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

Re: Is x > y? (1) -4x + 2y < y - 3x (2) wx > wy
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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. 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”. _________________

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

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