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Math Expert V
Joined: 02 Sep 2009
Posts: 55277
Is x an integer ? (1) 2x + 1 is an integer (2) 5x – 1 is an integer  [#permalink]

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Difficulty:   45% (medium)

Question Stats: 57% (01:03) correct 43% (00:54) wrong based on 37 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: 18 Aug 2016
Posts: 618
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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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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Senior PS Moderator V
Joined: 26 Feb 2016
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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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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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Joined: 19 Jul 2017
Posts: 85
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Concentration: General Management, Strategy
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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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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?
Senior PS Moderator V
Joined: 26 Feb 2016
Posts: 3386
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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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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Joined: 19 Jul 2017
Posts: 85
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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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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# Is x an integer ? (1) 2x + 1 is an integer (2) 5x – 1 is an integer

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