SHSAT MATH SAMPLE TEST WITH ANSWERS

Question 11 :

If a * b means a^b, then 2*(3*2) is

(A)  512  (B)  256  (C)  81  (D)  64  (E) 12

Solution :

a * b = a^b

 2*(3*2)

First let us evaluate the statement in parenthesis 

2*(3*2)  =   2 * (3²)

  =   2 * 9

  =   2⁹

Question 12 :

Let n be an integer from 9 to 38.  For how many values of n will n/5 be a prime?

(A)  3  (B)  4  (C)  6  (D)  8  (E)  29

Solution :

9 to 38

n  =  10 + 10 + 10

n  =  30

n/5  =  30/5  =  6

Question 13 :

|2 – 8| - |7 – 3| =

(A)  -10  (B)  -2  (C)  2  (D)  10  (E)  none of these

Solution :

  =  |2 – 8| - |7 – 3|

  =  |-6| - |4|

  =  6 - 4

  =  2

Hence the answer is 2.

Question 14 :

Mary is m years old now.  Joe is 3 years younger than Mary.  Express Joe’s age 10 years from now in terms of m.

(A)  13 - m  (B)  m - 3  (C)  m + 7 

(D)  m + 10  (E)  m + 13

Solution :

Age of Mary  =  m

Age of Joe  =  m - 3

After 10 years :

Age of Joe  =  m - 3 + 10

  =  m + 7

Question 15 :

The smaller angle between the hands of a clock at 10:00 is

(A)  15°  (B)  30°  (C)  45°  (D)  60°  (E)  75°

Solution :

Angle between two consecutive numbers in a clock

  =  360/12 

  =  30

Angle between the hands of a clock 10 : 00 is 2(30)  =  60

Hence the angle at 10 : 00 is 60 degree.

Question 16 :

Find the smallest positive integer that is a multiple of both 21 and 77.

(A)  7  (B)  33  (C)  98  (D)  231  (E)  1,617

Solution :

7 is not a multiple of both 21 and 77.

The number 231 is divisible by 21 and 77.

Hence 231 is the least number which is divisible by both 21 and 77.

Question 17 :

Over which interval was the growth in the value of the stock of the ABC Company most rapid?

(A)  March to April  (B)  April to May  (C)  May to June

(D)  June to July  (E)  July to August

Solution :

We must find the one one month interval, where the graph rises most quickly.

This is between March and April.

Question 18 :

Express the sum of 1.2 x 10² and 1.2 x 10³ in scientific notation.

(A)  0.144 x 10⁸  (B)  1.32 x 10³  (C)  1.44 x 10⁵ 

(D)  2.4 x 10⁵  (E)  2.4 x 10⁶

Solution :

  =  (1.2 x 10²) + (1.2 x 10³)

  =  1.2 x 100 + 1.2 x 1000

  =  120 + 1200

  =  1320

By writing 1320 in scientific notation, we get

  =  1.32 x 10³ 

Question 19 :

Today is Saturday.  What day of the week will it be 65 days from today?

(A)  Sunday  (B)  Monday  (C)  Tuesday 

(D)  Wednesday  (E)  Thursday

Solution :

By dividing 65 by 7, we get

According to days arithmetic 0 stands for "Sunday"

1 - Monday 

2 - Tuesday .............. 6 - Saturday

63^rd day is Saturday, 64^th day is Sunday and 65^th day is Monday.

Question 20 :

The circles are  “tangent” to the rectangle and to each other, as shown.  If the area of each circle is 16π, then the area of the rectangle is

(A)  32  (B)  48  (C)  96  (D)  128  (E)  512

Solution :

Area of circle  =  16π

πr²  =  16π

r²  =  16 ==>  r  =  4

Diameter of the circle  =  8 units (width of rectangle)

diameter of 2 circles  =  2 (8)  =  16 (length of rectangle)

Area of rectangle  =  length (width)

  =  16 (8)

  =  128 square units

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