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

[BTGmoderatorDC]

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

1) x<0

2) y<10

OA A

Source: GMAT Prep

[Brent@GMATPrepNow]

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

[fskilnik@GMATH]

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.