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

Question

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

ENGRTOMBA2018 · Answer

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

GMATinsight · Answer

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

Bunuel · Answer

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.

riyazgilani · Answer

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

GMATinsight · Answer

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

mjana89 · Answer

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.

MathRevolution · Answer

x^3 > y^2 > z Option I: x < y < z: For x = 3; y = 4 and z = 5 Option I holds Option II: x < z < y: For x = 3; y = 5 and z = 4 Option II holds Option III: y < x < z : For x = 4, y = 3 and z = 5 Option III holds Answer E

Adarsh_24 · Answer

Hi  Bunuel ,

Do you have such problems where E is not the answer?

I was thinking,

x^3> x^2>x is possible in x>1

Since, the functions z, y^2 and x^3 extend to infinity. At some point we will have all kinds of x,y,z combinations possible.
Is there any merit to this argument?

anshikag22 · Answer

Since this question mentions "could be true" we just need to prove the statement true in 1 scenario, right? So we don't need to test multiple numbers?

Bunuel · Answer

Correct.

"MUST BE TRUE" ("ALWAYS TRUE"/"IS TRUE") questions:
 These questions ask which statement is always true for  every  valid set of numbers. If you can find just one valid set of numbers where a statement is not true, it means the statement is not always true and therefore not the correct answer.

So,  for 'MUST BE TRUE' questions, the plug-in method is good for eliminating an option, but it does not provide a 100% guarantee that an option is always true.

For "MUST BE TRUE" questions, when using the plug-in method, if you find that more than one option appears to be correct for a particular number or set of numbers, try using different numbers to double-check. Reevaluate only those options that were previously considered correct.

"COULD BE TRUE" questions:
 The questions that ask which of the following statements could be true are different.  If you can demonstrate that a statement is true for a specific set of numbers, it implies that the statement could be true and therefore is a correct answer .

You can practice more questions of this type  HERE .

Hope it helps.

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

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