SAT MATH QUESTIONS PERCENTAGE

Question 1 :

Before a big test, James memorized 10 percent more words than Zach. Zach memorized 30 percent more words than Amy. If Amy memorized a words, how many words did James memorize in terms of a?

A) (1.10)(1.30a)

B) a/[(1.10)(1.30)]

C) a/[(0.9)(0.7)]

D) 1.40a

Answer :

Number of words memorized by Amy = a

Zach memorized 30 percent more words than Amy.

Number of words memorized by Zach :

= (100 + 30)% of a

= 130% of a

= 1.30a

James memorized 10 percent more words than Zach.

Number of words memorized by James :

= (100 + 10)% of 1.30a

= 110% of 1.30a

= (1.10)(1.30)a

The correct answer choice is (A).

Question 2 :

This year, Roger beat Rafael in 25% of their tennis matches. If Rafael won 18 matches, how many matches did Roger win?

A) 2

B) 3

C) 4

D) 6

Answer :

Given : Roger beat Rafael in 25% of their matches.

It means Roger won 25% and Rafael won 75% of their matches.

Let x be the total number matches between Roger and Rafael in this year.

It is given that Rafael won 18 matches.

75% of x = 18

0.75x = 18

Divide both sides by 0.75.

x = 24

This year, total number of matches between Roger and Rafael is 24 in which Rafael won 18 matches.

Number of matches won by Roger :

= 24 - 18

= 6

The correct answer choice is (D).

Question 3 :

The price of a textbook this year is 20% greater than the price last year. If this year's price is p, what was last year's price in terms of p?

A) (1/5)p

B) (4/5)p

C) (5/6)p

D) (6/5)p

Answer :

Let x be the price of the textbook last year.

Given : This year, the price is 20% greater than last year and p is the price for this year.

p = (100 + 20)% of x

p = 1.2x

p (12/10)x

p = (6/5)x

Multiply both sides by 5/6.

(5/6)p = x

The price of the textbook last year was (5/6)p.

The correct answer choice is (C).

Question 4 :

Taylor has a bank account earning 5 percent interest compounded annually. If her initial deposit was $1,000 and she makes a a withdrawal of $200 after 3 years, which of the following represents the total amount in her account after 7 years?

A) 1,000(1.05)⁷ - 200

B) 1,000(1.05)³ + 800(1.05)⁴

C) 1,000(1.05)³ - 200(1.05)⁴

D) 1,000(1.05)⁷ - 200(1.05)⁴

Answer :

Formula to find the final value of a deposit in compound interest when interest is compounded annually :

A = p(1 + r)^t

A ----> final value of the deposit

p ----> principal value

r ----> rate of interest

t ----> number of years

Calculate the final value of the deposit $1,000 for 7 years with 5 percent interest compounded annually.

Substitute p = 1000, r = 5/100 and  t = 7 in the above formula.

A = 1,000(1 + 5/100)⁷

= 1,000(1 + 0.05)⁷

= 1,000(1.05)⁷ ----(1)

Given : Taylor makes a withdrawal of $200 after three years. 

Since she makes a withdrawal of $200 after 3 years, we have to subtract $200 + interest (for the next 4 years) from the final value of the deposit after 7 years.

Value of the deposit $200 for 4 years :

A = 200(1 + 5/100)⁴

= 200(1 + 0.05)⁴

= 200(1.05)⁴ ----(2)

Subtract (2) from (1) to find the total amount in her account after 7 years.

= 1,000(1.05)⁷ - 200(1.05)⁴

The correct answer choice is (D).

Question 5 :

When a certain gas tank is 70% empty, it contains 12 gallons. How many gallons can a full tank hold?

A) 30

B) 36

C) 40

D) 42

Answer :

When the gas tank is 70% empty, 30% of the tank is filled.

Given : When the gas tank is 70% empty, it contains 12 gallons.

That is, 30% of the gas tank contains 12 gallons of gas.

Let x be the capacity of the tank.

30% x = 12

0.3x = 12

Divide both sides by 0.3

x = 40

So, a full tank can hold 40 gallons of gas.

The correct answer choice is (C).

Question 6 :

If M is 30% of N, N is 40% of O, and P is 50% of O, then what is the value of M/P?

A) 6/25

B) 3/10

C) 2/5

D) 3/5

Answer :

To find the value of M/P, we have to get the values of both M and P in terms of the same variable.

M is 30% of N :

M = 30% of N

M = 0.3N ----(1)

N is 40% of O :

N = 40% of O

N = 0.4O

Substitute N = 0.4O in (1).

M = 0.3(0.4O)

M = 0.12O ----(2)

P is 50% of O :

P = 50% of O

P = 0.5O ----(3)

(2) ÷ (3) :

M/P = 0.12O/0.5O

= 0.12/0.5

= 12/50

= 6/25

The correct answer choice is (A).

Question 7 :

Call center A handles 20% fewer calls than Call center B. Call center B handles 20% fewer calls than Call center C. If Call center A handles 1,200 calls, how many calls does Call center C handle?

Answer :

Let x be the number of calls handles by Call center C.

Given : Call center B handles 20% fewer calls than Call center C.

Number of calls handled by Call center B :

= (100 - 20)% of x

= 80% of x

= 0.8x

Given : Call center A handles 20% fewer calls than Call center B.

Number of calls handled by Call center A :

= (100 - 20)% of 0.8x

= 80% of 0.8x

= (0.8)(0.8x)

= 0.64x

Given : Call center A handles 1200 calls.

0.64x = 1200

Divide both sides by 0.64.

x = 1875

Call center C handles 1875 calls.

Question 8 :

If X is 20% of Y and Y is 30% of Z, then what percent of Z is X?

Answer :

Given : X is 20% of Y.

X = 0.2Y

Divide both sides by 0.2.

5X = Y

Given : Y is 30% of Z.

Y = 0.3Z

Substitute Y = 5X.

5X = 0.3Z

Divide both sides by 5.

X = 0.06Z

X = (6/100)Z

X = 6% of Z

6% of Z is X.

Question 9 :

A cylinder has a base radius of r and a height of h. If the radius is reduced by 30%, how would the volume of the cylinder change?

Answer :

Volume of a cylinder base radius of r and a height of h :

= πr²h

If the radius is decreased by 30%, then the new radius is 

= (100 - 30)% of r

= 70% of r

= 0.7r

Volume of the cylinder after the radius is reduced by 30% :

= π(0.7r)²h

= π(0.49r²)h

= 0.49(πr²h)

= (49/100)(πr²h)

= 49% of (πr²h)

100 - 49 = 51

Volume of the cylinder would decrease by 51%.

Question 10 :

A toy is on sale with 20% off. If the toy is sold for $38.40, find the original price of the toy.

Answer :

Let x be the original price of the toy.

It is given that the toy is sold for $38.40.

(100 - 20)% of x = 38.40

80% of x = 38.40

0.8x = 38.40

Divide both sides by 0.8.

x = 48

The original price of the toy is $48.

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