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GMAT Prep question

Expert replies
Source: — Problem Solving |

by [email protected] » Sun Sep 28, 2014 11:05 am
Hi anksm22,

This question can be solved by TESTing VALUES (and using some Number Property logic).

We're given:
0<R<1
1<S<2

We're asked which of the following MUST be less than 1.

I. R/S

If... R = .5 and S = 1.5, then R/S = .5/1.5 = 1/3 which IS less than 1.

The above example can help you to recognize the Number Property involved: R/S will ALWAYS be less than 1 because R and S are both positive AND the denominator will be larger than the numerator. That is THE definition of a positive fraction.
Roman Numeral I IS ALWAYS less than 1.

II. RS

Here, we can prove that RS is NOT ALWAYS less than 1:

If...R = .99 and S = 1.99, then RS would be (.99)(1.99) which is a little less than 2 and NOT less than 1.
Roman Numeral II is NOT ALWAYS less than 1.

III. S - R

Here, we can prove that S-R is NOT ALWAYS less than 1:

If...R = .01 and S = 1.99, then S - R = 1.98. This is NOT less than 1
Roman Numeral III is NOT ALWAYS less than 1.

Final Answer: A

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