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

a²  =  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  =  36²  =  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

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

Possible values of n are 11, 12, 13.

Hence there are 3 possible values.

Question 6 :

The function f is defined by f(x) = 3x - 40. If f(a) = 8, what is the value of a ?

(A)  -96  (B)  -16  (C)  16  (D)  -32/3  (E)  32/3

Solution :

f(x) = 3x - 40. If f(a) = 8

Applying x = a, we get

f(a) = 3x - 40

8 = 3x - 40

3x = 8 + 40

3x = 48

x = 48/3

x = 16

So, the value of a is 16. Option C is correct.

Question 7 :

If triangle ABC, if AB = 1 and BC = 100, which of the following must be true about the angles ?

A) The measure of ∠A is greatest.

B) The measure of ∠B is greatest

C) The measure of ∠A and ∠B are equal

D) The measure of ∠C is greatest

E) The measure of ∠C is least.

Solution :

AB = 1, BC = 100

The side which is opposite to greater angle measure is greater.

The measure of ∠A is greatest.

Question 8 :

Each time Sue rents a bicycle, she pays a fixed base cost plus an hourly rate for the time the bicycle is rented. Last Saturday she paid $12 to rent a bicycle for 6 hours and yesterday she paid $9.50 to rent a bicycle for 4 hours. Which of the following equations shows the total cost C in dollars for Sue to rent a bicycle for n hours ?

A) C = 1.25n     B) C = 1.25n + 4.50

C) C = 2n + 2.50    D)  C = 2.5n + 2    E) C = 4.5n + 1.25

Solution :

(6, 12) and (4, 9.5)

Slope (m) = (y₂ - y₁)/ (x₂ - x₁)

= (9.5 - 12)/(4 - 6)

= 2.5/2

= 1.25

y = 1.25n + b

Applying the point (6, 12), we get

12 = 1.25(6) + b

12 = 7.5 + b

b = 12 - 7.5

b = 4.5

C = 1.25 n + 4.5

Option B is correct.

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