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# If x is a non-zero integer and 0 < y < 1, which of the following must

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If x is a non-zero integer and 0 < y < 1, which of the following must  [#permalink]

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30 Aug 2018, 23:03
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Difficulty:

25% (medium)

Question Stats:

73% (01:21) correct 27% (01:19) wrong based on 67 sessions

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If x is a non-zero integer and $$0 < y < 1$$, which of the following must be greater than 1?

(A) $$x$$

(B) $$\frac{x}{y}$$

(C) $$xy^2$$

(D) $$x^2y$$

(E) $$\frac{x^2}{y}$$

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Re: If x is a non-zero integer and 0 < y < 1, which of the following must  [#permalink]

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30 Aug 2018, 23:21
X can be negative or positive integer.

Since Y is a decimal.

Only E will be greater than 1.

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Director
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Re: If x is a non-zero integer and 0 < y < 1, which of the following must  [#permalink]

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30 Aug 2018, 23:40
Bunuel wrote:
If x is a non-zero integer and $$0 < y < 1$$, which of the following must be greater than 1?

(A) $$x$$

(B) $$\frac{x}{y}$$

(C) $$xy^2$$

(D) $$x^2y$$

(E) $$\frac{x^2}{y}$$

x can be a -ve integer
that rules out answer choice A ,B ,C
for D let x=-1

for E let x = -1 and y = largest possible value
we have
1/0.9 = 10/9 > 1

So the answer should be E
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Re: If x is a non-zero integer and 0 < y < 1, which of the following must  [#permalink]

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31 Aug 2018, 00:17
Bunuel wrote:
If x is a non-zero integer and $$0 < y < 1$$, which of the following must be greater than 1?

(A) $$x$$

(B) $$\frac{x}{y}$$

(C) $$xy^2$$

(D) $$x^2y$$

(E) $$\frac{x^2}{y}$$

A. x, it could be <0. DISCARD
B. $$\frac{x}{y}$$, it could be <0. DISCARD
C $$xy^2$$, it could be <0. DISCARD
D. $$x^2y$$, it could be <1 when $$x^2=1$$. DISCARD
E. $$\frac{x^2}{y}$$>1 , since $$x^2\geq{1}$$ and y is a fraction, so division will yield a value greater than 1.

Ans. (E)
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Re: If x is a non-zero integer and 0 < y < 1, which of the following must  [#permalink]

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04 Sep 2018, 11:24
Bunuel wrote:
If x is a non-zero integer and $$0 < y < 1$$, which of the following must be greater than 1?

(A) $$x$$

(B) $$\frac{x}{y}$$

(C) $$xy^2$$

(D) $$x^2y$$

(E) $$\frac{x^2}{y}$$

We are given that x is an integer and that y is a decimal between 0 and 1.

We know that a positive integer divided by a decimal value between 0 and 1 will be greater than 1. However, x can be either a positive or a negative integer, so answer choices A, B, and C can be eliminated. We see that x^2 will always be a positive integer, so x^2/y will always be greater than 1.

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Re: If x is a non-zero integer and 0 < y < 1, which of the following must  [#permalink]

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04 Sep 2018, 12:38
Bunuel wrote:
If x is a non-zero integer and $$0 < y < 1$$, which of the following must be greater than 1?

(A) $$x$$

(B) $$\frac{x}{y}$$

(C) $$xy^2$$

(D) $$x^2y$$

(E) $$\frac{x^2}{y}$$

y is a fraction. Note: x could be negative or positive but non-zero integer.

When we divide a positive number by fraction, the number becomes even bigger.

we are looking for a value greater than 1.

x has to positive

Option E.
Re: If x is a non-zero integer and 0 < y < 1, which of the following must   [#permalink] 04 Sep 2018, 12:38
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