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If X and Y are non-zero integers, Is X/Y >= 5/7 ? (1) X^3 >= 125

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If X and Y are non-zero integers, Is X/Y >= 5/7 ? (1) X^3 >= 125 [#permalink]

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New post 12 Mar 2018, 04:51
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If X and Y are non-zero integers, Is X/Y >= 5/7 ?

(1) X^3 >= 125 and Y^2 <= 49

(2) X*Y <= 0
[Reveal] Spoiler: OA
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If X and Y are non-zero integers, Is X/Y >= 5/7 ? (1) X^3 >= 125 [#permalink]

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New post 12 Mar 2018, 05:08
amanvermagmat wrote:
If X and Y are non-zero integers, Is X/Y >= 5/7 ?

(1) X^3 >= 125 and Y^2 <= 49

(2) X*Y <= 0


(2) \(X*Y\leq{0}\)

This means that x & y have DIFFERENT sings hence x/y is laways negative and can't be >= 5/7.

Sufficient

(1) \(x^3\geq{125}\) and \(Y^2\leq{49}\)

\(x\geq{5}\) , -7<= Y <= 7

Let x = 5 & Y =1........5/1 =5...............Answer is Yes

Let x = 5 & Y =-1........5/1 =5...............Answer is NO

Insufficient

Answer: B
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Re: If X and Y are non-zero integers, Is X/Y >= 5/7 ? (1) X^3 >= 125 [#permalink]

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New post 19 Mar 2018, 12:32

SOLUTION



We are given:
    • \(X\) and \(Y\) are non-zero integers.

We need to find:
    • If \(\frac{X}{Y}\) is greater than \(\frac{5}{7}\) or not?

Let us analyze both the statements one by one.

Statement-1: \(X^3 >= 125\) and \(Y^2 <= 49\).

From \(X^3>=125\), we can write:
    • \(X >=5\).
From \(Y^2 <= 49\), we can write:
    • \(-7<= Y<= 7\)

For \(X=6\) and \(Y=7\), the value of \(\frac{X}{Y}\) is greater than \(\frac{5}{7}\).
However, for \(X=6\) and \(Y=-7\), the value of \(\frac{X}{Y}\) is less than \(\frac{5}{7}\).

Hence, Statement 1 alone is not sufficient to answer the question.

Statement-2 \(X*Y <= 0\).

Since \(X\) and \(Y\), both, are non-zero integers, \(X*Y\) can only be less than 0.

The product of \(X\) and \(Y\)is negative.
    • Hence, we can say that \(X\) and \(Y\) are of different sign.
      o Therefore, \(\frac{X}{Y}\) is also negative.

Hence, we can certainly say that \(\frac{X}{Y}\) is a negative value which is always less than \(\frac{5}{7}\).
Thus, Statement 2 alone is sufficient to answer the question.

Answer: B
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Re: If X and Y are non-zero integers, Is X/Y >= 5/7 ? (1) X^3 >= 125   [#permalink] 19 Mar 2018, 12:32
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