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Is x < y ? (1) z^2 < y (2) x < z

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Is x < y ? (1) z^2 < y (2) x < z [#permalink]

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New post 13 Mar 2017, 07:20
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Difficulty:

  45% (medium)

Question Stats:

54% (01:00) correct 46% (01:05) wrong based on 114 sessions

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Re: Is x < y ? (1) z^2 < y (2) x < z [#permalink]

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Bunuel wrote:
Is x < y ?

(1) z² < y
(2) x < z


Target question: Is x < y ?

Statement 1: z² < y
No information about x, so statement 1 is NOT SUFFICIENT

Statement 2: x < z
No information about y, so statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
NOTE: the error that many students will make is to assume that z < z², but this is not necessarily the case.
For example, if z = 1/2, then z² = 1/4, in which case z² < z
On the other hand, if z = 3, then z² = 3, in which case z < z²
This feature will create conflicting answers to the target question. Here's what I mean:
There are several values of x, y and z that satisfy BOTH statements. Here are two:
Case a: x = 0.3, y = 0.4, and z = 0.5 (which also means z² = 0.25). Notice that z² < y and x < z, so both conditions are met. In this case x < y
Case b: x = 0.4, y = 0.3, and z = 0.5 (which also means z² = 0.25). Notice that z² < y and x < z, so both conditions are met. In this case x > y
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

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Re: Is x < y ? (1) z^2 < y (2) x < z [#permalink]

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New post 15 Mar 2017, 05:30
y>z^2
for z>1, we can say that y>z
if 0<z<1 , we cannot say if y>z. take y,z be 0.05, 0.2 and 0.5, 0.2. plus we have no data about x. INSUFFICIENT

St 2: x<z. no idea about y. INSUFFICIENT

St 1 & St 2: as we cannot relate the value of y and z in st 1, using the st2 also we cannot relate x and y. INSUFFICIENT

Option E
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Re: Is x < y ? (1) z^2 < y (2) x < z [#permalink]

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New post 20 Mar 2017, 05:55
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Bunuel wrote:
Is x < y ?

(1) z^2 < y
(2) x < z


We need to determine whether x < y.

Statement One Alone:

z^2 < y

Since we do not have any information regarding x, statement one is not sufficient to answer the question.

Statement Two Alone:

x < z

Since we do not have any information regarding y, statement two is not sufficient to answer the question.

Statements One and Two Together:

Using the information in statements one and two, we still cannot answer the question. For instance, if y = 10, z = 2, and x = 1, then x is less than y. However, if z = 1/2, x = 1/3, and y = 1/3, then x IS NOT less than y.

Answer: E
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Re: Is x < y ? (1) z^2 < y (2) x < z   [#permalink] 20 Mar 2017, 05:55
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