Class 4 Maths Olympiad Practice Test – 35 Questions, 60 Minutes, No Negative Marking

Correct answer: (b) 11

1. Row 1 has 1 block, row 2 has 3, row 3 has 5, row 4 has 7. The step is always 2.

2. Row 5 has 9 blocks and row 6 has 11 blocks.

3. So the sixth row holds 11 blocks.

Usual mistake: Starting an arithmetic pattern from zero instead of from the first given term.

Correct answer: (d) 1/8

1. Cutting into 4 equal pieces makes each piece 1/4 of the whole ribbon.

2. Cutting one of those pieces in half makes the new piece 1/2 of 1/4.

3. Half of a quarter is 1/8 of the original ribbon.

Usual mistake: Stopping after the first cut, or halving 1/4 by 4 instead of by 2.

Correct answer: (d) odd

1. Adding two odd numbers always gives an even number.

2. The number added next is one of the original odd numbers.

3. An even number plus an odd number is always odd.

Usual mistake: Stopping after the first step, or inventing a divisibility rule from the number of terms.

Correct answer: (b) ₹40

1. Cost of 1 notebook is 180 divided by 12, which is Rs.15.

2. So the cost of the 8 notebooks sold is 8 times 15, which is Rs.120.

3. Profit is what he received minus what those 8 notebooks cost: 160 − 120 = Rs.40.

Usual mistake: Using the cost of the whole lot against the sale of only part of it.

Correct answer: (a) 165 cm

1. 1 metre is 100 centimetres, so 2 m 40 cm is 240 cm.

2. Cutting 75 cm off leaves 240 − 75 centimetres.

3. What remains is 165 cm long.

Usual mistake: Converting units once and then borrowing, which changes the arithmetic without being noticed.

Correct answer: (c) 36

1. Row n holds 1 + 2 + … + n triangles, which is n multiplied by n + 1, halved.

2. For the eighth row that is 8 times 9, halved.

3. 8 times 9 is 72, and 72 halved is 36 triangles.

Usual mistake: Carrying the same step forward instead of letting it increase by 1 each time.

Correct answer: (c) ₹30

1. 1/3 of Rs.60 is Rs.20, so Rs.40 is left after the book.

2. 1/4 of the Rs.40 that is left is Rs.10, spent on the notebook.

3. So Ravi has 40 − 10 = Rs.30 left.

Usual mistake: Applying the second fraction to the starting amount instead of the amount remaining.

Correct answer: (c) 180

1. 6, 9 and 15 are made from the prime factors 2, 3 and 5, and 9 needs 3 twice.

2. Their least common multiple is 2 times 9 times 5, which is 90.

3. 90 is not greater than 100, so the next multiple of 90 is 180.

Usual mistake: Giving the least common multiple when a larger one is asked for, or checking only some of the divisors.

Correct answer: (a) 8

1. One diagonal cuts a square into exactly 2 triangles.

2. There are 4 small squares, and each gives 2 triangles.

3. So there are 4 times 2 = 8 triangles altogether.

Usual mistake: Forgetting that a single diagonal produces two triangles, not one.

Correct answer: (c) 125 minutes

1. From 9:15 to 11:40 is 2 hours 25 minutes, which is 145 minutes.

2. The train was not moving for 20 of those minutes.

3. So the moving time is 145 − 20 = 125 minutes.

Usual mistake: Reading a journey time as moving time when a stoppage is mentioned.

Correct answer: (c) 73

1. Subtracting 3 from the number leaves something divisible by both 7 and 5.

2. A number divisible by both 7 and 5 is a multiple of 35.

3. So the number is 3 more than a multiple of 35. The values are 38 and 73, and 38 is too small.

4. So the smallest such number above 40 is 73.

Usual mistake: Finding the smallest match and stopping, without checking that it is above the stated limit.

Correct answer: (d) 9

1. Work backwards from 29. The last thing done was subtracting 7, so add 7: 29 + 7 = 36.

2. Before that the number was multiplied by 4, so divide by 4: 36 divided by 4 is 9.

3. So the number was 9.

Usual mistake: Reversing a subtraction as a subtraction instead of an addition.

