HARDEST SAT MATH QUESTIONS (Part - 5)

Question 1 :

x/2 - y/4  =  10

x/8 - y/8  =  19

Which ordered pair (x, y) satisfies the system of equations above?

(A) (-112, -264) 

(B) (64, 88)   

(C) (232/3, 224/3)   

(D) (288, 536)

Answer : 

Simplify the first equation :

x/2 - y/4  =  10

The least common multiple of the denominators 2 and 4 is 4. 

So, multiply each side by 4 to get rid of the denominators.

2x - y  =  40 ----(1)

Simplify the second equation :

x/8 - y/8  =  19

Multiply each side by 8 to get rid of the denominators.

x - y  =  152 ----(2)

Solve (1) and (2) for x and y.

(1) - (2) : 

x  =  -112

Substitute -122 for x in (2). 

-112 - y  =  152

Add 122 to each side. 

-y  =  264

Multiply each side -1.

y  =  -264

The solution to the above system of equation is

(-112, -264)

So, the correct answer is (A). 

Question 2 :

Point P is the center of the circle in the figure above. What is the value of x ?

Answer : 

The measure of an angle inscribed in a circle is half the measure of the central angle that intercepts the same arc.

m∠BAC  =  x°/2

The measures of interior angles of the quadrilateral ABPC  : 

m∠A  =  x°/2

m∠B  =  20°

m∠P  =  360° - x°

m∠C  =  20°

Sum of the interior angles of a quadrilateral  =  360°

m∠A + m∠B + m∠P + m∠C  =  360°

x/2 + 20 + 360 - x + 20  =  360

Simplify. 

x/2 - x + 400  =  360

Subtract 400 from each side. 

x/2 - x  =  -40

(x - 2x)/2  =  -40

-x/2  =  -40

Multiply each side -2.

Question 3 :

Tyra subscribes to an online gaming service that charges a monthly fee of $5.00 and $0.25 per hour for time spent playing premium games. Which of the following functions gives Tyra’s cost, in dollars, for a month in which she spends x hours playing premium games?

A. C(x) = 5.25x

B. C(x) = 5x + 0.25

C. C(x) = 5 + 0.25x

D. C(x) = 5 + 25x

Answer : 

It is given that $0.25 per hour for time spent playing premium games. 

If Tyra spends x hours playing premium games, then she pas to pay 0.25x.

Apart from this, she has to pay a monthly fee of $5.00. 

Then, the total cost in in dollars for the month, Tyra spends x hours playing premium games is given by the function :

C(x)  =  5 + 0.25x

So, the correct answer is (C). 

Question 4 :

On Saturday afternoon, Armand sent m text messages each hour for 5 hours, and Tyrone sent p text messages each hour for 4 hours. Which of the following represents the total number of messages sent by Armand and Tyrone on Saturday afternoon?

(A) 9mp        B) 20mp        (C) 5m + 4p        (D) 4m + 5p

Answer : 

Armand ----> m messages/hr for 5 hours

Number of messages sent by Armond in 5 hours  =  5m

Tyrone ----> p messages/hr for 4 hours

Number of messages sent by Tyrone in 4 hours  =  4p

Total number of messages sent by Armand and Tyrone : 

=  5m + 4p

So, the correct answer is (C). 

Question 5 :

Kathy is a repair technician for a phone company. Each week, she receives a batch of phones that need repairs. The number of phones that she has left to fix at the end of each day can be estimated with the equation

P = 108 - 23d,

where P is the number of phones left and d is the number of days she has worked that week. What is the meaning of the value 108 in this equation?

(A) Kathy will complete the repairs within 108 days.

(B) Kathy starts each week with 108 phones to fix.

(C) Kathy repairs phones at a rate of 108 per hour.

(D) Kathy repairs phones at a rate of 108 per day.

Answer : 

In the equation P = 108 - 23d, if d = 0, p = 108. That is, if Kathy has worked 0 days that week, the number of phones left to fix is 108.

In other words, before Kathy starts work for the week, the number of phones left to fix is 108.

It is clear that Kathy starts each week with 108 phones to fix. 

So, the correct answer is (B). 

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