nd number in that group is 222222. The sum of its digits is 2 × 6 = 12.
23
logic
medium
A jar of 30 chocolates is shared among Ann, Alice, and Alisha. Alice takes more than anyone else. What is the least number of chocolates she could have taken?
Show answer
Answer: 0011
If Alice took 10, the other two could each take at most 9 (since they must take strictly fewer than Alice), giving a maximum possible total of 10+9+9 = 28, which is less than 30 — impossible. If Alice takes 11, the other two need to make up the remaining 30−11 = 19 chocolates while each staying below 11 (e.g. 10 and 9), which is achievable (11+10+9 = 30). So the least number of chocolates Alice could have taken is 11.
24
arithmetic
easy
Few kids were playing cricket. Each of them carried 4 balls. While playing, 17 balls were hit outside the ground and lost. In the end, they were left with a total of 55 balls. How many kids were playing together?
Show answer
Answer: 0018
The total number of balls at the start was 55 + 17 = 72 (the 55 remaining plus the 17 lost). Since each kid carried 4 balls, the number of kids is 72 ÷ 4 = 18.
25
arithmetic
medium
Patrick started jumping every day. He jumped 10 times on Day 1. He jumped 8 more times on Day 2 than on Day 1. He jumped 8 more times on Day 3 than on Day 2. Every day, he continued to jump 8 more times than the previous day. Which day will be the first day when he would have jumped at least 100 times in one day?
Show answer
Answer: 0013
The number of jumps on Day n is 10 + 8(n−1). We need 10 + 8(n−1) ≥ 100, i.e. 8(n−1) ≥ 90, i.e. n−1 ≥ 11.25, i.e. n ≥ 12.25, so the smallest whole day number is n = 13. Checking: Day 12 gives 10+8×11 = 98 (< 100), and Day 13 gives 10+8×12 = 106 (≥ 100), confirming Day 13 is the first such day.