SHSAT PRACTICE TEST IN MATH

Question 1 :

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

Hence the answer is 5.

Question 2 :

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 3 :

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 4 :

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 5 :

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 6 :

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.

Question 7 :

In DXYZ above, what is the value of y?

(A) 24   (B) 28    (C) 48    (D) 72   (E) 78

Solution :

In the triangle at the bottom,

40 + 82 + x = 180

122 + x = 180

x = 180 - 122

x = 58

In the large triangle,

40 + 2x + y = 180

40 + 2(58) + y = 180

40 + 116 + y = 180

156 + y = 180

y = 180 - 156

y = 24

So, the value of y is 24, Option A is correct.

Question 8 :

In a bowl of fruit there are 4 apples, 3 oranges, 5 bananas, 2 plums, and 6 peaches. What is the probability that a piece of fruit chosen at random from the bowl is not a peach?

(A) 3/10    (B) 2/5   (C) 1/2    (D) 7/10    (E) 8/9

Solution :

Total number of fruits

= 4 apples + 3 oranges + 5 bananas + 2 plums + 6 peaches

= 20

Probability of choosing peach = 6/20

Probability of not choosing peach = 1 - 6/20

= 14/20

= 7/10

So, option D is correct.

Question 9 :

Five more than one-third of a certain number is 3 less than the number. What is the number?

(A) 3   (B) 5  1/3   (C) 6    (D) 7  2/3    (E) 12

Solution :

Let x be the number.

1/3 of x + 5 = x - 3

x/3 + 5 = x - 3

(x + 15)/3 = x - 3

x + 15 = 3(x - 3)

x + 15 = 3x - 9

x - 3x = -9 - 15

-2x = -24

x = 12

So, option E is correct.

Question 10 :

If m = 4n + 5 and p = 3n + 6, which of the following expresses n in terms of m and p ?

A) m + 2p - 3   B) m - p + 1

C) 3m - 2p  + 4    D) 4m + p + 1   E) 2m - 5p

Solution :

m = 4n + 5 ----(1)

p = 3n + 6 -----(2)

(1) - (2)

m - p = (4n + 5) - (3n + 6)

m - p = 4n + 5 - 3n - 6

m - p = n - 1

m - p + 1 = n

So, option B is correct.

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