Which of the following is equivalent to the pair of inequalities y -

Question

Which of the following is equivalent to the pair of inequalities y > -3x and -z > 2x ? (A) -2y < 6x < -3z (B) 2y < -6x < -3z (C) -3x < y < -z (D) 3x < z < -y (E) -3z < 12x < y

quantumliner · Answer

y > -3x --> Can be written as: -y < 3x --> Multiply both sides with 2 --> -2y < 6x --- Inequality A

-z > 2x ? --> Multiply both sides with 3 --> -3z > 6x --- Inequality B

Combining Inequalities A & B --> -2y < 6x < -3z

Answer: A

GMATinsight · Answer

y > -3x or 3x > -y multiplying 2 on both sides we get 6x > -2y -z > 2x or 2x < -z multiplying 3 on both sides we get 6x < -3z Combining both inequalities we get -2y < 6x < -3z Answer: Option A

KarishmaB · Answer

The first question might be what to do with these two inequalities - the solution is to look at the options. Each variable is independent in the inequality. So we shouldn't combine the inequalities. We need the relation of x, y and z so we need to keep the inequalities separate. To compare them then we need one common term. That has to be the x term so make it equal in both inequalities (like you do in ratios) You get 2y > -6x and -3z > 6x Now note that z is negative in 4 of the 5 options so keep z negative. Multiply the first inequality by -1 to get -2y < 6x and -3z > 6x We get -2y < 6x < -3z Answer (A)

Abhishek009 · Answer

(I) y > -3x (II) -z > 2x (I) * 2 = 2y > -6x (II)* -3 = -6x > 3z Now combine the two : 2y > -6x > 3z And if we multiply the inequality by -1 we have : -2y < 6x < -3z Thus, answer will be (A) -2y < 6x < -3z

BrentGMATPrepNow · Answer

We can also answer this question by examining only  one part

Take -z > 2x, which we can rewrite as  2x < -z

Now examine the answer choices and focus solely on the relationships between x and z
(A)  -2y <  6x < -3z
(B)  2y <  -6x < -3z
(C) -3x <  y <  -z
(D) 3x < z  < -y 
(E) -3z < 12x  < y

Can  2x < -z  be rewritten to match any of these answer choices? 
You bet.

Take  2x < -z  and multiply both sides by 3 to get:  6x < -3z 
This matches answer choice A

If we look further, we see that  2x < -z  CANNOT be rewritten to match any of the other 4 answer choices. 
So, the correct answer must be A

Cheers,
Brent

NandishSS · Answer

We Cannot combine y > -3x and -z > 2x Since we need one common term so multiple (y > -3x) * 2 = 2y > -6x & (-z > 2x)* -3 = -6x > 3z As we have a common term -6x we can compare now. We Get -2y < 6x < -3z (A)

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Which of the following is equivalent to the pair of inequalities y > -

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