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Kaplan - error?

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singhsa: Master | Next Rank: 500 Posts; Posts: 107; Joined: Sat Feb 27, 2010 11:10 am; GMAT Score:690

by singhsa » Tue Sep 21, 2010 5:35 pm

If x < 0 and 4 < 5 - xy < 5, which of the following must be true?

I y < 0
II xy < 1

In this question, the answer is
I and II

But, from the equation, we get that 0<xy<1. Thus xy must be between 0 and 1. If xy= -20, the statement would not be valid. So, how can we consider statement II from the question to be true?

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Source: Beat The GMAT — Problem Solving | Tue Sep 21, 2010 5:35 pm

Gurpinder: Legendary Member; Posts: 659; Joined: Mon Dec 14, 2009 8:12 amFollowed by: 3 members; Thanked: 32 times

by Gurpinder » Tue Sep 21, 2010 7:09 pm

If x < 0 and 4 < 5 - xy < 5, which of the following must be true?

I y < 0
II xy < 1

simplify 4 < 5 - xy < 5 and you get 1 > xy. so II is true.

x is a -ve. y cannot be < 0 because then -ve times -ve = +.

y is a positive fraction less than 1.

hence the answer should be II.

"Do not confuse motion and progress. A rocking horse keeps moving but does not make any progress."
- Alfred A. Montapert, Philosopher.

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Ian Stewart: GMAT Instructor; Posts: 2623; Joined: Mon Jun 02, 2008 3:17 amFollowed by: 355 members; Location: Montreal; Thanked: 1090 times; GMAT Score:780

by Ian Stewart » Tue Sep 21, 2010 11:18 pm

singhsa wrote:If x < 0 and 4 < 5 - xy < 5, which of the following must be true?

I y < 0
II xy < 1

In this question, the answer is
I and II

But, from the equation, we get that 0<xy<1. Thus xy must be between 0 and 1. If xy= -20, the statement would not be valid. So, how can we consider statement II from the question to be true?

If 0 < xy < 1, then it is certainly true that xy < 1; that's what the right-hand portion of the inequality 0 < xy < 1 says. If 0 < xy < 1, then it is impossible for xy to be equal to -20, so your example is not germane here. Note that you are not asked here to find an answer which is equivalent to the inequalities in the question. You are only asked to find one which must be true. If we had a third item which read, for example:

III) xy > -9

that would also be true here; we know that xy is between 0 and 1, so it's certainly bigger than -9.

Further, if we know that x is negative and that xy is positive, then y is certainly negative, so I must be true.

For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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singhsa: Master | Next Rank: 500 Posts; Posts: 107; Joined: Sat Feb 27, 2010 11:10 am; GMAT Score:690

by singhsa » Wed Sep 22, 2010 5:09 pm

Ian Stewart wrote:
III) xy > -9

that would also be true here; we know that xy is between 0 and 1, so it's certainly bigger than -9.

Further, if we know that x is negative and that xy is positive, then y is certainly negative, so I must be true.[/quote

Thanks Ian. This helps.

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