**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), here 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 50th symbol ?

**Solution :**

Each group consists of 6 different symbols. A group ends with the symbol upside, then the new starts with triangle.

Let us divide 50 by 6, we get the remainder 2. The symbol triangle must be filled in the 49th place and 50^{th} place should be 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)

a = 2x, b = 6x

(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.

After having gone through the stuff given above, we hope that the students would have understood, "SHSAT Practice Test Answers".

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