ISEE Middle Level Quantitative : How to find the part from the whole

Study concepts, example questions & explanations for ISEE Middle Level Quantitative

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Example Questions

Example Question #1 : How To Find The Part From The Whole

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?

Possible Answers:

Correct answer:

Explanation:

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:

Example Question #2 : How To Find The Part From The Whole

Which of the following is true if ?

Possible Answers:

Correct answer:

Explanation:

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.

Example Question #1 : How To Find The Part From The Whole

 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

Possible Answers:

(a) and (b) are equal

(a) is the greater quantity

It is impossible to determine which is greater from the information given

(b) is the greater quantity

Correct answer:

It is impossible to determine which is greater from the information given

Explanation:

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.

Example Question #2 : How To Find The Part From The Whole

 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.

Possible Answers:

(a) is the greater quantity

(a) and (b) are equal

It is impossible to determine which is greater from the information given

(b) is the greater quantity

Correct answer:

(a) and (b) are equal

Explanation:

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.

Example Question #3 : How To Find The Part From The Whole

 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

Possible Answers:

(b) is the greater quantity

(a) and (b) are equal

(a) is the greater quantity

It is impossible to determine which is greater from the information given

Correct answer:

(a) is the greater quantity

Explanation:

, 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.

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