Correct answer: (d) 10

1. An average of 15 across 4 numbers means the four numbers add up to 4 times 15, which is 60.

2. The three known numbers add up to 12 + 18 + 20, which is 50.

3. The fourth number is 60 − 50 = 10.

Usual mistake: Thinking the average is another value in the list rather than a balance of the total.

Correct answer: (a) 24

1. The first place can take any of the 4 digits, the second place then has 3 choices, the third has 2, and the last has 1.

2. So the total is 4 times 3 times 2 times 1.

3. That gives 24 different numbers.

Usual mistake: Keeping some digits fixed in a set position instead of letting every digit move.

Correct answer: (a) All cats are animals.

1. The first statement tells us that at least some cats are black, which says nothing about the rest.

2. The second statement says that every cat is an animal, without exception.

3. So all cats are animals must be true.

Usual mistake: Turning a statement about some members into a statement about all members.

Correct answer: (b) 1

1. Number the places 1 to 5 from the left. Second from the left is place 2 and second from the right is place 4.

2. Only place 3 lies between place 2 and place 4.

3. So 1 child stands between them.

Usual mistake: Counting positions moved rather than positions in between.

Correct answer: (a) 57

1. Each remainder is 1 less than the divisor, so adding 3 to the number makes it divisible by 4, by 5 and by 6.

2. The least common multiple of 4, 5 and 6 is 60, so the number is 60 − 3, which is 57.

3. Checking: 57 = 4 times 14 + 1, 57 = 5 times 11 + 2, and 57 = 6 times 9 + 3, so all three conditions hold.

4. So the number is 57.

Usual mistake: Not checking a candidate against every one of the conditions it has to satisfy.

Correct answer: (a) 49

1. 1, 4, 9, 16, 25 and 36 are 1 squared, 2 squared, 3 squared, 4 squared, 5 squared and 6 squared.

2. 36 is 6 squared, so the next number is 7 squared.

3. 7 times 7 is 49.

Usual mistake: Continuing a sequence of differences without noticing that the differences are themselves increasing by 2.

Correct answer: (c) 8

1. The three numbers are 3, then 7, then 11, because each step adds 4.

2. There are two steps from the smallest to the largest.

3. Two steps of 4 is 2 times 4 = 8.

Usual mistake: Reporting one of the intermediate values rather than the requested difference.

Correct answer: (d) 31

1. The sum of the two numbers is 99 and the larger one is 68.

2. The smaller one is 99 − 68.

3. 99 − 68 is 31, and 68 written backwards is 86, which is not a two-digit reverse of 68, so the pair that matters is 68 and 31.

Usual mistake: Getting tangled in the reversal detail instead of using the sum that is given.

Correct answer: (c) 81 square cm

1. The perimeter of a square is 4 times its side, so the side is 36 divided by 4, which is 9 cm.

2. The area of a square is the side multiplied by itself, so it is 9 times 9.

3. 9 times 9 is 81 square cm.

Usual mistake: Confusing perimeter and area, or dividing the perimeter by 2 instead of by 4.

Correct answer: (a) 12

1. Each glass holds 1/3 of a litre, so the number of glasses in 4 litres is the number of thirds in 4.

2. 4 thirds is 3 + 3 + 3 + 3, which is 4 times 3.

3. So 12 glasses are needed.

Usual mistake: Multiplying by a fraction when the question needs the number of parts, which is a division.

Correct answer: (a) 15

1. Step 1 uses 1, step 2 uses 1 + 2 = 3, step 3 uses 3 + 3 = 6, step 4 uses 6 + 4 = 10.

2. Step 5 uses 10 + 5 = 15 matchsticks altogether.

3. After 5 steps the total is 15 matchsticks.

Usual mistake: Stopping one step early, or doubling a total instead of adding to it.

Correct answer: (c) 12

1. Each of the 6 faces is a square with 4 edges, which counts 24 edges in total across the faces.

2. But every edge of a cube is shared by exactly 2 faces, so each real edge was counted twice.

3. So the cube has 24 divided by 2 = 12 edges.

Usual mistake: Counting an edge once for each face it belongs to instead of remembering that two faces share each edge.

