Whole and Part - ISEE Middle Level Quantitative Reasoning
Card 0 of 775
Albert sent a letter to his penpal everyday for the entire month of January and February. How many letters did Albert send his penpal?
Albert sent a letter to his penpal everyday for the entire month of January and February. How many letters did Albert send his penpal?
Add the total days in January and February:
Answer: Albert sent his penpal 59 letters.
Add the total days in January and February:
Answer: Albert sent his penpal 59 letters.
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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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After a discount of 20%, a boom box costs $144.
Which is the greater quantity?
(a) The price of the boom box before the discount
(b) $172.80
After a discount of 20%, a boom box costs $144.
Which is the greater quantity?
(a) The price of the boom box before the discount
(b) $172.80
Paying for something at 20% discount is the same as paying for it at 80% of the price.
If the boom box costs $172.80 before a 20% discount, then afterward, it costs 80% of this, or
Therefore, the original price must have been greater than $172.80.
Paying for something at 20% discount is the same as paying for it at 80% of the price.
If the boom box costs $172.80 before a 20% discount, then afterward, it costs 80% of this, or
Therefore, the original price must have been greater than $172.80.
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Using the information given in each question, compare the quantity in Column A to the quantity in Column B.
Column A Column B
120% of 80% of 100 130% of 70% of 105
Using the information given in each question, compare the quantity in Column A to the quantity in Column B.
Column A Column B
120% of 80% of 100 130% of 70% of 105
Remember that "percent" means "per 100" and "of" means to multiply.
So 120% of 80% of 100 =
and 130% of 70% of 105 =
Column A is greater.
Remember that "percent" means "per 100" and "of" means to multiply.
So 120% of 80% of 100 =
and 130% of 70% of 105 =
Column A is greater.
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Which is the greater quantity?
(a) 
(b) 
Which is the greater quantity?
(a)
(b)
can be rewritten as 
, and restated as 
.
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is a positive number. Which of the following is the greater quantity?
(A) 50% of 
(B) 20% of 
(A) 50% of
(B) 20% of
50% of 
is equal to 
.
20% of 
is equal to 
Since 
is positive and 
,
,
and (B) is greater.
50% of
20% of
Since
and (B) is greater.
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What is 60% of 60% of 25,000?
What is 60% of 60% of 25,000?
60% of 25,000 is equal to 
60% of that is 
60% of 25,000 is equal to
60% of that is
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Katie collects trading cards. 15% of her collection are rare cards. If there are a total of 500 cards in Katie's collection, how many of them are rare?
Katie collects trading cards. 15% of her collection are rare cards. If there are a total of 500 cards in Katie's collection, how many of them are rare?
To begin, you can set up a proportion:
When trying to find a percent of a number, convert the percent into a decimal. To do this, divide the percent by 100.
You then multiply 500 by 0.15. Since 500 represents 100% of Katie's cards, multiplying by 0.15 will give you how many cards equal 15% of the total.
The result is your answer.
To begin, you can set up a proportion:
When trying to find a percent of a number, convert the percent into a decimal. To do this, divide the percent by 100.
You then multiply 500 by 0.15. Since 500 represents 100% of Katie's cards, multiplying by 0.15 will give you how many cards equal 15% of the total.
The result is your answer.
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What is 10% of 30% of 100?
What is 10% of 30% of 100?
This question asks you to find a percentage of a smaller part of 100. You must first figure out what the smaller part of 100 equals. Since percents are based off of 100, 30% of 100 is the number 30. You must then find 10% of this number.
To do this, multiply 30 times 10%. First, divide the percentage by 100.
Multiply the result times 30.
The new result is your answer.
This question asks you to find a percentage of a smaller part of 100. You must first figure out what the smaller part of 100 equals. Since percents are based off of 100, 30% of 100 is the number 30. You must then find 10% of this number.
To do this, multiply 30 times 10%. First, divide the percentage by 100.
Multiply the result times 30.
The new result is your answer.
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Amir will be selling 20% of his stamp collection. If he has 60 stamps now, how many will he have after he sells some of his stamps?
Amir will be selling 20% of his stamp collection. If he has 60 stamps now, how many will he have after he sells some of his stamps?
If Amir gets rid of 20% of his cards, he will only have 80% of his cards remaining afterwards.
