7th GRADE MATH PRACTICE PROBLEMS

Question 1 :

The unit digit of 13¹⁷ + 17¹³ is 

(A) 0                     (B) 9                   (C) 1

Solution :

(The order is repeated after every multiple of 4)

Hence the unit digit of 13¹⁷ is 3

Units digit of 17¹³ = 7

Units digit of sum of both the numbers = 3+7 = 0

Answer = 10

(The order is repeated after every multiple of 4)

Question 2 :

If the diameter of a circle is 376216 inches, using the approximation π = 3:14, compute the ratio of the its area, in square inches, to its circumference in inch.

(A) 94054:5      (B) 94554:1      (C) 94054:1

Solution :

Radius of circle  =  376216/2  =  188108

Area of circle  :  Circumference of circle

πr²  :  2 πr

r : 2

188108 : 2

Divide both terms by 2

188108/2 : 2/2

94054 : 1

Question 3 :

If 1/7 is written in decimal form, then the 100th digit after the decimal point is 

(A) 8                       (B) 3                       (C) 7

Solution :

1/7  =  0.142857142857............

From the above decimal value, we come to know that this 6 digits is repeating.

Now let us calculate how many 6 are in 100.

16 (6)  =  96

1 is the 97^th digit 

4 is the 98^th digit 

2 is the 99^th digit 

8 is the 100^th digit 

Question 4 :

The length of the two parallel sides of a trapezium are 15 cm and 10 cm. If its area is 100 sq. cm. Find the distance between the parallel sides. 

(A)  12 cm         (B)  16 cm          (C)   8 cm

Solution

Given: a = 15 cm, b = 10 cm, Area = 100 sq. cm.

Area of the trapezium = 100

(1/2) h (a + b)  =  100

(1/2) h (15 + 10)  =  100

h  =  200/25

h  =  8

Hence the distance between the parallel sides = 8 cm.

Question 5 :

.If a, b, and c are nonzero numbers satisfying 3a = 4b and 5b = 6c, what is c/(a + b) ?

(A) 5/14          (B) 3/10               (C) 2/19

Solution :

c/(a + b)  =  (5b/6)/((4b/3) + b)

  =  (5b/6)/(7b/3)

  =  (5b/6)⋅(3/7b)

  =  (5/2)⋅(1/7)

  =  5/14

Hence the answer is 5/14.

Question 6 :

The radii of two spheres are of 2 and 6, then the ratio of the volume of the larger sphere to the volume of the smaller sphere is

(A)  1 : 27     (B) 2 : 15           (C) 5 : 14

Solution :

Volume of sphere  =  (4/3) πr³

(4/3) πR³  :  (4/3) πr³

R³ : r³

2³ : 6³  ==>  (2 ⋅ 2 ⋅ 2)/(6 ⋅ 6 ⋅ 6)

1 / 27

1 : 27

Hence the required ratio is 1 : 27

Question 7 :

If P be the product of the first nine multiples of 19 (i.e. P = 19x38x57……….152x171). What is the unit digit of P?

(A) 5                  (B) 9               (C) 0

Solution :

  =  19 x 38 x 57……….152 x 171

  =  (1 x 19) x (2 x 19) x (3 x 19)……….(9 x 19)

  =  19 (1 + 2 + 3 + .......... + 9)

  =  19 ( 9(9+1) / 2)

  =  19 (9 ⋅ 10 / 2)

  =  19  ⋅ 45

  =  855

So, the unit digit is 5.

Question 8 :

Find the perimeter of the rectangle whose length is 5cm and breadth is 3 cm.

(A) 10 cm         (B) 16 cm          (C) 15 cm

Solution :

Perimeter of rectangle  =  length x breadth

 =  5 (3)

  =  15 cm

Hence the perimeter of rectangle is 15 cm.

Let us look into solution of next problem on "Grade 7 math worksheet 8 answers".

Question 9 :

What is the value of 1 + 3 + 5 +…………………… + 195 + 197 + 199?

(A) 10500         (B) 10001       (C) 10000

Solution :

Sum of odd numbers  =  [(l + 1)/2]²

=  [(199 + 1)/2]²

=  (200/2)²

=  100²

=  10000

Hence the answer is 10000.

Question 10 :

The number of positive divisors of 120 are divisible by 4 are

(A) 7          (B) 3                    (C) 8

Solution :

Divisors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120

From the above numbers 4, 8, 12, 20, 24, 40, 60, 120 are divisible by 4.

So, the answer is 8.

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