Percentage - ISEE Middle Level Quantitative Reasoning
Card 0 of 20
Using the information given in each question, compare the quantity in Column A to the quantity in Column B.
Jack scores a 40 on his first test and improves his score by 80% on his second test. Jill scores 50 on her first test, and her second test is 130% of her first test.
Column A Column B
Jack's 2nd Jill's 2nd
test score test score
Using the information given in each question, compare the quantity in Column A to the quantity in Column B.
Jack scores a 40 on his first test and improves his score by 80% on his second test. Jill scores 50 on her first test, and her second test is 130% of her first test.
Column A Column B
Jack's 2nd Jill's 2nd
test score test score
Jack improves by 80%, so we multiply his original score by 1.8 (the 1 to represent his earlier score and the .8 to add on his improvement). 40% times 1.8 equals 72%.
Jill's second test is 130% of her first test (that is, a 30% improvement). To find her new score we multiply her first score by 1.3. 50% times 1.3 equals 65%.
Thus, Jack's second test score is higher.
Jack improves by 80%, so we multiply his original score by 1.8 (the 1 to represent his earlier score and the .8 to add on his improvement). 40% times 1.8 equals 72%.
Jill's second test is 130% of her first test (that is, a 30% improvement). To find her new score we multiply her first score by 1.3. 50% times 1.3 equals 65%.
Thus, Jack's second test score is higher.
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1,111 is 
of 999
999 is 
of 1,111
Which is the greater quantity?
(a) 
(b) 
1,111 is
999 is
Which is the greater quantity?
(a)
(b)
No calculation is necessary. In (a), the part is greater than the whole, so the percent 
must be greater than 100. In (b) The part is less than the whole, so 
must be less than 100. Therefore, 
No calculation is necessary. In (a), the part is greater than the whole, so the percent
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of 2,001 is 1
of 1,999 is 1
Which is the greater quantity?
(a) 
(b) 
Which is the greater quantity?
(a)
(b)
No calculation is necessary. The whole in (b) is less, so 1 is a greater portion of that whole than the whole in (a). This makes (b) greater.
No calculation is necessary. The whole in (b) is less, so 1 is a greater portion of that whole than the whole in (a). This makes (b) greater.
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Which is the greater quantity?
(a) 
(b) 
Which is the greater quantity?
(a)
(b)
can be rewritten as 
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There were 48 pieces of fruit brought to the brunch. Twelve of the pieces of fruit were bananas. What percentage of the fruit were bananas?
There were 48 pieces of fruit brought to the brunch. Twelve of the pieces of fruit were bananas. What percentage of the fruit were bananas?
Percentage involves part over whole. The total number of fruit was 48. The number of bananas was 12. Therefore, you can make a fraction from those numbers: 
. Then, to find the percentage, divide 12 by 48. This gives you 0.25. To find the percentage, move the decimal point to the right two places. This gives you 25%.
Percentage involves part over whole. The total number of fruit was 48. The number of bananas was 12. Therefore, you can make a fraction from those numbers:
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70% of 4,000 is equal to what percent of 6,400?
70% of 4,000 is equal to what percent of 6,400?
70% of 4,000 is equal to 
, which is
percent of 6,400.
Evaluate:
The correct response is 
70% of 4,000 is equal to
Evaluate:
The correct response is
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What is 0.5% of 1,000,000?
What is 0.5% of 1,000,000?
Convert the percentage to a decimal:
Multiply by 1,000,000 to get our answer.
Convert the percentage to a decimal:
Multiply by 1,000,000 to get our answer.
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What is 200% of 1,000?
What is 200% of 1,000?
Convert the percentage to a decimal.
Multiply 1,000 by the decimal value to find the answer.
Convert the percentage to a decimal.
Multiply 1,000 by the decimal value to find the answer.
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is a positive number. Which of the following is the greater quantity?
(A) 70% of 40% of
(B) 40% of 70% of
(A) 70% of 40% of
(B) 40% of 70% of
40% of a number is the number multplied by 0.40; 70% of the number is the number multiplied by 0.70.
40% of is 
; 70% of that is 
70% of is 
; 40% of that is 
Regardless of the value of 
, the quantities are equal.
40% of a number is the number multplied by 0.40; 70% of the number is the number multiplied by 0.70.
40% of
70% of
Regardless of the value of
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is a positive integer. Which is the greater quantity?
(A) 25% of 
(B) 50% of 
(A) 25% of
(B) 50% of
The greater of the two can be shown to depend on the value of 
.
Example 1: 
Then 25% of 
is equal to
and 50% of 
is equal to
This makes (A) greater.
Example 2: 
Then 25% of 
is equal to
and 50% of 
is equal to
This makes (B) greater.
Therefore, insufficient information is given in the problem to determine which is the greater.
The greater of the two can be shown to depend on the value of
Example 1:
Then 25% of
and 50% of
This makes (A) greater.
Example 2:
Then 25% of
and 50% of
This makes (B) greater.
Therefore, insufficient information is given in the problem to determine which is the greater.
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is a positive number. Which is greater?
(A) 60% of 40% of 
(B) 50% of 50% of 
(A) 60% of 40% of
(B) 50% of 50% of
40% of 
is equal to 
; 60% of that is 
50% of 
is equal to 
; 50% of that is 
Since 
is positive and 
,
,
and (B) is greater.
40% of
50% of
Since
and (B) is greater.
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is positive.
Which is the greater quantity?
(A) Three multiplied by 75% of 
(B) Six multiplied by 35% of 
Which is the greater quantity?
