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# Is x > y? (1) -4x + 2y < y - 3x (2) wx > wy

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Math Expert
Joined: 02 Sep 2009
Posts: 53066
Is x > y? (1) -4x + 2y < y - 3x (2) wx > wy  [#permalink]

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25 Jul 2018, 02:35
00:00

Difficulty:

35% (medium)

Question Stats:

61% (00:58) correct 39% (00:51) wrong based on 129 sessions

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Is x > y?

(1) -4x + 2y < y - 3x

(2) wx > wy

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Joined: 13 Feb 2018
Posts: 156
GMAT 1: 640 Q48 V28
Re: Is x > y? (1) -4x + 2y < y - 3x (2) wx > wy  [#permalink]

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25 Jul 2018, 02:50
1
1 stm: -4x + 2y < y - 3x if we add 4x to both sides and subtract both sides by y, we get y<x suff
2 stm: If x=2 y=1 w=5 then x>y wx>xy, But if x=-1 y=-2 w=-5 x>y, wx<wy insuff

IMO
Ans: A
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Joined: 02 Aug 2009
Posts: 7335
Re: Is x > y? (1) -4x + 2y < y - 3x (2) wx > wy  [#permalink]

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25 Jul 2018, 02:55
Is x > y?

(1) -4x + 2y < y - 3x
$$-4x+2y<y-3x.........2y-y<4x-3x.......y<x$$
Sufficient

(2) wx > wy
wx-wy>0.........w(x-y)>0
If w>0, then x-y>0 or x>y
if w<0, then x-y<0 or x<y
Insufficient

A
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html

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Re: Is x > y? (1) -4x + 2y < y - 3x (2) wx > wy  [#permalink]

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25 Jul 2018, 08:00
Bunuel wrote:
Is x > y?

(1) -4x + 2y < y - 3x

(2) wx > wy

Upon rearranging statement 1 we get

-x<-y => x>y

Statement 1 is sufficient

from Statement 2 we do not anything about the value of W.So clearly it is insufficient.

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Re: Is x > y? (1) -4x + 2y < y - 3x (2) wx > wy  [#permalink]

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27 Dec 2018, 03:17
Solution:

To find: x > y?
No other information given in the question stem lets directly analyze the statements!

Analysis of statement 1: $$-4x + 2y < y - 3x$$
Let’s solve the given inequality: $$-4x+2y<y-3x$$
We get $$-4x+3x<y-2y$$
$$-x< -y$$
Multiplying the above inequality by (-1), [The sign of the inequality will swap]
$$x>y$$. We get a definite answer as “YES” to the question.
Hence statement 1 is sufficient to answer. We can eliminate options B, C and E.

Analysis of statement 2: $$wx > wy$$
By analyzing the statement 2 we get two cases here,
Case 1: $$wx>wy$$
$$wx-wy>0$$;
$$w(x-y)> 0$$
If $$w>0$$ ,then $$x-y>0$$;this means $$x>y$$.
Hence gives definite “yes” to the question.
Case 2: $$wx>wy$$
$$wx-wy>0$$;
$$w(x-y)> 0$$
If $$w<0$$ ,then $$x-y<0$$;this means $$x<y$$.
Hence gives definite “no” to the question.

The correct answer option is “A”.
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Re: Is x > y? (1) -4x + 2y < y - 3x (2) wx > wy  [#permalink]

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19 Jan 2019, 05:50
Top Contributor
Bunuel wrote:
Is x > y?

(1) -4x + 2y < y - 3x

(2) wx > wy

Target question: Is x > y?

Statement 1: -4x + 2y < y - 3x
Add 4x to both sides to get: 2y < y + x
Subtract y from both sides to get: y < x
Perfect, the answer to the target question is YES, x IS greater than y
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: wx > wy
ASIDE: We must resist the temptation to divide both sides of the inequality by w to get: x > y, because we don't know whether w is NEGATIVE or POSITIVE.
If we divide both sides of an inequality by a NEGATIVE number, we must REVERSE the direction of the inequality symbol.
To better understand what I mean, consider the following.
There are several values of w, x and y that satisfy statement 2. Here are two:
Case a: w = 1, x = 2 and y = 1. Notice that wx = (1)(2) = 2, and wy = (1)(1) = 1, so wx > wy. In this case, the answer to the target question is YES, x IS greater than y
Case b: w = -1, x = -2 and y = -1. Notice that wx = (-1)(-2) = 2, and wy = (-1)(-1) = 1, so wx > wy. In this case, the answer to the target question is NO, x is NOT greater than y
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Cheers,
Brent

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Re: Is x > y? (1) -4x + 2y < y - 3x (2) wx > wy   [#permalink] 19 Jan 2019, 05:50
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