PRACTICE PROBLEMS ON PERCENTAGE FOR SAT

Problem 1 :

In March, a city zoo attracted 32000 visitors to its polar bear exhibit. In April, the number of visitors to the exhibit increased by 15%. How many visitors did the zoo attract to its polar bear exhibit in April ?

a)  32,150     b)  32, 480     c)  35, 200     d)  36800

Solution :

Number of visitors in March = 32000

We should assume 32000 is 100% of visitors.

In the month of April 15% increased.

Number of visitors in the month of April = 115% of 32000

= 1.15(32000)

= 36800

Problem 2 :

Miguel is following a recipe for marinara sauce that requires half a table spoon of vinegar. If one cup is equivalent to 16 tablespoons approximately what percent of a cup of vinegar is the amount required by the recipe ?

a)  2.3%     b)  3.1%     c)  9.4%     d)  12.5%

Solution :

1 cup = 16 table spoons

To make a recipe, we need half a table spoon of vinegar

= (1/2)/16

= 0.5 / 16

Converting into percentage, we get

= (0.5 / 16) x 100%

= 0.03125x100%

= 3.125%

So, option b is correct.

Problem 3 :

If x is 50% larger than z, and y is 20% larger than z, then x is what percent larger than y ?

a)  15%      b) 20%        c)  25%       d) 30%

Solution :

Let z be the 100%.

x is 50% larger than z :

x = 150% of z

y is 20% larger than z :

y = 120% of z

x = how much larger than y ?

So, option b is correct.

Problem 4 :

Veronica has a bank account that earns m% interest compounded annually. If she opened the account with $200, the expression $200 (x)^t represents the amount in the account after t years. Which of the following gives x in terms of m ?

a)  1 + 0.01m      b) 1 + m       c)  1 - m      d)  1 + 100m

Solution :

p(x) = $200 (x)^t

x = 1 + m%

x = 1 + m/100

x = 1 + 0.01 m

So, option a is correct.

Problem 5 :

A charity organization collected 2140 donations last month. With the help of 50 additional volunteers, the organization collected 2690 donations this month, To the nearest tenth of a percent, what was the percent increase in the number of donations the charity organization collected ?

a)  20.4%      b)  20.7%    c)  25.4%      d)  25.7%

Solution :

Number of donations collected last month = 2140

Number of donations collected this month = 2690

Percentage increase = [(2690 - 2140)/2140] x 100%

= (550/2140) x 100%

= 0.257 x 100%

= 25.7%

So, option d is correct.

Problem 6 :

The discount price of  book is 20% less than the retail price. James manages to purchase the book at 30% off the discount price at a special book sale. What percent of the retail price did James pay ?

a)  42%     b)  48%    c)  50%     d)  56%

Solution :

Let x be the retail price.

Price after discount = 80% of x

Purchasing price by James = 30% of 80% of x

= 0.70(0.80 x)

= 0.56x

= 56% of x

So, option d is correct.

Problem 7 :

Each day, Robert eats 40% of the pistachios left in his jar at that time. At the end of the second day, 27 pistachios remain. How many pistachios were in the jar at the start of the first day ?

a)  75    b)  80     c) 85      d) 95

Solution :

Let x be the number of pistachios initially.

At the end of the first day 60% of x will be there. At the end of the second day 60% of (60% of x) will be there in jar.

60% of (60% of x) = 27

0.60 (0.60x) = 27

x = 27 / 0.60(0.60)

x = 75

So, 75 pistachios was there in the jar initially.

Problem 8 :

Joanne bought a doll at a 10 percent discount off the original price of $105.82. However, she had to pay a sales tax of x% on the discounted price. If the total amount she paid for the doll was $100, what is the value of x ?

a)  2    b)  3     c) 4      d) 5

Solution :

After 10% discount, amount paid by Joanne for the doll

90% of $105.82

= 0.90(105.82)

= 95.238

Amount paid including sales tax of x% on the discounted price.

95.238 + x% of 95.238 = 100

95.238(1+x%) = 100

1 + x% = 100/95.238

1 + x% = 1.050

x% = 1.050 - 1

x% = 0.050

x % = 5%

So, option d is correct,

Problem 9 :

In 2010, the number of houses built in Town A was 25 percent greater than the number of houses built in Town B. If 70 houses were built in Town A during 2010, how many were built in Town B ?

Solution :

Number of houses built in Town A in 2010 = 70

Let x be the number of houses built in Town B. Then,

125% of x = 70

x = 70/1.25

x = 56

So, number of houses built in Town B was 56.

Problem 10 :

Over a two week span, John ate 20 pounds of chicken wings and 15 pounds of hot dogs. Kyle at 20 percent more chicken wings and 40 percent more hot dogs. Considering only chicken wings and hot dogs. Kyle ate approximately x percent more food, by weight, than John. What is x(rounded to the nearest percent) ?

a)  25    b)   27      c)  29      d)  30

Solution :

Quantity of chicken wings ate by Kyle = 120% of 20

= 1.20(20)

= 24 pounds

Quantity of hot dogs ate by Kyle = 140% of 15

= 1.40(15)

= 21 pounds

Quantity of food ate by John = 20 + 15

= 35 pounds

Quantity of food ate by Kyle = 24 + 21

= 45 pounds

Percentage increase = [(45 - 35)/35] x 100%

= (10/35) x 100%

= 0.285 x 100%

= 28.5%

Approximately 29%