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Math Expert V
Joined: 02 Sep 2009
Posts: 55801
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: 59% (01:05) correct 41% (00:54) wrong based on 38 sessions

HideShow timer Statistics Is x an integer ?

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

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Senior PS Moderator V
Joined: 26 Feb 2016
Posts: 3364
Location: India
GPA: 3.12
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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You've got what it takes, but it will take everything you've got
Senior PS Moderator V
Joined: 26 Feb 2016
Posts: 3364
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!
_________________
You've got what it takes, but it will take everything you've got
Current Student P
Joined: 18 Aug 2016
Posts: 617
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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Luckisnoexcuse
Manager  B
Joined: 19 Jul 2017
Posts: 85
Location: India
Concentration: General Management, Strategy
GPA: 3.5
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?
Manager  B
Joined: 19 Jul 2017
Posts: 85
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]

Show Tags

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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