1
place-value
easy
Which of the following numbers has the digit 8 in the tens place?
1
3852
2
3582
3
8532
4
5328
Show answer
Answer: 2
In 3582, the digits are 3 (thousands), 5 (hundreds), 8 (tens) and 2 (ones), so the tens digit is 8. In 3852 the tens digit is 5, in 8532 it is 3, and in 5328 it is 2.
2
place-value
easy
[?] is 200 less than 4283. What is the missing number?
1
4483
2
4083
3
4093
4
2283
Show answer
Answer: 2
4283 − 200 = 4083.
3
divisibility
easy
Which one of the following numbers has no remainder when divided by 9?
1
315
2
548
3
724
4
860
Show answer
Answer: 1
315 ÷ 9 = 35 exactly, so it has no remainder. 548 ÷ 9 = 60 remainder 8, 724 ÷ 9 = 80 remainder 4, and 860 ÷ 9 = 95 remainder 5.
4
money
medium
Count the amount of money shown below. How much more is needed to make 20 dollars?
1
1 dollar 10 cents
2
1 dollar 20 cents
3
1 dollar 30 cents
4
1 dollar 40 cents
Show answer
Answer: 3
The notes total 10+5+2=18 dollars. The coins total 1+0.50+0.20=1.70 dollars. Altogether: 18+1.70=18.70 dollars. To make 20 dollars, 20−18.70=1.30 dollars more is needed.
5
geometry
medium
The figure below is made up of straight lines. Name a pair of parallel lines in the figure.
1
XY and TU
2
PQ and TU
3
PQ and RS
4
TU and RS
Show answer
Answer: 3
PQ and RS are both horizontal and never meet, so they are parallel. XY is a vertical line and TU is a slanting line, so neither of them is parallel to any of the other lines.
6
time
medium
Meera left her house at 14 35 to visit her grandmother. She took 55 minutes to get there. She was 12 minutes early for lunch. What time was lunch?
1
2.47 p.m.
2
3.18 p.m.
3
3.42 p.m.
4
3.54 p.m.
Show answer
Answer: 3
14:35 + 55 min = 15:30 (3.30 p.m.), when Meera arrived. Since she was 12 minutes early, lunch was at 15:30 + 12 min = 15:42, i.e. 3.42 p.m.
7
area
hard
Each square represents 1 square unit. Each triangle represents 1/2 square unit. Which one of the following figures has the greatest area?
1
Figure A
2
Figure B
3
Figure C
4
Figure D
Show answer
Answer: 4
Figure A has 5 full squares and 2 triangles = 5+2×0.5=6 sq units. Figure B has 4 full squares and 4 triangles = 4+4×0.5=6 sq units. Figure C has 6 full squares and no triangles = 6 sq units. Figure D has 5 full squares and 3 triangles = 5+3×0.5=6.5 sq units. Even though A, B and C all look different, they all work out to exactly the same area of 6 sq units — only Figure D, with its extra half-unit triangle, has the greatest area.
8
fractions
medium
A jar had a number of marbles. 3/8 of them were blue, 1/4 of them were yellow, and the rest were green. What fraction of the marbles were green?
1
3/8
2
5/8
3
1/8
4
7/8
Show answer
Answer: 1
3/8 + 1/4 = 3/8 + 2/8 = 5/8 of the marbles were blue or yellow, so the fraction that were green is 1 − 5/8 = 3/8.
9
capacity
medium
There was 3200 ml of juice in a jug. Ravi poured the juice equally into 8 identical cups and had 400 ml of juice left in the jug. What was the volume of juice in each cup?
1
350 ml
2
400 ml
3
300 ml
4
450 ml
Show answer
Answer: 1
Juice poured out = 3200 − 400 = 2800 ml. Each cup received 2800 ÷ 8 = 350 ml.
10
time
medium
The clock shown below is 20 minutes fast. What is the actual time?
1
4.05 p.m.
2
4.25 p.m.
3
5.05 p.m.
4
5.25 p.m.
Show answer
Answer: 2
The clock shows 4.45 p.m. Since the clock is 20 minutes fast, the actual time is 20 minutes earlier: 4.45 p.m. − 20 min = 4.25 p.m.
11
fractions
medium
Which of the figures below shows 5/8 of the figure shaded?
1
Figure A
2
Figure B
3
Figure C
4
Figure D
Show answer
Answer: 2
Figure B is a rectangle split into 8 equal squares with 5 shaded, showing exactly 5/8. Figure A is split into 5 unequal parts with 3 shaded — not eighths at all. Figure C is split into 8 equal sectors but only 4 are shaded, showing 4/8, not 5/8. Figure D is split into 8 unequal strips with 5 shaded, but since the strips are not the same size, the shaded part is not exactly 5/8 of the figure.
12
perimeter
medium
The figure below is made up of 2 identical rectangles and 1 square. Each rectangle measures 10 cm by 20 cm, and the square has the same side length as the shorter side of the rectangles. Find the perimeter of the figure.
