**SHSAT Practice Test Answers :**

Here we are going to see some practice worksheets for SHSAT exams. Each question paper consists of 20 question. For each questions, you can find solution with detailed explanation.

**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 = πr^{2}/2

= 4(πr^{2}/2) = 2 πr^{2}

= 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} = (8^{2}) ^{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) - 2^{3}, 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) - 2^{3}

= 12(3) - 8

= 36 - 8

(6 ⊏ ⊐ 2) = 28

3 ⊏ ⊐ 28 = 3(28) (3/28) - 2^{3}

= 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}⋅y^{3}⋅y^{4}⋅y^{5}⋅y^{6}) / (y^{6}⋅y^{5}⋅y^{4})

**Solution :**

= y^{-1 }⋅y^{3}

= y ^{(-1 + 3)}

= y^{2}

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

After having gone through the stuff given above, we hope that the students would have understood, how to solve practice problems on SHSAT exams.

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