Percentage - ISEE Middle Level Quantitative Reasoning
Card 0 of 2255
Harvey bought a suit at a 25% employee discount at the store where he works. The suit originally cost $350.00. How much did he end up paying?
Harvey bought a suit at a 25% employee discount at the store where he works. The suit originally cost $350.00. How much did he end up paying?
Finding 25% of a number is the same as multiplying it by 0.25; to get the discount, multiply 0.25 by the original purchase price of $350.00
To get the price Harvey paid, subtract the discount from the original price:
Finding 25% of a number is the same as multiplying it by 0.25; to get the discount, multiply 0.25 by the original purchase price of $350.00
To get the price Harvey paid, subtract the discount from the original price:
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is a positive integer. Which is the greater quantity?
(a) The remainder if 
is divided by 5
(b) The remainder if 
is divided by 4
(a) The remainder if
(b) The remainder if
The information is insufficient.
For example, if 
:
.
.
This gives the division in (b) the greater remainder.
But if 
:
.
.
This gives the division in (a) the greater remainder.
The information is insufficient.
For example, if
This gives the division in (b) the greater remainder.
But if
This gives the division in (a) the greater remainder.
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Which of the following is true if 
?
Which of the following is true if
Two expressions are equivalent in modulo 9 arithmetic if and only if, when each is divided by 9, the same remainder is yielded.
,
so
, so
is the correct choice.
Two expressions are equivalent in modulo 9 arithmetic if and only if, when each is divided by 9, the same remainder is yielded.
so
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is a positive even integer. Which is the greater quantity?
(a) The remainder if 
is divided by 6
(b) The remainder if 
is divided by 3.
(a) The remainder if
(b) The remainder if
Since 
is an even integer, by definition, there is an integer 
such that
.
; therefore,
; the remainder is 0.
Also,
; the remainder is 0.
The two remainders are both equal to 0.
Since
Also,
The two remainders are both equal to 0.
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is a positive odd integer. Which is the greater quantity?
(a) The remainder if is divided by 8
(b) The remainder if 
is divided by 4
(a) The remainder if
(b) The remainder if
, with a remainder of 0.
If 
were to yield a remainder of 0, then 
must be a whole number; this can only happen if 
is even. Since 
is odd, it follows that 
is not a whole number, and 
must yield a nonzero remainder. (a) must be the greater quantity.
If
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150% of what number is 9,000?
150% of what number is 9,000?
Taking 150% of a number is the same as multiplying that number by 1.5. We can find our number, therefore, by dividing 9,000 by 1.5:
Taking 150% of a number is the same as multiplying that number by 1.5. We can find our number, therefore, by dividing 9,000 by 1.5:
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is a multiple of 2, but not a multiple of 6. If 
is divided by 6, What could be the remainder?
If the remainder of dividing 
by 6 is 0, then 
must be a multiple of 6, which contradicts what we are given.
Suppose we call 
and 
the quotient and remainder, respectively, of dividing 
by 6. Then
If the remainder is 1, then
, as a product of two integers, one even, is an even number; if 1 is added, the result is odd. Therefore, if 1 is the remainder, 
is odd, which also contradicts what we are given about 
. 1 cannot be the remainder, and for similar reasons, neither can 3.
This leaves 2, which can be the remainder; for example, 8, which is a multiple of 2, but not a multiple of 6, yields a quotient of 1 and a remainder of 2 when divided by 2.
If the remainder of dividing
Suppose we call
If the remainder is 1, then
This leaves 2, which can be the remainder; for example, 8, which is a multiple of 2, but not a multiple of 6, yields a quotient of 1 and a remainder of 2 when divided by 2.
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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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