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Official GMAT PS question - Doubtful about the OA

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Official GMAT PS question - Doubtful about the OA

by Vishnu88 » Thu Jun 16, 2011 7:33 am
If d > 0 and 0 < 1- c/d < 1, which of the following
must be true?

I. c > 0
II. c/d < 1
III. c^2 + d^2 > 1

(A) I only
(B) II only
(C) I and II only
(D) II and III only
(E) I, II, and III

I think the OA should be E as opposed to C.

In case I am mistaken, appreciate if you could substantiate with an example [spoiler](for including excluding III)[/spoiler].
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by vineeshp » Thu Jun 16, 2011 7:41 am
0 < 1- c/d
c/d < 1
c < d

1- c/d < 1
0- c/d < 0
- c/d < 0
c/d > 0 ==> c>0 and d>0 (already given)

This is no gurantee that c < d and both positive mean that sum of squares are greater than 1.
For eg. c = 1/3 and d= 1/2 satisfy this condition.
It is possible that I made some error while typing and solving.

But my point is that OG OA will not be wrong. Or else gmat would have released a correction ages ago.
Vineesh,
Just telling you what I know and think. I am not the expert. :)
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by GMATGuruNY » Thu Jun 16, 2011 7:55 am
Vishnu88 wrote:If d > 0 and 0 < 1- c/d < 1, which of the following
must be true?

I. c > 0
II. c/d < 1
III. c^2 + d^2 > 1

(A) I only
(B) II only
(C) I and II only
(D) II and III only
(E) I, II, and III

I think the OA should be E as opposed to C.

In case I am mistaken, appreciate if you could substantiate with an example [spoiler](for including excluding III)[/spoiler].
To satisfy the condition that 0 < 1- c/d < 1, c/d must be a positive fraction between 0 and 1.
Thus, II must be true.
Eliminate A.

Since d>0, in order for c/d to be a positive fraction between 0 and 1, c>0.
Thus, I must be true.
Eliminate B and D.

If c = 1/4 and d = 3/4, then c/d = (1/4)/(3/4) = 1/3, which is a positive fraction between 0 and 1.
(1/4)² + (3/4)² = 1/16 + 9/16 = 10/16 = 5/8.
Thus, III does not have to be true.
Eliminate E.

The correct answer is C.
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by Vishnu88 » Thu Jun 16, 2011 8:00 am
Thank you Vineesh and Mitch.

I did not factor in the possibility of using fractions.
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by rohu27 » Thu Jun 16, 2011 8:28 am
whts the official source of this one plz? i mean OG, gmatprep etc?
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by Vishnu88 » Thu Jun 16, 2011 8:29 am
Tagged it along with the question.

Source: GMAT Paper Tests
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by gmat062011 » Sat Jun 18, 2011 2:05 pm
Option II, does not say that fraction (c/d) is positive (i.e. between 0 and 1). Option II, is correct only if c > 0.

Which means that we must choose option I, if we want to choose option II.

Am I correct ?
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by saketk » Tue Aug 09, 2011 9:41 am
gmat062011 wrote:Option II, does not say that fraction (c/d) is positive (i.e. between 0 and 1). Option II, is correct only if c > 0.

Which means that we must choose option I, if we want to choose option II.

Am I correct ?
Hi,
Agreed, option 2 does not say that fraction (c/d) is positive, but if you see the information given in the question, which says -- d> 0 and 0<1- (c/d) < 1.

Now, if we solve the second condition: - i.e. transfer 1 to both sides of inequality, we get

-1< (-c/d) < 0 or 1> (c/d) > 0 [sign changes when we multiply by negative value] ...

This gives us -- c/d < 1. Option II fulfilled.

Hence the correct option is C.
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