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If x^3 > y^2 > z, which of the statements could be true?

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If x^3 > y^2 > z, which of the statements could be true?  [#permalink]

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New post 15 Jul 2015, 02:03
2
7
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

61% (02:26) correct 39% (02:22) wrong based on 232 sessions

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If x^3 > y^2 > z, which of the statements could be true?

I. x < y < z
II. x < z < y
III. y < x < z

A. I only
B. III only
C. I and II only
D. II and III only
E. I, II and III


Kudos for a correct solution.

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Re: If x^3 > y^2 > z, which of the statements could be true?  [#permalink]

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New post 15 Jul 2015, 03:17
1
Bunuel wrote:
If x^3 > y^2 > z, which of the statements could be true?

I. x < y < z
II. x < z < y
III. y < x < z

A. I only
B. III only
C. I and II only
D. II and III only
E. I, II and III


Kudos for a correct solution.



For proving statement 1, x =4 , y=7 , z=9 ---> x^3 > y^2 > z and x < y < z . Thus this statement could be true. ---> eliminate B and D

for proving statement 3, x=7, y =4, z=9 ----> x^3 > y^2 > z and y < x < z. Thus this statement could be true ---> eliminate A and C

Correct answer is E
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If x^3 > y^2 > z, which of the statements could be true?  [#permalink]

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New post 15 Jul 2015, 03:56
1
Bunuel wrote:
If x^3 > y^2 > z, which of the statements could be true?

I. x < y < z
II. x < z < y
III. y < x < z

A. I only
B. III only
C. I and II only
D. II and III only
E. I, II and III


Kudos for a correct solution.


The best strategy in such questions is to check one of the conditions with values and eliminate options based on its validity

Given : x^3 > y^2 > z

I. x < y < z is true for x=3, y=4, z=5 i.e. Answers can only be Options A, C or E

II. x < z < y is true for x=3, y=5, z=4 i.e. Answers can only be Options C or E

III. y < x < z is true for x=4, y=3, z=5 i.e. Answers can only be Options E

Answer: option E
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Re: If x^3 > y^2 > z, which of the statements could be true?  [#permalink]

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New post 19 Jul 2015, 11:43
Bunuel wrote:
If x^3 > y^2 > z, which of the statements could be true?

I. x < y < z
II. x < z < y
III. y < x < z

A. I only
B. III only
C. I and II only
D. II and III only
E. I, II and III


Kudos for a correct solution.


800score Official Solution:

Choice I is possible: x = 3, y = 4, z = 5
Choice II is possible: x = 3, y = 5, z = 4
Choice III is possible: x = 4, y = 3, z = 6

The correct answer is E.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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If x^3 > y^2 > z, which of the statements could be true?  [#permalink]

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New post 23 Jul 2015, 05:04
GMATinsight wrote:
Bunuel wrote:
If x^3 > y^2 > z, which of the statements could be true?

I. x < y < z
II. x < z < y
III. y < x < z

A. I only
B. III only
C. I and II only
D. II and III only
E. I, II and III


Kudos for a correct solution.


The best strategy in such questions is to check one of the conditions with values and eliminate options based on its validity

Given : x^3 > y^2 > z

I. x < y < z is true for x=3, y=4, z=5 i.e. Answers can only be Options A, C or E

II. x < z < y is true for x=3, y=5, z=4 i.e. Answers can only be Options C or E

III. y < x < z is true for x=4, y=3, z=5 i.e. Answers can only be Options E

Answer: option E


I am finding it difficult to come up with nos for number picking...? any tips..?
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Re: If x^3 > y^2 > z, which of the statements could be true?  [#permalink]

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New post 23 Jul 2015, 05:18
riyazgilani wrote:
GMATinsight wrote:
Bunuel wrote:
If x^3 > y^2 > z, which of the statements could be true?

I. x < y < z
II. x < z < y
III. y < x < z

A. I only
B. III only
C. I and II only
D. II and III only
E. I, II and III


Kudos for a correct solution.


The best strategy in such questions is to check one of the conditions with values and eliminate options based on its validity

Given : x^3 > y^2 > z

I. x < y < z is true for x=3, y=4, z=5 i.e. Answers can only be Options A, C or E

II. x < z < y is true for x=3, y=5, z=4 i.e. Answers can only be Options C or E

III. y < x < z is true for x=4, y=3, z=5 i.e. Answers can only be Options E

Answer: option E


I am finding it difficult to come up with nos for number picking...? any tips..?


Tips:

1) Try the Positive Integer Values starting from the smallest value. Checking Bigger values might make it more difficult for you so check smaller values first.

2) Try the Negative Integer Values starting from the smallest Absolute values i.e. (-1, -2, -3 etc)

3) Try the Values in the range 0 to 1 and pick easier Numbers (e.g. 1/2, 1/3) in case you have to take square root of values then pick numbers like 1/4, 1/9 etc. Check the similar value in the Values of Negative Range i.e. 0 to (-1)

Summary: The values should be checked in the following 4 ranges
Between 0 and 1
Between 0 and -1
Greater than +1
Less than -1
and Don't forget to check at zero if the Scenario requires it.

Practice applying them in questions and in some time you will understand the best values to pick for specific cases

I hope it Helps
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Re: If x^3 > y^2 > z, which of the statements could be true?  [#permalink]

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New post 06 Dec 2017, 05:49
Choosing and comparing values for x, y, z could be easier if we represent the values in the number line as in the attachment.
Clearly option E.
Attachments

Capture.JPG
Capture.JPG [ 16.6 KiB | Viewed 598 times ]

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Re: If x^3 > y^2 > z, which of the statements could be true? &nbs [#permalink] 06 Dec 2017, 05:49
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If x^3 > y^2 > z, which of the statements could be true?

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