Which of the following is equivalent to the pair of inequalities y > -3x and -z > 2x ?

[BTGModeratorVI]

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

Answer: A
Source: GMAT Hacks

[Brent@GMATPrepNow]

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

Answer: A
Source: GMAT Hacks

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

[Scott@TargetTestPrep]

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

Answer: A
Source: GMAT Hacks

Let’s multiply the first inequality by -2. Notice that we have to reverse the direction of the inequality since we are multiplying by a negative number:

-2y < (-3x)(-2)

-2y < 6x

Next, we multiply the second inequality by 3. We don’t reverse the direction since we are multiplying by a positive number:

-3z > 6x

Combining the two inequalities above, we get -2y < 6x < -3z.

Answer: A