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

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

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New post 25 Jul 2018, 02:35
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A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

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

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

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New post 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


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

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

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New post 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.

Hence A is the Answer.
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Re: Is x > y? (1) -4x + 2y < y - 3x (2) wx > wy  [#permalink]

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New post 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.
As this statement gives us a contradictory answer, statement 2 is not sufficient to answer. We can eliminate the answer option D.

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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New post 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

Answer: A

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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