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 :
= πr^{2}h
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)^{2}h
= π(0.49r^{2})h
= 0.49(πr^{2}h)
= (49/100)(πr^{2}h)
= 49% of (πr^{2}h)
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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