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

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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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New post 28 Aug 2017, 04:06
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

59% (01:05) correct 41% (00:54) wrong based on 38 sessions

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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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New post 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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Is x an integer ? (1) 2x + 1 is an integer (2) 5x – 1 is an integer  [#permalink]

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New post 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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Re: Is x an integer ? (1) 2x + 1 is an integer (2) 5x – 1 is an integer  [#permalink]

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New post 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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Is x an integer ? (1) 2x + 1 is an integer (2) 5x – 1 is an integer  [#permalink]

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New post 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?
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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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New post 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 !!
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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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