# 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 40th 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 40th 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

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

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

Possible values of n are 11, 12, 13.

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