**SHSAT Math Test with Solution :**

Here we are going to see some practice questions questions for SHSAT exams.

SHSAT Math Test with Solution

To find questions from 1 to 5, please visit the page "SHSAT Math Practice for 9th Graders"

To find questions from 6 to 10, please visit the page "SHSAT Math Test with Answers"

**Question 11 :**

The sum of 7 unequal positive integers is 61. What is the largest possible value that any of those integers can have?

(A) 55 (B) 40 (C) 39 (D) 13 (E) 9

**Solution :**

If the the largest number be 55, then the sum of other 6 numbers be 11. So, it is not possible.

If the the largest number be 40, then the sum of other 6 numbers be 21.

The possible 6 numbers are 1, 2, 3, 4, 5, 6 which are unequal and gives the sum 21.

**Question 12 :**

In the set {1, 5, x, 10, 15}, the integer x is the median. The mean of the five numbers is one less than x. The value of x is

(A) 6 (B) 7 (C) 8 (D) 9 (E) none of these.

**Solution :**

Mean of 5 numbers = (1 + 5 + x + 10 + 15)/5

x - 1 = (31 + x)/5

5(x - 1) = 31 + x

5x - 5 = 31 + x

5x - x = 31 + 5

4x = 36

x = 9

Hence the required value of x is 9.

**Question 13 :**

If 7/50 < 1/x < 8/51 where x is an integer, then x =

(A) 8 (B) 7 (C) 6 (D) 5 (E) 4

**Solution :**

**7/50 < 1/x < 8/51 **

7x < 50 7x < 7 1/7 x < 7 1/7 |
1/x < 8/51 51 < 8x 6 3/8 < 8x 6 3/8 < x |

By combining these two inequalities, we get

6 3/8 < x < 7 1/7

Since x must be an integer, the value of x is 7.

**Question 14 :**

Half of 2^{8} is

(A) 2^{7} (B) 2^{6} (C) 2^{4} (D) 1^{8} (E) 8

**Solution :**

** = Half of 2 ^{8}**

** = (1/2) **⋅ **2 ^{8}**

** = **2^{7}

Hence the answer is 2^{7}.

**Question 15 :**

If x is greater than 1/2 but less than 1, which of the following has the largest value?

(A) 2x – 1 (B) x^{2} (C) 1/x (D) 1 – x (E) x^{3}

**Solution :**

1/2 < x < 1

**Let us test option A :**

Multiply 2 through out the inequality

1 < 2x < 2

Subtract 1,

0 < 2x - 1 < 1

The value of 2x - 1 lies between 0 and 1.

**Option B :**

1/2 < x < 1

Taking squares,

1/4 < x^{2} < 1

**Option C :**

1/2 < x < 1

Taking reciprocals,

2 < 1/x < 1

The value of 1/x lies between 1 and 2.

**Option D :**

1/2 < x < 1

Subtract 1,

1 - 1/2 < 1 - x < 1 - 1

1/2 < 1 - x < 0

The value of 1 - x lies between 0 and 1/2.

**Option E :**

1/2 < x < 1

1/8 < x^{3} < 1

Hence the largest value is between 1 and 2. So, option C is correct.

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