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Is x<1<y?

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Math Revolution GMAT Instructor
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Joined: 16 Aug 2015
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Is x<1<y? [#permalink]

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New post 28 Mar 2017, 01:28
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A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

52% (01:39) correct 48% (01:14) wrong based on 56 sessions

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Is x<1<y?

1) \(x<√x<y\)
2) \(x<√y<y\)
[Reveal] Spoiler: OA

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Expert Post
Math Revolution GMAT Instructor
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Re: Is x<1<y? [#permalink]

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New post 30 Mar 2017, 01:16
==> In the original condition, there are 2 variables (x,y) and in order to match the number of variables to the number of equations, there must be 2 equations. Since there is 1 for con 1) and 1 for con 2), C is most likely to be the answer. By solving con 1) and con 2), from x<√x, you get 0<x<1, and from √y<y, you get y>1. Then, you get x<1<y, hence always yes.

The answer is C.
Answer: C
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Re: Is x<1<y? [#permalink]

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New post 11 Apr 2017, 07:48
MathRevolution wrote:
Is x<1<y?

1) \(x<√x<y\)
2) \(x<√y<y\)

Please, help me: what is wrong with A?

if x<\sqrt{x} then x<1. and from x<\sqrt{x}<y we know that x<y. With the second statement everything clear- insufficient. So why not A?
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Re: Is x<1<y? [#permalink]

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New post 11 Apr 2017, 08:45
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Why not A ?
Ans:

x < root(x) < y

1/4 < 1/2 < 2 (possible) -> x<1 < y

1/4 < 1/2 < 2/3 (possible) -> x < 1 but y not >1

2 different results. Hence, not suff.

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Re: Is x<1<y?   [#permalink] 11 Apr 2017, 08:45
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