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

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

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Example Questions

Example Question #211 : Numbers And Operations

150% of what number is 9,000?

Possible Answers:

Correct answer:


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:

Example Question #2 : Whole And Part

 is a multiple of 2, but not a multiple of 6. If  is divided by 6, What could be the remainder?

Possible Answers:

Correct answer:


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.

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