Whole and Part - ISEE Middle Level Quantitative Reasoning

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.

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.

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.

, 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.

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.

can be rewritten as , and restated as .

50% of is equal to .

20% of is equal to

Since is positive and ,

,

and (B) is greater.

60% of 25,000 is equal to

60% of that is

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.

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.

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 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.

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.

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.

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.

To figure out what 18% of any number is, first divide the percentage by 100.

Then, multiply this result times the original number.

The result is your answer.

To figure out what 18% of any number is, first divide the percentage by 100.

Then, multiply this result times the original number.

The result is the tip. To figure out the total amount paid, add the tip to the original price of the bill.

The question asks you to figure out what 50% more than a smaller part of 40 is. To do this, you must first solve what 15% of 40 is. First, divide the percentage by 100.

Then, multiply the result times 40.

You then must figure out what 50% more than this new number is. 50% more is equal to 150% of the original value. Just like before, divide this percentage by 100.

Then, multiply the result times 6.

This result is your answer.

The question asks you to figure out what 20% more than a smaller amount of 40 is. To do this, you must first solve for the smaller amount. So, first divide 40 by 2 since it asks for half of 40.

Since 20% than a number is equal to 120% of the original value of that number, multiply 20 by 120%. To do this, first divide the percentage by 100.

Then, multiply the result times 20.

This result is your answer.