OLYMPIAD MATH PRACTICE PROBLEMS 5TH GRADE

Question 1 :

A girl had 12 coins. They were made up of $2 coins and $1 coins. Altogether she had $16. How many $2 coins did she have ?

(A)  3   (B)  2   (C)  4  (D)  5

Solution :

Let x and y be the number of $2 and $1 coins respectively.

x + y  =  12  ----(1)

2x + 1y  =  16  ------(2)

From (1), we have

x  =  12 - y 

Applying the value of x in (2), we get

2(12 - y) + 1y  =  16

24 - 2y + 1y  =  16

24 - y  =  16

y  =  24 - 16

y  =  8

Finding the value of x, when y  =  8.

x  =  12 - 8

x  =  4

So, the number of $2 coins is 4.

Question 2 : 

A man had some money in the bank in march. He deposited $125 every month from April to June. At the end of June he had $700. How much money did he have in March ?

(A)  325   (B)  525   (C)  400  (D)  520

Solution :

Let x be the amount he has in March

From April to June, we have 3 months (April, May and June)

In each month, he is depositing $125.

x + 3(125)  =  700

x + 375  =  700

x  =  700 - 375

x  =  325

Therefore at March he would have $325.

Question 3 :

This graph shows the number of balloons in Ravi's birthday party. Study the graph carefully and answer the question.

During the party, the children burst half of the red and yellow ballons. How many balloons left after this ?

(A)  5   (B)  15   (C)  70  (D)  85

Solution :

Number of red balloons  =  50

Number of red balloons busted by children  =  25

Number of yellow balloons  =  30

Number of yellow balloons busted by children  =  15

Number of balloons left over  =  25 + 25 + 20 + 15

  =  85

Question 4 :

What is the value of : 

268 + 1375 + 6179 - 168 - 1275 - 6079 ?

Solution :

  =  268 + 1375 + 6179 - 168 - 1275 - 6079

  =  7822 - 7522

  =  300

Question 5 :

Each of 8 boxes contains one or more marbles. Each box contains a different number of marbles, except for two boxes which contain the same number of marbles. What is the smallest total number of marbles that the 8 boxes could contain?

Solution :

Number of marble in the 1^st box  =  1

Number of marble in the 2^nd box  =  1

Number of marble in the 3^rd box  =  2

Number of marble in the 4^th box  =  3

Number of marble in the 5^th box  =  4

Number of marble in the 6^th box  =  5

Number of marble in the 7^th box  =  6

Number of marble in the 8^th box  =  7

Total number of marbles  =  1 + 1 + 2 + 3 + 4 + 5 + 6 + 7

  =  29

Hence the smallest number of marbles in 8 boxes is 29.

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