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# Is x an integer? (1) The average (arithmetic mean) of x – 1 and x +

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Is x an integer? (1) The average (arithmetic mean) of x – 1 and x +  [#permalink]

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09 Jan 2018, 23:32
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54% (01:14) correct 46% (01:23) wrong based on 45 sessions

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Is x an integer?

(1) The average (arithmetic mean) of x – 1 and x + 1 is an integer.
(2) The average (arithmetic mean) of x and –x is an integer.

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Re: Is x an integer? (1) The average (arithmetic mean) of x – 1 and x +  [#permalink]

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10 Jan 2018, 00:11
Bunuel wrote:
Is x an integer?

(1) The average (arithmetic mean) of x – 1 and x + 1 is an integer.
(2) The average (arithmetic mean) of x and –x is an integer.

(1) Average of x-1 and x+1 is = (x-1 + x+1)/2 = 2x/2 = x, which is given to be an integer. So x is an integer. Sufficient.

(2) Average of x and -x is = (x - x)/2 = 0/2 = 0. Whatever be the value of x (integer or non-integer), sum of x and -x will always be 0, and thus average will also be 0. So we cant say whether x is an integer or not based on this information. Insufficient.

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Re: Is x an integer? (1) The average (arithmetic mean) of x – 1 and x +  [#permalink]

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10 Jan 2018, 11:43
X could be a decimal also right ? Will A be the sufficient answer ?

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Re: Is x an integer? (1) The average (arithmetic mean) of x – 1 and x +  [#permalink]

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10 Jan 2018, 20:37
Bunuel wrote:
Is x an integer?

(1) The average (arithmetic mean) of x – 1 and x + 1 is an integer.
(2) The average (arithmetic mean) of x and –x is an integer.

Stmnt 1: Let X = 1.. we get average as Integer, let x = 1/2 we get average as Integer.. So not suffiecient.
Stmn 2: X = 1, Average Integer... X = 1/2, Average = Integer

So E.
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Re: Is x an integer? (1) The average (arithmetic mean) of x – 1 and x +  [#permalink]

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10 Jan 2018, 21:12
Average of x-1 and x+1 is X which is given to be an integer so X is an integer so sufficient. Statement 2 the average is 0 which does not give any idea abt X. So not sufficient. So answer is A.

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Re: Is x an integer? (1) The average (arithmetic mean) of x – 1 and x +  [#permalink]

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10 Jan 2018, 21:30
rahul16singh28 wrote:
Bunuel wrote:
Is x an integer?

(1) The average (arithmetic mean) of x – 1 and x + 1 is an integer.
(2) The average (arithmetic mean) of x and –x is an integer.

Stmnt 1: Let X = 1.. we get average as Integer, let x = 1/2 we get average as Integer.. So not suffiecient.
Stmn 2: X = 1, Average Integer... X = 1/2, Average = Integer

So E.

I
Average of x-1 and x+1 is nothing but x itself and it is given as integer, so x is integer..
average of x-1 and x+1 is $$\frac{x-1+x+1}{2}=\frac{2x}{2}=x$$
so statement I is suff..

II
Whatever be value of x, the average of x and -x should be 0
so statement II does not tell anything new
insuff

A
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Re: Is x an integer? (1) The average (arithmetic mean) of x – 1 and x +  [#permalink]

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10 Jan 2018, 21:38
Average is 0 in statement 2 and not the value of x. X can be integer or non integer the average of X and -x is always 0. So it doesnt say the type of X

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Re: Is x an integer? (1) The average (arithmetic mean) of x – 1 and x +  [#permalink]

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10 Jan 2018, 22:43
akhilbatra06 wrote:
Zero is an integer

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Hi

Yes, zero is an integer. So average of x and -x will be 0, which is an integer. If x=2, then also average of x and -x is zero. If x=1.5, then also average of x and -x is zero.
So zero being an integer doesnt tell us anything whether x will be an integer or not. '

So answer should be A.
Re: Is x an integer? (1) The average (arithmetic mean) of x – 1 and x +   [#permalink] 10 Jan 2018, 22:43
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# Is x an integer? (1) The average (arithmetic mean) of x – 1 and x +

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