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If (x-y)^3 > (x-y)^2, then which of the following must be true?

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If (x-y)^3 > (x-y)^2, then which of the following must be true? [#permalink]

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New post 21 Apr 2017, 10:24
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If \((x-y)^3>(x-y)^2\), then which of the following must be true?


A. \(x^3<y^2\)

B. \(x^5<y^4\)

C. \(x^3>y^2\)

D. \(x^5>y^4\)

E. \(x^3>y^3\)



Source-> NOVA.
[Reveal] Spoiler: OA

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Last edited by stonecold on 21 Apr 2017, 13:40, edited 2 times in total.
Renamed the topic and edited the question.

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Re: If (x-y)^3 > (x-y)^2, then which of the following must be true? [#permalink]

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New post 21 Apr 2017, 20:48
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(x−y)^3>(x−y)^2

Clearly Implies (X-Y)^3 > 0

which Implies X>Y-----Option E states X^3 > Y^3 -------X>Y
Hence E Must be true
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Re: If (x-y)^3 > (x-y)^2, then which of the following must be true? [#permalink]

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New post 27 Apr 2017, 22:03
Here is what i did on this one ==>

Questions such as these are best solved by using Test Cases.

First and Foremost ==> (x-y)^3>(x-y)^2
Hence (x-y)>1

So x>y+1


Option 1 =>
Taking x=10 y=1 => REJECTED.

Option 2 =>
Taking x=10 and y=1 => REJECTED.

Option 3 =>
Taking x=-10 and y=-100 => REJECTED.

Option 4 =>
Taking x=-10 and y=-100 => REJECTED.


Only option left is E.

SMASH THAT E.

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Re: If (x-y)^3 > (x-y)^2, then which of the following must be true? [#permalink]

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New post 30 Apr 2017, 00:04
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(x-y)^3 will be positive if
i) both x and y are +ve and x>y,
ii) both x and y are -ve and y<x
iii) x is +ve and y is -ve

Case i-Let's assume that both X&Y are positive numbers.
x=3 and y=1
(x-y)^3 > (x-y)^2
Checking validity of the given options
a) x^3 < y^2 Incorrect.
b) x^5 < y^4 Incorrect.
c) x^3 >y^2 Correct.
d) x^5 > y^4 Correct.
e) x^3 > y^3 Correct.

Case ii-Let's assume that both X&Y are negative numbers and y<x
x=-2 and y=-5
(x-y)^3 > (x-y)^2
Checking validity of the given options
a) x^3 < y^2 Correct.
b) x^5 < y^4 Correct.
c) x^3 >y^2 Incorrect.
d) x^5 > y^4 Incorrect.
e) x^3 > y^3 Correct.

Case iii-Let's assume that both X is +ve and y is -ve
x=3 and y=-1
(x-y)^3 > (x-y)^2
Checking validity of the given options
a) x^3 < y^2 Incorrect.
b) x^5 < y^4 Incorrect.
c) x^3 >y^2 Correct.
d) x^5 > y^4 Correct.
e) x^3 > y^3 Correct.

Only option E is correct in all 3 scenarios.

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Re: If (x-y)^3 > (x-y)^2, then which of the following must be true? [#permalink]

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New post 29 Aug 2017, 15:56
If (x−y)^3>(x−y)^2, then which of the following must be true?

Let (x−y) = a

so , a^3> a^2 implies a>0

that is x-y>0 , so that means x>y (but we cannot say for sure if x, y is >or< 0)
Also X can be integers and or fractions . Don't assume that its only integer.

Now if we see all options we have

A. x^3<y^2 ( Not always true )

B. x^5<y^4 ( Not always true )

C. x^3>y^2 ( Not always true)

D. x^5>y^4 ( Not always true)

E. x^3>y^3 Yes ( true even in case of fractions)
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Re: If (x-y)^3 > (x-y)^2, then which of the following must be true?   [#permalink] 29 Aug 2017, 15:56
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