9th GRADE SHSAT PRACTICE TEST WITH SOLUTIONS

Question 1 :

Maria, Anoki, and Boris are teenagers, and the sum of their ages now is 49.  The sum of their ages 8 years from now will be F, and the sum of their ages 10 years ago was P.  The value of F – P is

(A)  54  (B)  18  (C)  17  (D)  6  (E)  2

Solution :

Sum of ages of Maria, Anoki and Boris  =  49

Sum of their ages 8 years from now  =  49 + 8 + 8 + 8

F  =  73

Sum of their ages 10 years ago  =  49 - 10 - 10 - 10

  =  49 - 30

 P  =  19

F - P  =  73 - 19

=  54

Hence the value of F - P is 54.

Question 2 :

 If (1/4) + (1/x) = 1, then x =

(A)  1/8  (B)  2/3  (C)  4/3  (D)  2  (E)  3

Solution :

(1/4) + (1/x) = 1

(x + 4) / 4x  =  1

x + 4  =  4x 

Subtract x on both sides

-3x + 4  =  0

Subtract 4 on both sides,

-3x  =  -4

x  =  4/3

Hence the value of x is 4/3.

Question 3 :

When the integer N is divided by 7,  the quotient is Q and the remainder is 5.  When N + 24 is divided by 7, the remainder is ‘

(A)  4  (B)  3  (C)  2  (D)  1  (E)  0

Solution :

Let us choose a number which gives the remainder 5 by dividing it by 7.

Let N = 12, by dividing 12 by 7, we get 5 as remainder.

By adding 12 by 24, we get 6. Now let us divide 36 by 7, we get the remainder 1.

Hence 1 is the answer.

Question 4 :

Point B is on line segment AD, and point E is on line segment BC.  The value of x is

(A)  20  (B)  40  (C)  50  (D)  60  (E)  70

Solution  :

In triangle ABC,

<A + <ABC + <C  =  180

50 + <ABC + 70  =  180

<ABC  =  180 - 120  =  60

In triangle EBD,

<EBD + <BDE + <DEB  =  180

120 + 20 + x  =   180

x  =  180 - 140

 x = 40

Hence the required angle is 40.

Question 5 :

Three-fourths of a number is equal to L.  What is three-halves of that original number, in terms of L?

        (A)  4/3L  (B)  3/2L  (C)  2L  (D)  3L  (E)  4L

Solution :

Let the number be "N"

(3/4) of N  =  L  --(1)

  =  (3/2) of N

Form (1), N = 4L/3

  =  (3/2) (4L/3)

  =  2 L

Hence the answer is 2 L.

Question 6 :

7m = 5(n + p)

The given equation relates the positive number m, n and p. Which equation correctly gives n in terms of m and p ?

(A)  n = 5p/7m          (B)  n = (7m/5) - p

(C)  n = 5(7m) + p       (D)  n = 7m - 5 - p

Solution :

7m = 5(n + p)

7m = 5n + 5p

5n = 7m - 5p

n = (7/5)m - (5/5)p

n = (7/5)m - p

So, option B is correct.

Question 7 :

x + 2y = 6

x - 2y = 4

The solution to the given system of equations is (x, y). What is the value of x ?

A) 2.5       B) 5       C) 6      D) 10

Solution :

x + 2y = 6 -----(1)

x - 2y = 4 -----(2)

(1) + (2)

x + 2y + x - 2y = 6 + 4

2x = 10

x = 5

So, the value of x is 5, option B is correct.

Question 8 :

The table shows the frequency of values in a data set

What is the minimum value of the data set?

Solution :

Minimum value of the data set is 19.

Question 9 :

A number x is at most 17 less than 5 times the value of y. If the value of y is 3, what is the greatest possible value of x ?

Solution :

x ≤ 5y - 17

When y = 3

x ≤ 5(3) - 17

x ≤ 15 - 17

x ≤ -2

So, the greatest possible value of x is -2.

Question 10 :

In the figure shown, lines r and s are parallel, and line m intersects both lines. If y < 65 , which of the following must be true? 

A) x < 115   B) x > 115    C)  x + y < 180  D)  x + y > 180

Solution :

y < 65

If y = 65

x + y = 180

x + 65 = 180

x = 180 - 65

x = 115

When y = 64

x + 64 = 180

x = 180 - 64

x = 116

Then the value of x must be greater than 115. Option B is correct.

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