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If a > x > y , which of the following must be true ? a > 0 x > y a2x
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20 Mar 2023, 05:17

Expert Reply

Question Stats:

If \(a > x > y\) , which of the following must be true ?

Indicate all that apply

\(a > 0\)

\(x > –y\)

\(a^2x ≥ a^2y\)

Post A Detailed Correct Solution For The Above Questions And Get A Kudos.

Question From Our Project: Free GRE Prep Club Tests in Exchange for 20 Kudos

\(\Longrightarrow\) GRE - Quant Daily Topic-wise Challenge

\(\Longrightarrow\) GRE INEQUALITIES

Indicate all that apply

\(a > 0\)

\(x > –y\)

\(a^2x ≥ a^2y\)

Post A Detailed Correct Solution For The Above Questions And Get A Kudos.

Question From Our Project: Free GRE Prep Club Tests in Exchange for 20 Kudos

\(\Longrightarrow\) GRE - Quant Daily Topic-wise Challenge

\(\Longrightarrow\) GRE INEQUALITIES

Re: If a > x > y , which of the following must be true ? a > 0 x > y a2x
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11 Apr 2023, 10:55

Expert Reply

1) a could be also negative

2) x+y>0 we do know that is positive but this is not guaranteed. We do not the sign of x and y

3) dividing both side by a^2 what is left is \(x \geq y\) and is given that x>y

This is the only true option

2) x+y>0 we do know that is positive but this is not guaranteed. We do not the sign of x and y

3) dividing both side by a^2 what is left is \(x \geq y\) and is given that x>y

This is the only true option

Re: If a > x > y , which of the following must be true ? a > 0 x > y a2x
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07 Oct 2023, 06:22

Carcass wrote:

1) a could be also negative

2) x+y>0 we do know that is positive but this is not guaranteed. We do not the sign of x and y

3) dividing both side by a^2 what is left is \(x \geq y\) and is given that x>y

This is the only true option

2) x+y>0 we do know that is positive but this is not guaranteed. We do not the sign of x and y

3) dividing both side by a^2 what is left is \(x \geq y\) and is given that x>y

This is the only true option

For 3) after dividing by a^2, we get x >= y. This implies that x could be = y which is in violation of the given constraint. Therefore, none of the given options is correct.

Re: If a > x > y , which of the following must be true ? a > 0 x > y a2x
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08 Oct 2023, 21:31

1

The following statements must be true based on the inequality "a > x > y":

1. a > 0

2. x > -y

So, both "a > 0" and "x > -y" are correct. However, "a^2x ≥ a^2y" is not necessarily true based solely on the given inequality.

1. a > 0

2. x > -y

So, both "a > 0" and "x > -y" are correct. However, "a^2x ≥ a^2y" is not necessarily true based solely on the given inequality.

Re: If a > x > y , which of the following must be true ? a > 0 x > y a2x
[#permalink]
11 Nov 2023, 12:12

1

Great problem to apply process of elimination, since it is a MUST be true.

A) Nope. Consider a=-1, x=-2, y=-3.

B) Nope. Consider the same x=-2 and y=-3.

Since A and B are out, C must be true (since it requires an answer).

A) Nope. Consider a=-1, x=-2, y=-3.

B) Nope. Consider the same x=-2 and y=-3.

Since A and B are out, C must be true (since it requires an answer).

gmatclubot

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