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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7372
GMAT 1: 760 Q51 V42 GPA: 3.82
M61-07  [#permalink]

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Difficulty:   45% (medium)

Question Stats: 58% (02:28) correct 42% (02:43) wrong based on 12 sessions

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If $$0 < 2x + 3y < 10$$ and $$-10 < 3x+2y < 0$$, then which of the following must be true?

I. $$x < 0$$

II. $$y < 0$$

III. $$x < y$$

A. I only
B. II only
C. I and II only
D. I and III only
E. I, II, and III

_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7372
GMAT 1: 760 Q51 V42 GPA: 3.82
M61-07  [#permalink]

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Official Solution:

If $$0 < 2x + 3y < 10$$ and $$-10 < 3x+2y < 0$$, then which of the following must be true?

I. $$x < 0$$

II. $$y < 0$$

III. $$x < y$$

A. I only
B. II only
C. I and II only
D. I and III only
E. I, II, and III

Label the inequalities as follows:

$$0 < 2x+3y < 10$$ --- (1)

$$-10 < 3x+2y < 0$$ --- (2)

We consider each statement individually.

Statement I:

Multiplying (1) by -2 yields $$-20 < -4x – 6y < 0$$, and multiplying (2) by 3 yields $$-30 < 9x + 6y < 0$$. Adding these inequalities gives $$-50 < 5x < 0$$ or $$-10 < x < 0$$.

This statement is true.

Statement II:

Multiplying (1) by 3 yields $$0 < 6x + 9y < 30$$, and multiplying (2) by -2 yields $$0 < -6x – 4y < 20$$. Adding these inequalities gives $$0 < 5y < 50$$ or $$0 < y < 10$$.

This statement is false.

Statement III:

Multiplying (1) by – 1 yields $$-10 < -2x – 3y < 0$$. Adding this to inequality (2) yields $$-20 < x – y < 0$$.
This implies that $$x < y$$, and statement III is true.

Answer: D
_________________

Originally posted by MathRevolution on 18 Jun 2018, 01:26.
Last edited by MathRevolution on 05 Aug 2018, 23:05, edited 1 time in total.
Intern  Joined: 14 Jul 2018
Posts: 2
Re: M61-07  [#permalink]

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Must do before exam. It teaches a lot of concepts. This is an easy question. If someone has command over inequalities can surely do it correctly.
Intern  Joined: 26 Mar 2019
Posts: 1
Re: M61-07  [#permalink]

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why did you decide to multiply by each number? Re: M61-07   [#permalink] 08 Apr 2019, 11:02
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# M61-07

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