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# Is 1/x greater than 1/y?

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Math Expert
Joined: 02 Sep 2009
Posts: 51072
Is 1/x greater than 1/y?  [#permalink]

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05 Nov 2017, 01:12
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Difficulty:

35% (medium)

Question Stats:

67% (01:01) correct 33% (00:46) wrong based on 78 sessions

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Is 1/x greater than 1/y?

(1) x is greater than 1.
(2) x is less than y.

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Manager
Joined: 06 Aug 2017
Posts: 86
GMAT 1: 570 Q50 V18
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Re: Is 1/x greater than 1/y?  [#permalink]

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05 Nov 2017, 05:13
Bunuel wrote:
Is 1/x greater than 1/y?

(1) x is greater than 1.
(2) x is less than y.

The answer should be C as follows.

(1) x is greater than 1.
Since only value of x is give, y can be anything
INSUFFICIENT

(2) x is less than y
Here, there will be 3 cases

Case 1: When both x and y are positive
E.G. let x=2 and y=3
$$\frac{1}{x}=\frac{1}{2}=0.5$$
$$\frac{1}{y}=\frac{1}{3}=0.333$$
in this case $$\frac{1}{x}>\frac{1}{y}$$

Case 2: When x is negative and y is positive
E.G. x = -2 and y=3
$$\frac{1}{x}=\frac{1}{(-2)}= -0.5$$
$$\frac{1}{y}=\frac{1}{3}=0.333$$
in this case $$\frac{1}{x}<\frac{1}{y}$$

Case 2: When both x and y are negative
E.G. x = -2 and y=-1 (Since x<y)
$$\frac{1}{x}=\frac{1}{(-2)}= -0.5$$
$$\frac{1}{y}=\frac{1}{(-1)}= -1$$
in this case $$\frac{1}{x}<\frac{1}{y}$$

ICUFFICIENT

Note: Case 3 was really not required to be considered as case 1 and case 2 themselves produced the conflicting results.

Combining both, the condition will become, x<y and x is greater than 1. This will be an spacial scenario of case 1 of statement 2 in the question.
Since x>1, both x and y will be positive
E.G. x=2 and y=3
$$\frac{1}{x}=\frac{1}{2}=0.5$$
$$\frac{1}{y}=\frac{1}{3}=0.333$$
in this case $$\frac{1}{x}>\frac{1}{y}$$

SUFFICIENTS

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Re: Is 1/x greater than 1/y?  [#permalink]

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05 Nov 2017, 06:20
Please correct me if I am wrong.

What the question is asking is 1/x > 1/y

So can we not say -x>-y
and hence x<y I think this is what they are asking.

So only B statement proves it.

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Re: Is 1/x greater than 1/y?  [#permalink]

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05 Nov 2017, 10:34
1
meetsampat wrote:
Please correct me if I am wrong.

What the question is asking is 1/x > 1/y

So can we not say -x>-y
and hence x<y I think this is what they are asking.

So only B statement proves it.

Hi meetsampat,

You cant cross multiply variable unless you consider signs of those variable.

Here you have to consider the following cases.

1. Both x and y are positive
2. Both x and y are negative
3. x is positive, y is negative
4. x is negative and y is positive

Based on the signs of the variable, the inequality sign will change while doing cross-multiplication.
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GMAT PREP 2: Q50 V34 - 700

Veritas Test 5: Q47 V33 - 650
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Intern
Joined: 05 Dec 2016
Posts: 6
Re: Is 1/x greater than 1/y?  [#permalink]

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05 Nov 2017, 12:04
Jabjagotabhisavera wrote:
meetsampat wrote:
Please correct me if I am wrong.

What the question is asking is 1/x > 1/y

So can we not say -x>-y
and hence x<y I think this is what they are asking.

So only B statement proves it.

Hi meetsampat,

You cant cross multiply variable unless you consider signs of those variable.

Here you have to consider the following cases.

1. Both x and y are positive
2. Both x and y are negative
3. x is positive, y is negative
4. x is negative and y is positive

Based on the signs of the variable, the inequality sign will change while doing cross-multiplication.

Yes... I did not think on signs..Thanks !!
Manager
Joined: 10 Dec 2011
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GMAT Date: 09-28-2012
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Re: Is 1/x greater than 1/y?  [#permalink]

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11 Nov 2017, 06:45
C.
for 1/x > 1/y, X has to be less than Y. And B says exactly that. Wait, if X is negative, signs change. Therefore, X also has to be positive. And A states exactly that. Therefore C.
Further, just for info, none can be 0 otherwise division wont be possible. But both the choices are complete in themselves and take care of that.
Re: Is 1/x greater than 1/y? &nbs [#permalink] 11 Nov 2017, 06:45
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