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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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Joined: 21 Aug 2013
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Location: India
If X and Y are non-zero integers, Is X/Y >= 5/7 ? (1) X^3 >= 125  [#permalink]

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12 Mar 2018, 03:51
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Difficulty:

55% (hard)

Question Stats:

59% (01:56) correct 41% (02:48) wrong based on 41 sessions

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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
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Joined: 26 Mar 2013
Posts: 1910
If X and Y are non-zero integers, Is X/Y >= 5/7 ? (1) X^3 >= 125  [#permalink]

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12 Mar 2018, 04:08
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

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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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19 Mar 2018, 11:32

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.

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Re: If X and Y are non-zero integers, Is X/Y >= 5/7 ? (1) X^3 >= 125 &nbs [#permalink] 19 Mar 2018, 11:32
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