SHSAT MATH TEST WITH ANSWERS

Question 1 :

(16 + 5x) – (8 – 2x) =

(A)  8 + 3x  (B)  8 - 3x (C)  8 - 7x

(D)  8 + 7x (E)  24 - 7x

Solution :

  =   (16 + 5x) – (8 – 2x)

  =  16 + 5x - 8 + 2x

  =  8 + 7x

Hence the answer is 8 + 7x.

Question 2 :

The three lines shown intersect in a point.  The value of x

(A)  is 100.  (B)  is 80.  (C)  is 50.  (D)  is 20. 

(E)  cannot be determined from the given information

Solution :

x + 60 + 40  =  180

x + 100  =  180

x  =  180 - 100

x  =  80

Hence the required angle is 80.

Question 3 :

The straight line graph shows how many people are in a large cafeteria eating lunch at different times.  If the people leave at a steady rate, at what time will only 150 people remain?

(A)  1:15 P.M.  (B)  1:30 P.M.  (C)  1:45 P.M. 

(D)  2:15 P.M.  (E)  3:30 P.M.

Solution :

For every half an hour, we are losing 100 people 

At 1 : 00 PM 300 people will remain, at 1 : 15 PM 350 people will remain.

Question 4 :

Two congruent circles have centers P and Q as shown.  What is the measure of angle PXQ?

(A)  30°  (B)  45°  (C)  55°  (D)  60°  (E)  75°

Solution :

Here PX is radius of the first circle, QX is the radius of the second circle. PQ is the distance between two centers.

PX  =  PQ  =  QX

Hence the required angle 60°.

Question 5 :

Andrew has d dollars.  He has one-third as many dollars as Bruce has.  Carlos has $80 less than half the total of Andrew’s and Bruce’s dollars.  In terms of d, how many dollars does Carlos have?

(A)  4d – 40  (B)  2d – 40  (C)  2d + 40 

(D)  2d + 80  (E)  2d – 80

Solution :

Andrew has d dollars. 

Bruce has 3d dollars

Number of dollars that Carlos has  =  (1/2)(d + 3d) - 80

  =  (1/2) 4d  - 80

  =  2d - 80

Hence the answer is 2d - 80.

Question 6 :

In the xy-plane, the graph of linear inequality contains the points (0, 2), (1, 1) and (4, 0). Which of the following could be the inequality ?

(A)  y ≤ (-1/2)x + 2  (B)  y ≥ (-1/2)x + 2  (C)  y ≤ -2x + 4 

(D)  y ≥ -2x + 4

Solution :

Option A :

y ≤ (-1/2)x + 2

Applying the given points one by one, we get

Since the given points satisfy the inequality, option A is correct.

Question 7 :

In 1947, milk cost $0.75 per gallon and bananas cost $0.15 per pound. Donna bought two gallons of milk and some bananas for a total of $2.25 in 1947. How many pounds of bananas did she buy?

Solution :

Cost of one gallon of milk = $0.75

Cost of two gallons of milk = 2 x 0.75

= 1.5

Let x be the number of bananas.

Cost of one banana = $0.15

Total cost = $2.25

2.25 = 0.15x + 1.5

Solving for x, we get

2.25 - 1.5 = 0.15x

0.15x = 0.75

x = 0.75/0.15

x = 5

So, the required number of bananas is 5.

Question 8 :

4x - 5y = 24

x - 2y = 3

If (x, y) is the solution to the system of equations above, what is the value of x ?

Solution :

4x - 5y = 24 ------(1)

x - 2y = 3 -----(2)

From (2), x = 3 + 2y

Applying the value of x in (1), we get

4(3 + 2y) - 5y = 24

12 + 8y - 5y = 24

3y = 24 - 12

3y = 12

y = 12/3

y = 4

Applying y = 4, we get

x = 3 + 2(4)

x = 3 + 8

x = 11

So, the value of x is 11.

Question 9 :

The length of line segment AB is 380. The length of line segment CD is 95% of the length of line segment AB. What is the length of line segment CD ? 

A) 285     B) 361    C) 380    D) 400

Solution :

Length of line segment AB = 380

Length of line segment = 95% of 380

= 0.95 (380)

= 361

So, option B is correct.

Question 10 :

The population density of Cedar County is 230 people per square mile. The county has a population of 85,100 people. What is the area, in square miles, of Cedar County?

Solution :

Ratio between number of people and number of square mile.

Let x be the number of square miles.

230 : 1 = 85100 : x

230/1 = 85100/x

x = 85100/230

x = 370

So, the required area is 370 square miles.

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