SHSAT PRACTICE TEST ONLINE

Question 11 :

(60 ⋅ 30) / (60 + 30) =

(A) 2 (B) 20 (C) 200 (D) 2000 (E) None of these

Solution :

= (60 ⋅ 30) / (60 + 30)

= (60 ⋅ 30) / 90

= 60/3

= 20

Hence the answer is 20.

Question 12 :

Which of the following is closest in value to 0.213 ?

(A) 1/2 (B) 1/3 (C) 1/4 (D) 1/5 (E) 1/6

Solution :

1/2 = 0.5, 1/3 = 0.333..., 1/4 = 0.25, 1/5 = 0.2 and

1/6 = 0.166....

The decimal value of 1/5 is 0.2, which is closest to 0.213.

Question 13 :

In a triangle ABC, CD bisects angle ACB. Compute the value of x + y, in degrees.

(A) 45 (B) 70 (C) 80 (D) 110 (E) 135

Solution :

<ADC + <CDB = 180

70 + <CDB = 180

<CDB = 180 - 70 ==> 110

In triangle CDB,

<CDB + <DBC + <BCD = 180

110 + 45 + y = 180

y = 180 - 155

y = 25

<ACD + <DCB = <ACB

<ACB = 50

In triangle ACB,

<CAB + <ACB + <CBA = 180

x+50+45 = 180

x+95 = 180

x = 180-95

x = 85

x+y = 85+25

x+y = 110

Hence the answer is 110.

Question 14 :

The consecutive odd primes, such as 11 and 13 are, are called a pair of "twin primes". How many pairs of twin primes are there between 15 and 45.

(A) 2 (B) 3 (C) 4 (D) 5 (E) 7

Solution :

17 and 19 - Twin primes

29 and 31 - Twin primes

41 and 43 - Twin primes

Hence there are 3 twin primes lies between 15 and 45.

Question 15 :

For any number x, the symbol ⌈x⌉ means the smallest integer that is greater than or equal to x. For example ⌈3.2⌉ is 4. what is √156.3 ?

(A) 11 (B) 12 (C) 13 (D) 156 (E) 157

Solution :

⌈3.2⌉ = 4

√156.3 = ⌈12.51⌉ = 13

Hence the answer is 13.

Question 16 :

Eight years from now, Oana will be twice as old as her brother is now. Oana is now 12 years old. How old is her brother now ?

(A) 2 (B) 4 (C) 6 (D) 10 (E) 16

Solution :

Let x be Oana's brother's age.

After 8 years :

Oana's age + 8 = 2x

12 + 8 = 2x

2x = 20

x = 20/2 = 10 years

Hence the answer is 10 years.

Question 17 :

Suppose a snail crawls 2/5 inch per second. At this rate, what is the total number of inches the snail crawls in 2 minutes ?

(A) 48 (B) 30 (C) 24 (D) 5 (E) 4/5

Solution :

2 minutes = 120 seconds

Number of inches the snail crawls = 120 (2/5)

= 24 (2)

= 48 inches

Question 18 :

The straight line graph shows the relationship between the number of tickets sold and amount of money in the cash register if the register contained $150 before any tickets were sold. What is the price of 1 ticket.

x axis = no of tickets sold, y axis in cash register

(A) $100 (B) $20 (C) $15 (D) 12.50 (E) $10

Solution :

Cost of 1 ticket = "x"

From the graph,

30 x = 600

x = 600/30

x = 20

Hence the price of 1 ticket is $20.

Question 19 :

If 15 - 2x < 7, then for all possible values of x that make the inequality true.

(A) x < 8 (B) x > 8 (C) x > 4 (D) x < 4 (E) x > 1/4

Solution :

15 - 2x <7

Subtract 15 on both sides

-2x < 7 - 15

-2x < -8

Divide both sides by -2.

x > 4 (Since we divide by negative sign, we have to flip the inequality sign).

Question 20 :

Four congruent circles are enclosed in a square as shown. The perimeter of the square is 64. What is the circumference of one of the circles (in terms of π)