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which of the following must be less than 1

Expert replies
by nikhilsrl » Sun Mar 20, 2011 2:57 am
if 0<r<1<s<2, which of the following must be less than 1?

I. r/s
II. rs
III. s - r

a) I only
b) II only
c) III only
d) I and II
e) I and III

OA is A. I am not able to eliminate II.

Please help solve this.
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Source: — Problem Solving |

by Anurag@Gurome » Sun Mar 20, 2011 3:40 am
nikhilsrl wrote:if 0<r<1<s<2, which of the following must be less than 1?

I. r/s
II. rs
III. s - r

a) I only
b) II only
c) III only
d) I and II
e) I and III
0 < r < 1 < s < 2

I. As 0 < r < s, r/s < 1

II. Say r = 0.6 and s = 1.9 => rs = 1.14 > 1

III. Say r = 0.6 and s = 1.9 => (s - r) = 1.3 > 1

The correct answer is A.
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by GMATGuruNY » Sun Mar 20, 2011 3:42 am
nikhilsrl wrote:if 0<r<1<s<2, which of the following must be less than 1?

I. r/s
II. rs
III. s - r

a) I only
b) II only
c) III only
d) I and II
e) I and III

OA is A. I am not able to eliminate II.

Please help solve this.
Try to disprove the answer choices.

II. rs < 1.
If r = 2/3 and s = 3/2, rs = 2/3 * 3/2 = 1.
Eliminate any answer choice that includes II.
Eliminate B and D.

III. s-r < 1.
If s = 3/2 and r = 1/2, s-r = 3/2 - 1/2 = 1.
Eliminate any answer choice that includes III.
Eliminate C and E.

The correct answer is A.
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by force5 » Sun Mar 20, 2011 9:43 am
IMO- A
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by luiscarlos59 » Tue Mar 22, 2011 7:05 pm
should we use extreme's in order to attack this kind of problems?
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