(A) Three multiplied by 75% of
(B) Six multiplied by 35% of
75% of 
is 
; three multiplied by this is
.
35% of 
is 
; six multiplied by this is
.
Since 
and 
is positive, 
, so (A) is greater regardless of the value of 
.
75% of
35% of
Since
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There is a total of 50 houses in a neighborhood. 20 of the houses have red roofs and 15 of the houses have black roofs. The rest of the houses have green roofs. What percentage of the houses have green roofs?
There is a total of 50 houses in a neighborhood. 20 of the houses have red roofs and 15 of the houses have black roofs. The rest of the houses have green roofs. What percentage of the houses have green roofs?
If there are a total of 50 houses and the total of red and black roofed houses is 35, there must be 15 green houses in this neighborhood.
To figure out what percentage a number makes up of any larger amount, divide the part by the whole. Since there are 15 green roofed houses, you should divide 15 by 50.
When you multiply the decimal by 100, your result will be the percentage the smaller number makes up of the larger amount.
Therefore, the answer is 30%
If there are a total of 50 houses and the total of red and black roofed houses is 35, there must be 15 green houses in this neighborhood.
To figure out what percentage a number makes up of any larger amount, divide the part by the whole. Since there are 15 green roofed houses, you should divide 15 by 50.
When you multiply the decimal by 100, your result will be the percentage the smaller number makes up of the larger amount.
Therefore, the answer is 30%
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There is a total of 50 houses in a neighborhood. 20 of the houses have red roofs and 15 of the houses have black roofs. The rest of the houses have green roofs. What percentage of the houses have black roofs?
There is a total of 50 houses in a neighborhood. 20 of the houses have red roofs and 15 of the houses have black roofs. The rest of the houses have green roofs. What percentage of the houses have black roofs?
To figure out what percentage a number makes up of any larger amount, divide the part by the whole. Since there are 15 black roofed houses, you should divide 15 by 50.
When you multiply the decimal by 100, your result will be the percentage the smaller number makes up of the larger amount.
Therefore, the answer is 30%
To figure out what percentage a number makes up of any larger amount, divide the part by the whole. Since there are 15 black roofed houses, you should divide 15 by 50.
When you multiply the decimal by 100, your result will be the percentage the smaller number makes up of the larger amount.
Therefore, the answer is 30%
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On a farm, there are 12 pigs, 10 cows, and 8 horses. What percent of the animals are pigs?
On a farm, there are 12 pigs, 10 cows, and 8 horses. What percent of the animals are pigs?
In order to figure out what percentage a number is of a larger amount, divide the smaller number by the larger one.
Since there are 12 pigs, divide 12 by 30, the total.
When you multiply the decimal by 100, you are left with your percent.
In order to figure out what percentage a number is of a larger amount, divide the smaller number by the larger one.
Since there are 12 pigs, divide 12 by 30, the total.
When you multiply the decimal by 100, you are left with your percent.
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A school board plans to renovate one of its schools in order to make room for more people. After the renovation, the school's maximum capacity will increase by 20%. If the school's current maximum capacity is 1020 people, what will its maximum capacity be after the renovation?
A school board plans to renovate one of its schools in order to make room for more people. After the renovation, the school's maximum capacity will increase by 20%. If the school's current maximum capacity is 1020 people, what will its maximum capacity be after the renovation?
A 20% increase is equal to 120% of the original value. To figure out how much more space the building will have if expanded 20%, you must multiply the existing maximum capacity (1020) by 120%. To do this, first divide 120 by 100.
Then, multiply the result times the existing maximum capacity.
The result is your answer.
A 20% increase is equal to 120% of the original value. To figure out how much more space the building will have if expanded 20%, you must multiply the existing maximum capacity (1020) by 120%. To do this, first divide 120 by 100.
Then, multiply the result times the existing maximum capacity.
The result is your answer.
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What is 5 more than 20% of 20?
What is 5 more than 20% of 20?
The question asks you to find 5 more than 20% of 20. In other words, what is 20% of 20 plus 5.
First, multiply 20 times 20%. To do this, divide 20% by 100:
Multiply your result times 20:
4 is 20% of 20.
Add 5 to this number.
The question asks you to find 5 more than 20% of 20. In other words, what is 20% of 20 plus 5.
First, multiply 20 times 20%. To do this, divide 20% by 100:
Multiply your result times 20:
4 is 20% of 20.
Add 5 to this number.
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What percentage of 12 is 3?
What percentage of 12 is 3?
We can start to solve by setting up a proportion:
In order to figure out what percentage a smaller makes up of a larger value, divide the smaller number by the larger one. So, divide 3 by 12.
Multiply the result of this operation by 100. The new result will be your percentage.
We can start to solve by setting up a proportion:
In order to figure out what percentage a smaller makes up of a larger value, divide the smaller number by the larger one. So, divide 3 by 12.
Multiply the result of this operation by 100. The new result will be your percentage.
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What is the percent change from 20 to 25?
What is the percent change from 20 to 25?
Given that the change between 20 and 25 is an increase in 5 from the base of 20, the first step is to calculate the fractional increase.
Given that 
, there is a 25 percent increase. Thus, "25 percent increase" is the correct answer.
Given that the change between 20 and 25 is an increase in 5 from the base of 20, the first step is to calculate the fractional increase.
Given that
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What is the percent change from 60 to 54?
What is the percent change from 60 to 54?
The change from 60 to 54 is a decrease in 6 from the base of 60.
Given that 
, there is a 10 percent decrease. Thus, "10 percent decrease" is the correct answer.
The change from 60 to 54 is a decrease in 6 from the base of 60.
Given that
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