1
80 cm
2
100 cm
3
120 cm
4
140 cm
Show answer
Answer: 3
The square has side 10 cm. Tracing the outline: 10 cm (top of tall rectangle) + 20 cm (down its side) + 20 cm (top of the lying rectangle) + 10 cm (down to the base) + 30 cm (along the bottom) + 30 cm (up the left side) = 120 cm. (The overall shape fits inside a 30 cm × 30 cm square with one 20 cm × 20 cm corner missing, and for such an L-shape the perimeter always equals 2×(30+30)=120 cm regardless of the missing corner's size.)
13
division
medium
A group of 85 tourists wants to cross a river using boats. Each boat can carry at most 7 tourists. What is the least number of boats needed to carry all the tourists at the same time?
1
11
2
12
3
13
4
14
Show answer
Answer: 3
85 ÷ 7 = 12 remainder 1. 12 boats carry 84 tourists, leaving 1 tourist who still needs a 13th boat. So 13 boats are needed in total.
14
area
medium
Devika drew a figure on a square grid. Each small square represents 1 unit by 1 unit. Find the area of the figure.
1
32 square units
2
34 square units
3
36 square units
4
38 square units
Show answer
Answer: 2
The bounding rectangle is 8 units by 5 units = 40 square units. A 2×2 notch (4 square units) is cut from the top-left corner and a 2×1 notch (2 square units) is cut from the bottom-right corner, so the area of the figure is 40 − 4 − 2 = 34 square units.
15
patterns
medium
A table can seat 4 people. 20 such tables are placed side by side in a row as shown. How many people can be seated at the tables?
1
40
2
42
3
44
4
80
Show answer
Answer: 2
Each square table normally seats 1 person per side. When tables are placed side by side, the 2 end tables keep 3 free sides each, while each of the other 18 tables in between keeps only 2 free sides (one side is shared with each neighbour). Total seats = 2×3 + 18×2 = 6 + 36 = 42.
16
algebra
medium
The mass of oranges in box A was 96 kg. The mass of oranges in box B was 18 kg less than the mass of oranges in box C. The total mass of oranges in boxes A, B and C was 258 kg. Find the mass of oranges in box C. Give your answer in kg. [Enter your answer only between 0 and 9999]
Show answer
Answer: 90
Let the mass in box C be C kg, so box B = (C−18) kg. 96 + (C−18) + C = 258 → 2C + 78 = 258 → 2C = 180 → C = 90.
17
algebra
medium
Farah and Grace baked 350 cookies. Grace and Hana baked 230 cookies. Farah baked 4 times as many cookies as Hana. How many cookies did Grace bake? [Enter your answer only between 0 and 9999]
Show answer
Answer: 190
(Farah+Grace) − (Grace+Hana) = Farah − Hana = 350 − 230 = 120. Since Farah = 4×Hana, 4×Hana − Hana = 120 → 3×Hana = 120 → Hana = 40, so Farah = 160. Grace = 230 − Hana = 230 − 40 = 190.
18
data-handling
medium
The graph shows the number of hours Tara spent revising for her examination in the month of March. Tara spent a total of 85 hours revising. How many hours did she spend revising Art? Give your answer in hours. [Enter your answer only between 0 and 9999]
Show answer
Answer: 18
English (19) + Mathematics (27) + Science (21) = 67 hours. Art = 85 − 67 = 18 hours.
19
area
medium
In the figure below, rectangle PQRS is made up of 2 identical squares and 3 smaller identical rectangles. One of the rectangles is shaded. The side of each square is 12 cm. PE = EF. Find the difference between the area of rectangle PQRS and the area of the shaded rectangle. Give your answer in cm². [Enter your answer only between 0 and 9999]
Show answer
Answer: 384
Since PE = EF = 12 cm (the square's side), rectangle PQRS has width 12+12+12=36 cm and height 12 cm, so its area is 36×12=432 cm². The middle 12 cm × 12 cm column is split into 3 equal rectangles, each 12 cm × 4 cm = 48 cm², and the shaded one has area 48 cm². The difference is 432 − 48 = 384 cm².
20
algebra
medium
Nadia saved a total of 156 dollars in 4-dollar coins and 10-dollar notes. She had 24 pieces of these coins and notes in total. How many 10-dollar notes did she have? [Enter your answer only between 0 and 9999]
Show answer
Answer: 10
Let the number of 10-dollar notes be n, so the number of 4-dollar coins is (24−n). 10n + 4(24−n) = 156 → 10n + 96 − 4n = 156 → 6n = 60 → n = 10.
21
area
medium
A rectangular playground measures 28 m by 20 m, as shown below. The shaded part is the area covered by a sandpit. What is the area of the playground not covered by the sandpit? Give your answer in m². [Enter your answer only between 0 and 9999]
Show answer
Answer: 440
The sandpit's height is 20 − 7 − 5 = 8 m and its width is 28 − 9 − 4 = 15 m, so its area is 15×8=120 m². The playground's area is 28×20=560 m². The area not covered by the sandpit is 560 − 120 = 440 m².