Correct answer: (b) ₹580

1. The 2 adult tickets cost 2 times 120, which is Rs.240.

2. The 3 child tickets cost 3 times 60, which is Rs.180. The total is 240 + 180 = Rs.420.

3. The change is 1000 − 420 = Rs.580.

Usual mistake: Reporting the cost instead of the change, or using one price for every ticket.

Correct answer: (b) 20

1. Work backwards. 8 marbles were left over, so the marbles that were shared out number 20 − 8.

2. Alternatively, build it forwards: 4 children at 3 marbles each is 4 times 3, which is 12, and the 8 left over must be added.

3. So there were 12 + 8 = 20 marbles.

Usual mistake: Leaving out the remainder when rebuilding the original amount.

Correct answer: (d) 10

1. 2 litres is 2000 millilitres.

2. Each cup holds 200 millilitres, so the number of full cups is 2000 divided by 200.

3. 2000 divided by 200 is 10 cups.

Usual mistake: Guessing a different cup size instead of using the size that is given.

Correct answer: (c) ₹149

1. The 5 apples cost 5 times 25, which is Rs.125.

2. The 3 bananas cost 3 times 8, which is Rs.24.

3. The total is 125 + 24 = Rs.149.

Usual mistake: Answering with the change rather than the amount spent.

Correct answer: (b) 24

1. Let the tens digit be a and the units digit be b. The number is 10a + b and the product of the digits is a multiplied by b.

2. So 10a + b = 3ab. Testing the digits from 1 to 9 leaves only two answers: 15, because 3 times 1 times 5 is 15, and 24, because 3 times 2 times 4 is 24.

3. The largest of the two is 24.

Usual mistake: Assuming a property must survive reversing the digits.

Correct answer: (b) 36

1. 1, 4, 9 and 16 are the squares of 1, 2, 3 and 4, so layer n holds n multiplied by n cubes.

2. The fifth layer would hold 5 multiplied by 5, which is 25, and the sixth layer holds 6 multiplied by 6.

3. 6 multiplied by 6 is 36 cubes.

Usual mistake: Counting the layers back from the end, or adding the layer sizes instead of squaring.

Correct answer: (d) The box labelled Mixed

1. Because every label is wrong, no box contains what its label says.

2. So the box labelled Mixed is definitely not mixed. It must hold all apples or all mangoes.

3. One fruit drawn from that box tells us which it is, and the other two boxes are then fixed by elimination. So the right box to draw from is the box labelled Mixed.

Usual mistake: Choosing a box that is simply not one thing, without checking whether it could be the mixture.

Correct answer: (b) 34

1. Subtracting 4 from the number leaves something divisible by both 6 and 5.

2. A number divisible by both 6 and 5 is a multiple of 30.

3. So the number is 4 more than a multiple of 30. The values are 4 and 34, and 4 is too small.

4. So the smallest such number above 20 is 34.

Usual mistake: Finding the first match and stopping without checking that it clears the stated bound.

Correct answer: (b) 9

1. 36 can be written as 2 multiplied by 2 multiplied by 3 multiplied by 3, that is 2 squared times 3 squared.

2. For the prime 2 raised to the power 2 there are 3 choices of power, 1, 2 and 4, and the same for the prime 3 with 1, 3 and 9.

3. The factors are 1, 2, 3, 4, 6, 9, 12, 18 and 36, and 3 times 3 gives 9.

Usual mistake: Counting multiples instead of factors, or double counting by counting from both ends.

Correct answer: (a) 27

1. Upward triangles of side 1 number 1 + 2 + 3 + 4, which is 10, and there are 6, 3, 1 and 0 of side 2, 3 and 4, so 20 upward triangles in all.

2. Downward triangles number 6 of side 1 and 1 of side 2, so 7 downward triangles.

3. That gives 20 + 7 = 27 triangles altogether.

Usual mistake: Counting only the triangles that point the same way as the outline.

Correct answer: (d) 157.5 degrees

1. The minute hand points at the 9, which is 45 times 6, or 270 degrees, round from 12.

2. By 3:45 the hour hand has moved past 3 by three quarters of an hour, so it is at 3 and three quarters of 30 degrees, which is 112.5 degrees.

3. The angle between them is 270 − 112.5 = 157.5 degrees, and that is the smaller of the two angles.

Usual mistake: Treating the hour hand as still sitting exactly on the hour mark when the minutes have moved on.