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# Is x an integer ? (1) 2x + 1 is an integer (2) 5x – 1 is an integer

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Joined: 02 Sep 2009
Posts: 59628
Is x an integer ? (1) 2x + 1 is an integer (2) 5x – 1 is an integer  [#permalink]

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28 Aug 2017, 04:06
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Difficulty:

45% (medium)

Question Stats:

61% (01:10) correct 39% (00:54) wrong based on 39 sessions

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Is x an integer ?

(1) 2x + 1 is an integer
(2) 5x – 1 is an integer

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Joined: 26 Feb 2016
Posts: 3302
Location: India
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Re: Is x an integer ? (1) 2x + 1 is an integer (2) 5x – 1 is an integer  [#permalink]

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28 Aug 2017, 04:27
1
1. 2x + 1 is an integer
x can be 1 or $$\frac{1}{2}$$. In both the cases, 2x + 1 is an integer,
but x=1 is an integer but x = $$\frac{1}{2}$$ is not an integer. Insufficient
2. 5x – 1 is an integer
x can be 1 or $$\frac{1}{5}$$. In both the cases, 5x - 1 is an integer,
but x=1 is an integer but x = $$\frac{1}{5}$$ is not an integer. Insufficient

On combining the information from both the statements,
x has to be an integer (Sufficient) (Option C)
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Senior PS Moderator
Joined: 26 Feb 2016
Posts: 3302
Location: India
GPA: 3.12
Is x an integer ? (1) 2x + 1 is an integer (2) 5x – 1 is an integer  [#permalink]

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28 Aug 2017, 06:10
1
Arsh4MBA wrote:
pushpitkc wrote:
1. 2x + 1 is an integer
x can be 1 or $$\frac{1}{2}$$. In both the cases, 2x + 1 is an integer,
but x=1 is an integer but x = $$\frac{1}{2}$$ is not an integer. Insufficient
2. 5x – 1 is an integer
x can be 1 or $$\frac{1}{5}$$. In both the cases, 5x - 1 is an integer,
but x=1 is an integer but x = $$\frac{1}{5}$$ is not an integer. Insufficient

On combining the information from both the statements,
x has to be an integer (Sufficient) (Option C)

Hello pushpitkc , I understand combining 1 & 2 helps to conclude if its an integer or not ?
But how are we sure its an integer. Can you throw some light?

Hi Arsh4MBA,

On combining the information on both the statements,
the only option when both the expression 2x + 1 and 5x - 1 are integers is when x is an integer

If x is a fraction, the fraction has to have both 2 and 5 in its denominator.
The minimum such value of x is $$\frac{1}{(2*5)}$$, but neither of the expressions will yield an integer

Hope that helps!
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Posts: 593
Concentration: Strategy, Technology
GMAT 1: 630 Q47 V29
GMAT 2: 740 Q51 V38
Re: Is x an integer ? (1) 2x + 1 is an integer (2) 5x – 1 is an integer  [#permalink]

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28 Aug 2017, 04:21
Bunuel wrote:
Is x an integer ?

(1) 2x + 1 is an integer
(2) 5x – 1 is an integer

(1) x = 1/2 or 1
not sufficient

(2) x=1/5 or 1
not sufficient

on combining
only integer value of x satisfies
C
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Thanks
Luckisnoexcuse
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Posts: 82
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Is x an integer ? (1) 2x + 1 is an integer (2) 5x – 1 is an integer  [#permalink]

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28 Aug 2017, 05:27
pushpitkc wrote:
1. 2x + 1 is an integer
x can be 1 or $$\frac{1}{2}$$. In both the cases, 2x + 1 is an integer,
but x=1 is an integer but x = $$\frac{1}{2}$$ is not an integer. Insufficient
2. 5x – 1 is an integer
x can be 1 or $$\frac{1}{5}$$. In both the cases, 5x - 1 is an integer,
but x=1 is an integer but x = $$\frac{1}{5}$$ is not an integer. Insufficient

On combining the information from both the statements,
x has to be an integer (Sufficient) (Option C)

Hello pushpitkc , I understand combining 1 & 2 helps to conclude if its an integer or not ?
But how are we sure its an integer. Can you throw some light?
Manager
Joined: 19 Jul 2017
Posts: 82
Location: India
Concentration: General Management, Strategy
GPA: 3.5
Re: Is x an integer ? (1) 2x + 1 is an integer (2) 5x – 1 is an integer  [#permalink]

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28 Aug 2017, 07:14
pushpitkc wrote:
Arsh4MBA wrote:
pushpitkc wrote:
1. 2x + 1 is an integer
x can be 1 or $$\frac{1}{2}$$. In both the cases, 2x + 1 is an integer,
but x=1 is an integer but x = $$\frac{1}{2}$$ is not an integer. Insufficient
2. 5x – 1 is an integer
x can be 1 or $$\frac{1}{5}$$. In both the cases, 5x - 1 is an integer,
but x=1 is an integer but x = $$\frac{1}{5}$$ is not an integer. Insufficient

On combining the information from both the statements,
x has to be an integer (Sufficient) (Option C)

Hello pushpitkc , I understand combining 1 & 2 helps to conclude if its an integer or not ?
But how are we sure its an integer. Can you throw some light?

Hi Arsh4MBA,

On combining the information on both the statements,
the only option when both the expression 2x + 1 and 5x - 1 are integers is when x is an integer

If x is a fraction, the fraction has to have both 2 and 5 in its denominator.
The minimum such value of x is $$\frac{1}{(2*5)}$$, but neither of the expressions will yield an integer

Hope that helps!

Yes It helps. Thanks a lot !!
Re: Is x an integer ? (1) 2x + 1 is an integer (2) 5x – 1 is an integer   [#permalink] 28 Aug 2017, 07:14
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