# HARDEST SAT MATH QUESTIONS (Part - 3)

Question 1 :

If a is an odd integer and b is an even integer, which of the following is an odd integer ?

(A) 3b     (B) a + 3     (C) 2(a + b)     (D) a + 2b

It is given that 'a' is an odd integer 'b' is an even integer.

Then, let a = 1 and b = 2.

3b  =  3(2)  =  6 (even) ----(A) is incorrect.

a + 3  =  1 + 3  =  4 (even) ----(B) is incorrect

2(a + b)  =  2(1 + 2)  =  2(3)  =  6 (even) ----(C) is incorrect

a + 2b  =  1 + 2(2)  =  1 + 4  =  5(odd) ----(D) is correct

So, the correct answer is (D).

Question 2 :

If √x + √y = 4√y, where x > 0 and y > 0, what is x in terms of y?.

(A) 16y         (B) 9y         (C) 6y         (D) 4y

√x + √y  =  4√y

Subtract √y from each side.

√x  =  3√y

Square each side to get rid of the square root.

(√x)2  =  (3√y)2

x  =  32(√y)2

x  =  9y

So, the correct answer is (B).

Question 3 :

Alma bought a laptop computer at a store that gave a 20 percent discount off its original price. The total amount she paid to the cashier was p dollars, including an 8 percent sales tax on the discounted price. Which of the following represents the original price of the computer in terms of p?

(A) 0.88p   (B) p/0.88   (C) (0.8)(1.08)p   (D) p/[(0.8)(1.08)]

Let x represent the original price of the computer.

After 20 % discount, the price is

=  0.8x

After 8 % sales tax, the price is

=  (1.08)(0.8)x

The final price of the computer is (1.08)(0.08)x.

Then,

(1.08)(0.08)x  =  p

Divide each side by (0.08)(1.08).

x  =  p/[(0.8)(1.08)]

So, the correct answer is (D).

Question 4 :

A high school counselor conducted a study over consecutive quarters to determine the number of students with part-time jobs. Each student in the 2014 graduating class is surveyed once per quarter for all four years of high school. The graph below shows the data for each quarter the survey was conducted. During which of the following periods is the increase in the number of students with part-time jobs largest?

A) Quarters 4 through 6

B) Quarters 7 through 10

C) Quarters 11 through 14

D) Quarters 13 through 16

When we compare the graph and given options, it is clear  that the increase in the number of students with part-time jobs largest is quarters 7 through 10.

Because the slope of the curve in the above graph is largest between the quarters 7 and 10.

So, the correct answer is (B).

Question 5 :

According to the Department of Agriculture, consuming 100 grams of banana provides 0.15 milligram of zinc. Which of the following is closest to the number of milligrams of zinc provided by 140 grams of banana?

(A) 0.15         (B) 0.21         (C) 0.25         (D) 0.93

Given : 100 grams of banana provides 0.15 milligram of zinc.

Amount of zinc in 1 gram of banana :

=  0.15/100

Amount of zinc in 140 gram of banana :

=  140(0.15/100)

=  0.21

So, the correct answer is (B).

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