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 28 is

(A)  27 (B)  26 (C)  24 (D)  18  (E)  8

Solution :

  =  Half of 28

  =  (1/2) ⋅ 28

  =  27

Hence the answer is 27.

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)  x2  (C)  1/x  (D)  1 – x  (E)  x3 

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 < x2 < 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 < x3 < 1

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

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