SHSAT PRACTICE TEST ANSWERS

Question 11 :

If today is Saturday, what day of the week will it be in 365 days from now?

Solution :

The problem starts with Saturday, every 7 days from Saturday, it will be Saturday.

By dividing 365 by 7, we get 1 as remainder.So the answer will be 1 day after Saturday. 

Hence the answer is Sunday. 

Question 12 :

What is the remainder of 7, 700, 000, 000, 202 divided by 9 ?

Solution :

If the sum of the digits is divisible by 9, then the given number is divisible by 9.

7 + 7 + 2 + 2  =  18

Since the sum of the digits is divisible 9, the given number is divisible by 9.

Hence the remainder is 0.

Question 13 :

In the figure above AB  =  BC  =  DE  =  EF  and the side of the square is 12. Point B and E are the midpoints of the square. Find the area of the shaded region.

Solution :

AC  =  12, AE  =  6

There are four semicircles.

Area of 4 semicircles with radius 6  =  πr²/2

   = 4(πr²/2)  =  2 πr²

  =  2π(6)²

  =  2π(36)

  =  72π

Hence the answer is 72π.

Question 14 :

8 ^{x + 3}  =  64 ^3x, what is the value of x?

Solution :

8 ^{x + 3}  =  64 ^3x

In order to compare the two terms, we have to convert with them having same base.

8 ^{x + 3}  =  (8²) ^3x

8 ^{x + 3}  =  8 ^6x

6x  =  x + 3 

6x - x  =  3

5x  =  3

x  =  3/5

Question 15 :

If A ⊏ ⊐ B  =  AB (A/B) - 2³, then what is the value of 3 ⊏ ⊐ (6 ⊏ ⊐ 2)

Solution :

First let us calculate the value of (6 ⊏ ⊐ 2),

Instead of A we have 6 and instead of B we have 2.

(6 ⊏ ⊐ 2)  =  6(2)(6/2) - 2³

  =  12(3) - 8

  =  36 - 8

(6 ⊏ ⊐ 2)  =  28

3 ⊏ ⊐ 28  =  3(28) (3/28) - 2³

=  84(3/28) - 8

=  3(3) - 8

  =  9 - 8 

 =  1

Hence the answer is 1.

Question 16 :

If the average of 11 numbers is 15, then what is the sum of these 11 numbers ?

Solution :

Average of 11 numbers  =  15

Sum of 11 numbers / 11  =  15

Sum of 11 numbers  =  15 (11)  =  165.

Hence the required answer is 165.

Question 17 :

What is the average of (9b - 7) + (7 - 3b) - (-3 -3b) + (6 + 3b)

Solution :

  =   (9b - 7) + (7 - 3b) - (-3 -3b) + (6 + 3b)

  =  9b - 7 + 7 - 3b + 3 + 3b + 6 + 3b

  =  9b + 3b + 9 

  =  12 b + 9 

Average of four terms  =  (12b + 9)/4

  =  3b + 9/4

Question 18 :

(y^-1⋅y³⋅y⁴⋅y⁵⋅y⁶) / (y⁶⋅y⁵⋅y⁴)

Solution :

  =  y^-1 ⋅y³

  =  y ^{(-1 + 3)}

  =  y²

Hence the answer is y^2.

Question 19 :

If the pattern continues, what will be the 50^th symbol ?

Solution :

Each group consists of 6 different symbols and it ends with the symbol upside arrow.

Let us divide 50 by 6, we get the remainder 2. Hence the 50^th place should be filled with the symbol heart.

Question 20 :

A trapezoid has base length in the ratio of 2 : 6. If the area of a trapezoid is 260 and altitude is 5, then what is the length of longer side ?

Solution :

Area of trapezoid  =  (1/2) ⋅ h ⋅ (a + b)

Here, a  =  2x, b = 6x and altitude (h)  =  5

 (1/2) ⋅ 5 ⋅ (2x + 6x)  =  260

(5/2)(8x)  =  260

x  =  260/20

x  =  13

2x  =  2(13)  =  26, 6x  =  6(13)  =  78

Hence the longer side is 78.

More Practice Test Papers

SHSAT math practice test - Paper 1

SHSAT math practice test - Paper 2

SHSAT math practice test - Paper 3

SHSAT math practice test - Paper 4

SHSAT math practice test - Paper 5

SHSAT math practice test - Paper 6

SHSAT math practice test - Paper 7

SHSAT math practice test - Paper 8

SHSAT math practice test - Paper 9

SHSAT math practice test - Paper 10

SHSAT math practice test - Paper 11

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