**SHSAT Math Sample Test with Answer :**

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

SHSAT Math Sample Test with Answer

**Question 1 :**

In the sequence of numbers 1, 2, 2, 3, 3, 3,. . . [assume the pattern of one 1, two 2s, three 3s, four 4s, and so on continues], the number in the 40^{th} position will be

(A) 8 (B) 9 (C) 10 (D) 11 (E) 40

**Solution :**

By adding the numbers appearing in the sequence, we get the ending position of a particular number.

For example,

1 + 2 + 3 = 6 (3 ends at 6th place)

1 + 2 + 3 + 4 = 10 (4 ends up with 10th place)

Like this, by finding the sum of the series which gives the answer 40, we get the required number.

1 + 2 + 3 + 4 + ........... + 8

= n(n + 1)/2

= 8(8+1)/2

= 4(9) = 36

So, 8 will end up with 36th position. Next we will have 9 nines.

Hence in 40^{th} position, we will have 9.

**Question 2 :**

Each side of a square is an integral number of inches, and its area is 576 square inches. If each side of the square is increased by 1 foot, forming a new square, the area of the new square, in square inches, is

(A) 577 (B) 588 (C) 720 (D) 1,296

(E) not determined

**Solution :**

Area of square = 576 square inches

a^{2} = 576

a = 24 inches

Side length of square is 24 inches

Here the side length is increasing 1 foot.

1 foot = 12 inches

side length of new square = 24 + 12 = 36 inches

Area of new square = 36^{2} = 1296 square inches

**Question 3 :**

Let P = 18/25, Q = 5/7, and R = 3/4. Then

(A) P < Q < R (B) P < R < Q (C) Q < P < R

(D) Q < R < P (E) R < P < Q

**Solution :**

In order to compare the given fractions, we have to make the denominators same.

P = 18/25, Q = 5/7, and R = 3/4

L.C.M of 25, 7, 4 = 700

Since we dont have any common divisor, we multiply 25, 7 and 4.

P = (18/25) ⋅ (28/28) = 504/700

Q = (5/7) ⋅ (100/100) = 500/700

R = (3/4) ⋅ (175/175) = 525/700

Now, we have same denominators and we may compare the numerators.

By arranging from least to greatest, we get Q < P < R.

Hence option c is correct.

**Question 4 :**

A water container is 3/4 full. After 20 ounces of water is removed, the container is 1/4 full. How many ounces of water does a full container hold?

(A) 20 (B) 40 (C) 60 (D) 80 (E) 100

**Solution :**

Quantity of water at initial = 3/4

Quantity of water removed = 3/4 - (1/4)

= 2/4 ==> 1/2

There is 20 ounces in 1/2 of the water in the container.

So, the full container will have 40 ounces.

**Question 5 :**

For how many integer values of n will the expression (n-10) / (14-n) have a positive value?

(A) 0 (B) 1 (C) 3 (D) 4 (E) 5

**Solution :**

To get the positive value,

n - 10 > 0 and 14 - n > 0

n - 10 > 0 Adding 10 on both sides n > 10 |
14 - n > 0 Subtracting 14 on both sides -n > -14 Multiply by (-) on both sides n < 14 |

By combining the above statements, we get 10 < n < 14

Possible values of n are 11, 12, 13.

Hence there are 3 possible values.

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