If xy=-18, is x less than y?

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pmFollowed by: 23 members

by BTGmoderatorDC » Sat Nov 03, 2018 5:34 pm

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If xy=-18, is x less than y?

1) x<0

2) y<10

OA A

Source: GMAT Prep

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Source: Beat The GMAT — Data Sufficiency | Sat Nov 03, 2018 5:34 pm

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Sun Nov 04, 2018 7:35 am

BTGmoderatorDC wrote:If xy = -18, is x less than y?

1) x < 0
2) y < 10

Given: xy = -18

Target question: is x less than y?

Statement 1: x < 0
In other words, x is NEGATIVE
So, our given information (xy = -18) becomes: (NEGATIVE)(y) = -18
In other words: (NEGATIVE)(y) = NEGATIVE
This tells us that y is POSITIVE
If y is POSITIVE, and x is NEGATIVE, the answer to the target question is YES, x IS less than y
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: y < 10
There are several values of x and y that satisfy statement 2 (and the given info). Here are two:
Case a: x = -9 and y = 2 (notice that xy = (-9)(2) = -18. In this case, the answer to the target question is YES, x IS less than y
Case b: x = 6 and y = -3 (notice that xy = (6)(-3) = -18. In this case, the answer to the target question is NO, x is NOT less than y
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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fskilnik@GMATH: GMAT Instructor; Posts: 1449; Joined: Sat Oct 09, 2010 2:16 pmFollowed by: 33 members; Thanked: 59 times

by fskilnik@GMATH » Sun Nov 04, 2018 10:36 am

BTGmoderatorDC wrote:If xy=-18, is x less than y?

1) x<0
2) y<10

Source: GMAT Prep

$$xy = - 18\,\,\,\left( * \right)$$
$$x\,\,\mathop < \limits^? \,\,\,y$$
$$\left( 1 \right)\,\,x < 0\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,y > 0\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\rm{YES}}} \right\rangle $$
$$\left( 2 \right)\,\,y < 10\,\,\,\left\{ \matrix{
\,{\rm{Take}}\,\,\left( {x,y} \right) = \left( {1, - 18} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\, \hfill \cr
\,{\rm{Take}}\,\,\left( {x,y} \right) = \left( { - 2,9} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{YES}}} \right\rangle \,\, \hfill \cr} \right.$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.

Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br

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