SHSAT PRACTICE TEST IN MATH

Question 15 :

Two sides of a right triangle are 3 and 4.  The third side is

(A)  1  (B)  3  (C)  5  (D)  7  (E)  not uniquely determined

Solution :

In a right triangle, the square of hypotenuse side is equal to the sum of the squares of other two sides.

Third side  =  √32 + 42

=  √(9 + 16)

=  √25

=  5

Question 16 :

A cube 3 by 3 by 3 is painted red on all six faces and then cut into 27 smaller 1 by 1 by 1 cubes.  How many of these new smaller cubes have exactly two faces that are painted red?

(A)  6  (B)  8  (C)  12  (D)  21  (E)  27

Solution :

Like this we may find 12 cubes under the given condition.

Question 17 :

If 2 blobs = 3 glops and 3 blobs = 2 chunks, then 1 chunk =

(A)  1 glop  (B)  2/3 glop  (C)  3/2 glops

(D)  4/9 glop  (E)  9/4 glops

Solution :

Given that :

2 blobs = 3 glops  ----(1)

3 blobs = 2 chunks ----(2)

1 glap  =  (2/3) blobs

1 blob  =  2/3 chunks

2/3 chunks  =  (2/3) blobs

1 chunk  =  1 blob

Hence 1 blob is the answer.

(18) and (19)  The two pie charts show the ice cream flavor preferences of the students at two high schools.

Question 18 :

The ratio of Montague students who prefer vanilla to Montague students who prefer chocolate is

(A)  10:9  (B)  4:3  (C)  3:10  (D)  3:4  (E)  2:5

Solution :

Percentage of students who prefer Vanilla flavor

=  40%

Percentage of students who prefer chocolate flavor

=  30%

=  40 : 30

=  4 : 3

The the answer is 4 : 3.

Question 19 :

If the number of Montague students who prefer vanilla is M and the number of Capulet students who prefer vanilla is C, then

(A)  M > 2C  (B) M = 2C  (C)  M = C  (D)  M < C

(E) The relationship cannot be determined from the given information

Solution :

In Montague high, percentage of students who prefer Vanilla flavor (M)  =  40%

In Capulet high, percentage of students who prefer Vanilla flavor (C)  =  20%

Hence the required relationship is M = 2C.

Question 20 :

If x is an integer, which one of the following must be odd?

(A)  3x + 1  (B)  3x + 2  (C)  4x - 1

(D)  4x - 2  (E)  5x – 2x

Solution :

Since x is an integer, it may be odd or even.By multiplying odd or even number by 4, we get even number and by subtracting even number by 1, we get odd integer.

Hence 4x - 1 is the correct answer.

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