GRADE 6 MATH REVIEW TEST 

Question 1 :

A work was assigned to Mike on a Tuesday. He completed the work after 72 days. On what day did he complete the work ?

(A) Sunday         (B) Tuesday           (C) Thursday

Solution :

Tuesday corresponds to 2 in 7 day clock arithmetic.

We want to know the day which is 72 days after Tuesday.

Step 1 :

Add 72 to 2

Step 2 :

Divide the result by the divisor 7

Step 3 :

Take the remainder

72 + 2  =  74

When 74 is divided by 7, the remainder is 4

4 corresponds to Thursday.

So, he will complete the work in Thursday.

Question 2 :

What month is 19 months after July?

(A) April         (B) March       (C) February

Solution :

July corresponds to 7 in month arithmetic

We want to know the month which is 19 months after July

Step 1 :

Add 19 to 7

Step 2 :

Divide the result by the divisor 12

Step 3 :

Take the remainder

7 + 19  =  26

When 26 is divided by 12, the remainder is 2 and it corresponds to February

So, 19 months after July is February.

Question 3 :

The wrong number of the sequence 1, 8, 27, 64, 124, 216, 343 is

(A) 150           (B) 124          (C) 117

Solution :

1  =  13

8  =  23

27  =  33

64  =  43

125  =  5 3

In the sequence every number is in the form of cube 1, 2, 3,.......... but 124 is not cube of any number.

So, the wrong number in the sequence is 124.

Question 4 :

A triangle with sides of length 6, 8 and 10 is a

(A) Equilateral triangle      (B) Scalene triangle

(C) Right triangle

Solution :

The measurement of three sides of triangles are different. So it must be a scalene triangle.

So the answer is Scalene triangle.

Question 5 :

James, David and Jack live in a row of three houses on the same street. Walking their houses, they pass a white house first, then a green house, then a blue house. David lives next door to the green house. Jack does not live next door to his friend who lives in the blue house. Who lives in the blue house ?

(A) Jack           (B) James           (C) David

Solution :

From left to right,

First, second and third houses are white, green and blue respectively.

Green is the middle house,  Since David lives next door to green house, he is living in the blue house.

So the answer is David.

Question 6 :

There are 3 large marbles, 2 medium marbles and 5 small marbles in a bag. If one of the marbles is chosen randomly, what is the probability that a small marble is chosen?

(A)  3/10      (B)  1/5    (C)  1/3     (D)  1/2

Solution :

Total number of marbles  =  3 + 2 + 5

n(s)  =  10

Let A be the event of getting small marble.

n(A)  =  5

p(A)  =  n(A)/n(S)

p(A)  =  5/10

p(A)  =  1/2

Question 7 :

In a triangle, the length of the first side is x. The length of the second side is 2 cm greater than first side. The third side is 5 cm greater than the first side. If the perimeter of the triangle is 13, what is the length of each side ?

(A) 7         (B) 4         (C) 2

Solution :

x - length of first side

length of the second side  =  x + 2

Length of third side  =  x + 5

Perimeter of the triangle  =  13

x + x + 2 + x + 5  =  13

3x + 7  =  13

3x  =  6

x  =  6/3

x  =  2

So, the length of first side is 2 cm.

Question 8 :

In a right angled triangle, the length of the opposite side and adjacent side are 3 cm and 4 cm respectively. What is the area of the triangle ?

(A) 5        (B) 6      (C) 4

Solution :

Area of triangle  =  (1/2) ⋅ base ⋅ height

=  (1/2) ⋅ 3 ⋅ 4

=  6 cm2

Question 9 :

Find the volume of the cylinder whose diameter is 7 inches and height is 6 inches.

(A) 243 cm3     (B) 7243 cm3      (C) 243 cm3 

Solution :

Volume of cylinder  =  πr2h

Radius  =  7/2 and height  =  6 cm

Volume of cylinder  =  (22/7) ⋅ (7/2)⋅ 6

  =  462 cm3

So, the volume of cylinder is 462 cm3.

Question 10 :

The reduced common fraction for the sum of (3/8) and (8/3) is

(A) 24/73     (B) 73/14        (C) 73/24

Solution :

Sum of (3/8) and (8/3)

=  (3/8) + (8/3)

=  (9 + 64)/24

=  73/24

So the answer is 73/24.

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