Question 1 :
A chemist mixes x mL of a 34% acid solution with a 10% acid solution. If the resulting solution is 40 mL with 25% acidity, what is the value of x?
(A) 18.5
(B) 20
(C) 22.5
(D) 25
Question 2 :
The price of a package of 4 pens is $8.00. The same pens are sold at $2.50 each. If Alex bought three packages of pens rather than buying 12 pens individually, the amount he saved on 12 pens is what percent of the amount he paid?
(A) 12%
(B) 20%
(C) 25%
(D) 30%
Question 3 :
There are 600 bottles of sports drinks in a store. 25% of the bottles are orange flavored drinks. On Monday 30% of the orange flavored drinks in the store were sold and on Tuesday 20% of the remaining orange flavored drinks were sold. How many bottles of orange flavored drinks were sold in the two days?
(A) 52
(B) 58
(C) 66
(D) 75
Question 4 :
A tablet with a list price of x dollars is discounted by 15% and then discounted an additional 12%. What is the final sale price of the tablet, in terms of x?
(A) 0.73x
(B) 0.748x
(C) 0.75x
(D) 0.765x
Question 5 :
There is a total of n pairs of shoes in a store, all of which are either black or brown. If there are m pairs of brown shoes in the store, then in terms of m and n, what percent of the shoes in the store are black?
(A) ᵐ⁄n%
(B) ⁽ⁿ ⁻ ᵐ⁾⁄n%
(C) (1 - ¹⁰⁰ᵐ⁄n)%
(D) 100(1 - ᵐ⁄n)%
Question 6 :
The numbers a, b, and c are positive and a equals 3.2bc. If b is increased by 150% and c is decreased by 60%, then a is
(A) increased by 90%
(B) increased by 10%
(C) unchanged
(D) decreased by 10%
Question 7 :
There are 10 history books in a bookcase. When the number of books increases by x percent, the new number of history books is 24. What is the value of x?
(A) 58
(B) 70
(C) 120
(D) 140
Question 8 :
Number n is 25 less than 120 percent of itself. What is the value of n?
(A) 125
(B) 120
(C) 105
(D) 90
Question 9 :
Of the 500 cars displayed in a certain car dealer, 7 percent are blue and 4 percent are red. The number of blue cars in the car dealer are what percent greater than the number of red cars?
(A) 30%
(B) 50%
(C) 75%
(D) 125%
Question 10 :
If 300% of 0.18 is equivalent to 20% of b, then b is equivalent to what number?
Question 11 :
Five people contributed $9,000 each toward the purchase of a sailboat. If they ended up paying $38,500 plus 8% sales tax for the boat, how much money should be refunded to each person?
Question 12 :
A store used to sell an MP3 for $72, which is 50% more than the wholesale cost. At a special holiday sale, the price of the MP3 was 20% less than the wholesale cost. What was the special sale price of the MP3?
1. Answer :
34% and 10% acid solutions are mixed to produce 40 mL of resulting solution.
34% acid solution ----> x mL
Resulting solution ----> 40 mL
10% acid solution ----> (40 - x) mL
Amount of acid in x mL of 34% acid solution :
= 34% of x
= 0.34x
Amount of acid in (40 - x) mL of 10% acid solution :
= 10% of (40 - x)
= 0.1(40 - x)
= 4 - 0.1x
After mixing both the solutions, amount of acid in the resulting solution :
= 0.34x + 4 - 0.1x
= 0.24x + 4
Given : Resulting solution has 25% acid.
0.24x + 4 = 25% of 40
0.24x + 4 = 0.25(40)
0.24x + 4 = 10
0.24x = 6
x = 25
Therefore, the correct answer is option (D).
2. Answer :
Cost of three packages of pens :
= 3 ⋅ $8
= $24
If pens are bought individually, the cost of 12 pens :
= 12 ⋅ $2.50
= $30
When pens are bought in packages, percent of savings :
= 25%
Therefore, the correct answer is option (C).
3. Answer :
Number of orange flavored drinks :
= 25% of 600
= 0.25(600)
150
Number of orange flavored drinks sold on Monday :
= 30% of 150
= 0.3(150)
= 45
Number of orange flavored drinks sold on Tuesday :
= 20% of (150 - 45)
= 0.2(105)
= 21
Number of orange flavored drinks sold in the two days :
= 45 + 21
= 66
Therefore, the correct answer is option (C).
4. Answer :
The price of the laptop is x dollars.
The price of the laptop after 15% discount :
= (100 - 15)% of x
= 85% of x
= 0.85x
The price of the laptop after additional 12% discount :
= (100 - 12)% of 0.85x
= 88% of 0.85x
= 0.88(0.85x)
= 0.748x
The final sale price of the tablet is 0.748x dollars
Therefore, the correct answer is option (B).
5. Answer :
Total number of shoes = n
Number of brown shoes = m
Number of black shoes = n - m
Percent of black shoes :
Therefore, the correct answer is option (D).
6. Answer :
a = 3.2bc
If b is increased by 150%,
= (100 + 150)% of b
= 250% of b
= 2.5b
If c is decreased by 60%,
= (100 - 60)% of c
= 40% of c
= 0.4c
a = 3.2(2.5b)(0.4c)
After changes,
a = 3.2(2.5b)(0.4c)
a = 3.2bc
The value of a is unchanged.
Therefore, the correct answer is option (C).
7. Answer :
There are 10 history books in a bookcase.
If the number of books increases by 10%, the new number of books is 24.
(100 + x)% of 10 = 24
⁽¹⁰⁰ ⁺ ˣ⁾⁄₁₀ = 24
100 + x = 240
x = 140
Therefore, the correct answer is option (D).
8. Answer :
Number n is 25 less than 120 percent of itself.
n = 120% of n - 25
n = 1.2n - 25
25 = 0.2n
125 = n
Therefore, the correct answer is option (A).
9. Answer :
Number of blue cars :
= 7% of 500.
= 0.07(500)
= 35
Number of red cars :
= 4% of 500.
= 0.04(500)
= 20
We have to find that the number of blue cars is what percent greater than the number of red cars.
So, we have to find the percentage increase from 20 to 35.
= 75%
Therefore, the correct answer is option (C).
10. Answer :
300% of 0.18 is equivalent to 20% of b
3(0.18) = 0.2b
0.54 = 0.2b
2.7 = b
11. Answer :
Total amount contributed by 5 people :
= 5 ⋅ $9,000
= $45,000
Purchase price of sailboat :
= $38,500 + 8% sales tax
= $38,500 + 0.08($38,500)
= $38,500 + $3,080
= $41,580
After purchase of sail boat, remaning amount of money:
= $45,000 - $41,580
= $3,420
Amount of money should be refunded to each person :
= ^{$}³⁴²⁰⁄₅
= $684
12. Answer :
Let x be the wholesale cost of the MP3.
(100 + 50)% of x = 72
150% of x = 72
1.5x = 72
x = 48
Given : At a special holiday sale, the price of the MP3 was 20% less than the wholesale cost.
Special price of the MP3 :
= (100 - 20)% of 48
= 80% of 48
= 0.8(48)
= $38.4
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