MATH OLYMPIAD PRACTICE PROBLEMS 6TH GRADE

Question 1 :

Peter is now 24p years old. He is thrice as old as John. Find their total age 4 years ago ?

(A)  23p - 4  (B)  32p - 8  (C)  8p - 32  (D)  4p - 32

Solution

Question 2 :

A cap costs n rupee and a belt and 2 caps but is short of $70. How much does he have ?

Express your answer in terms of n rupees.

(A)  3n   (B)  3n + 20  (C)  2n + 70  (D)  n + 70

Solution

Question 3 :

A delivery truck delivers goods from Town A to town B. It can travel at 90 km/h when it is empty but only at 60 km/h when it is loaded with goods. Find the distance between two towns if it can cover 6 trips in 12 hours.

(A)  48 km  (B)  36 km  (C)  72 km  (D)  12 km

Solution

Question 4 :

500 books are to be distributed unevenly to a certain number of libraries. Each library however, must not get more than 15 books. How many libraries, at least, will get the same number of books ?

(A)  4  (B)  5  (C)  33  (D)  45

Solution

Question 5 :

Last year, the ratio of the number of girls to the number of boys in the table tennis CCA was 4 : 7. This year, 18 girls joined the club and the number of girls joined the club and the number of girls and boys become the same. How many pupils were in the club this year ?

(A)  84  (B)  42  (C)  74  (E)  75

Solution

Question 6 :

The model of a bus is made using a scale  of 1:20. This means that 20 cm of the actual bus is represented by 1 cm of the model. If the length of actual bus is 12 m, calculate the length of the model. Express your answer in centimeters.

(A)  40 cm (B)  60 cm  (C)  50 cm (E)  70 cm

Solution

Question 7 :

Express 50 minutes  as the ratio of 2 hours 5 minutes.

(a)  2 : 3 (B)  4 : 5 (C)  2 : 5  (E)  3 : 5

Solution

Question 8 :

The figure shown below 3 identical rectangles A, B and C and 2 areas shaded in black are the same size.

Given that 2/5 of rectangle A is shaded in black, what is the ratio of the shaded areas to the area of the whole figure ?

(A)  2/15  (B)  4/15  (C)  4/7  (D)  4/11

Solution

Question 9 :

There were 4960 people at the carnival. The ratio of the number of men to the number of women was 5 : 6, while the ratio of the number of women to the number of children was 2 : 3.

Some people joined the carnival and some people left. After that there were 5208 people at the carnival. The ratio of the number of men to the number women to the number of children then becomes 1 : 2 : 5. What was the increase in the number of children ?

(A)  1023  (B)  845  (C)  948  (D)  1100

Solution

Question 10 :

The ratio of the number of marbles in box A to the number of marbles in box B is 3 : 5.

If 1/3 of the marbles in Box A are transferred to Box B and then 1/3 of the marbles in Box B is transferred to Box A, what will be the ratio of the number of marbles in Box A to the number of marbles in Box B ?

(A)  2 : 1  (B)  1 : 1  (C)  1 : 3  (D)  2 : 3

Solution

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