Therefore, we can figure out how many cards Amir will have after selling 20% of his cards by multiplying times 80% since that will be the amount of cards he will have left, compared to the original number.
To do this, first divide the percentage by 100.
Then, multiply the result of this times 60.
The result is your answer.
If Amir gets rid of 20% of his cards, he will only have 80% of his cards remaining afterwards.
Therefore, we can figure out how many cards Amir will have after selling 20% of his cards by multiplying times 80% since that will be the amount of cards he will have left, compared to the original number.
To do this, first divide the percentage by 100.
Then, multiply the result of this times 60.
The result is your answer.
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A store is having a 40% off clearance sale on items of clothing. Rosa bought a new dress from this store. If the dress's original price was $80, how much did Rosa pay?
A store is having a 40% off clearance sale on items of clothing. Rosa bought a new dress from this store. If the dress's original price was $80, how much did Rosa pay?
If the store sells the dress for 40% off, that means it is worth 60% of its original price.
Therefore, if you multiply 60% times the original price of the dress, you will know what the current price of the dress is.
To do this, first divide your percentage by 100.
Then, multiply the result of this times the original price of the dress.
The new result is your answer.
If the store sells the dress for 40% off, that means it is worth 60% of its original price.
Therefore, if you multiply 60% times the original price of the dress, you will know what the current price of the dress is.
To do this, first divide your percentage by 100.
Then, multiply the result of this times the original price of the dress.
The new result is your answer.
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What is 60% of 120?
What is 60% of 120?
In order to figure out what 60% of 120 is, multiply 60% by 120. To do this, first divide your percentage by 100.
Then, multiply the result times 120.
The new result is your answer.
In order to figure out what 60% of 120 is, multiply 60% by 120. To do this, first divide your percentage by 100.
Then, multiply the result times 120.
The new result is your answer.
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A clothing store discounted a shirt by 25% one week. The following week, they discounted that new price by another 20% What is currently the price of the shirt if it originally cost $20?
A clothing store discounted a shirt by 25% one week. The following week, they discounted that new price by another 20% What is currently the price of the shirt if it originally cost $20?
If the clothing store discounts an already discounted price, it means that we are trying to find a percentage of an already smaller part of the original number. First, if the original discount was 25%, that means that the shirt was sold for 75% the original price the first week.
So, we must first figure out what the shirt was worth at 75% the original price. To do this, divide the percentage by 100.
Multiply the result times the original price of the shirt.
This is the price of the shirt after the first discount. This new price is then discounted by another 20%. So, the newest price will be 80% of the value of the first discount.
To find out what the price is after this is done, multiply the percentage by the new price. So, first divide the percentage by 100.
Multiply this result by the discounted price.
The result is your answer.
If the clothing store discounts an already discounted price, it means that we are trying to find a percentage of an already smaller part of the original number. First, if the original discount was 25%, that means that the shirt was sold for 75% the original price the first week.
So, we must first figure out what the shirt was worth at 75% the original price. To do this, divide the percentage by 100.
Multiply the result times the original price of the shirt.
This is the price of the shirt after the first discount. This new price is then discounted by another 20%. So, the newest price will be 80% of the value of the first discount.
To find out what the price is after this is done, multiply the percentage by the new price. So, first divide the percentage by 100.
Multiply this result by the discounted price.
The result is your answer.
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What is 75% of 25% of 48?
What is 75% of 25% of 48?
The question asks you to find 75% of a smaller part of 48. In order to figure this out, you must first figure out what the value of the smaller part is. To figure out what 25% of 48 is, multiply 48 by 25%. First, divide the percentage by 100.
Then, multiply 48 by the result.
The second part of the question asks you to figure out what 75% of this new number is. Just like before, first divide the percentage by 100.
Then, multiply the result times 12.
The result is the answer.
The question asks you to find 75% of a smaller part of 48. In order to figure this out, you must first figure out what the value of the smaller part is. To figure out what 25% of 48 is, multiply 48 by 25%. First, divide the percentage by 100.
Then, multiply 48 by the result.
The second part of the question asks you to figure out what 75% of this new number is. Just like before, first divide the percentage by 100.
Then, multiply the result times 12.
The result is the answer.
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