22
algebra
medium
A vendor had a total of 420 red, blue and green balloons. She had 40 more red balloons than blue balloons. After selling 70 green balloons, the number of green balloons left became the same as the number of red balloons. How many red balloons did she have? [Enter your answer only between 0 and 9999]
Show answer
Answer: 130
Let blue = b, so red = b+40. Total: b + (b+40) + green = 420 → green = 380 − 2b. After selling 70 green balloons, green−70 = red → (380−2b)−70 = b+40 → 310−2b = b+40 → 270 = 3b → b=90. So red = 90+40 = 130.
23
algebra
medium
When a bus left Stop A, there were some passengers on the bus. At Stop B, 80 passengers got off while 540 passengers got on. At Stop C, 560 passengers got on and nobody got off. As a result, there were 4 times as many passengers on the bus when it left Stop C as the number of passengers when it left Stop A. How many passengers were on the bus when it left Stop A? [Enter your answer only between 0 and 9999]
Show answer
Answer: 340
Let the number of passengers leaving Stop A be a. After Stop B and Stop C: a − 80 + 540 + 560 = a + 1020. This equals 4a, so a + 1020 = 4a → 3a = 1020 → a = 340.
24
algebra
medium
Kabir is 39 years old and Tanvi is 5 years old. How old will Kabir be when he is 3 times as old as Tanvi? [Enter your answer only between 0 and 9999]
Show answer
Answer: 51
Let x more years pass. 39+x = 3(5+x) → 39+x = 15+3x → 24 = 2x → x=12. Kabir will be 39+12=51 years old.
25
algebra
medium
Meera and Sunil had the same amount of money. Meera bought 6 identical pens and had 22 dollars left. Sunil wanted to buy 9 such pens but realised he was short of 14 dollars. How much money did each of them have at first? Give your answer in dollars. [Enter your answer only between 0 and 9999]
Show answer
Answer: 94
Let each pen cost p dollars and each of them start with A dollars. 6p = A−22 → A=6p+22. 9p = A+14 → A=9p−14. So 6p+22=9p−14 → 36=3p → p=12. A=6×12+22=94.
26
patterns
hard
The figures below form a pattern. How many more white squares than shaded squares are there in Figure 40? [Enter your answer only between 0 and 9999]
Show answer
Answer: 46
Figure k is 3 rows tall and (k+2) columns wide, with k shaded squares in the centre of the middle row. Total squares = 3(k+2), shaded = k, so white = 3(k+2)−k = 2k+6. White − shaded = (2k+6)−k = k+6. For Figure 40: 40+6=46.
27
algebra
hard
Priya has 4 times as many stickers as Farhan. Meena has 15 stickers more than Farhan. Meena has 90 stickers fewer than Priya. How many stickers does Farhan have? [Enter your answer only between 0 and 9999]
Show answer
Answer: 35
Let Farhan have F stickers. Priya=4F, Meena=F+15. Priya−Meena=90 → 4F−(F+15)=90 → 3F−15=90 → 3F=105 → F=35.
28
money
hard
The following items were on sale at a store. A jacket cost 45 dollars 60 cents and a scarf cost 19 dollars 80 cents. Mrs Lim bought 2 identical jackets and 1 scarf. She gave the cashier four 50-dollar notes. How much change did she receive? Give your answer in dollars. [Enter your answer only between 0 and 9999]
Show answer
Answer: 89
Cost = 2×45.60 + 19.80 = 91.20 + 19.80 = 111.00 dollars. She paid 4×50=200 dollars. Change = 200 − 111 = 89 dollars.
29
patterns
hard
The following shows Pascal's Triangle. The numbers in each row follow a certain pattern. Find the sum of the numbers in Row 12. [Enter your answer only between 0 and 9999]
Show answer
Answer: 2048
Row 1 sums to 1=2⁰, Row 2 sums to 2=2¹, Row 3 sums to 4=2², and so on — each row's sum doubles the one before, so Row n sums to 2^(n−1). Row 12 sums to 2¹¹=2048.
30
algebra
hard
Ishaan had 5 times as much money as his brother. Ishaan then spent 240 dollars on a bicycle while his brother received 160 dollars from their grandparents. In the end, Ishaan and his brother had an equal amount of money. How much money did Ishaan's brother have in the end? Give your answer in dollars. [Enter your answer only between 0 and 9999]
Show answer
Answer: 260
Let the brother start with S dollars, so Ishaan starts with 5S. 5S−240 = S+160 → 4S=400 → S=100. The brother's final amount = 100+160=260 dollars.
31
time
hard
Nisha took 40 minutes to clean her room. Farah took 3 times as much time as Nisha to clean her room. The time taken for Farah to clean her room was 4 times as much as that for Wei. Wei started cleaning her room at 15 10. What time did she finish cleaning her room? Express your answer in the 24-hour clock, written as a 4-digit number such as 0730. [Enter your answer only between 0 and 9999]
Show answer
Answer: 1540
Farah took 3×40=120 minutes. Wei took 120÷4=30 minutes. Wei started at 15:10 and finished at 15:10+30 min=15:40, written as 1540.