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# Is a single digit integer x even? 1) Sum of all the factors of x is e

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Is a single digit integer x even? 1) Sum of all the factors of x is e  [#permalink]

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30 Jun 2017, 20:05
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Difficulty:

45% (medium)

Question Stats:

67% (01:51) correct 33% (01:41) wrong based on 48 sessions

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Is a single digit integer x even?

1) Sum of all the factors of x is equal to twice the number
2) x is divisible by 3

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Re: Is a single digit integer x even? 1) Sum of all the factors of x is e  [#permalink]

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30 Jun 2017, 20:29
Is a single digit integer x even?

1) Sum of all the factors of x is equal to twice the number
2) x is divisible by 3

X = 2k ?

St1: factors of x = 2* x
Let sum of factors of x= y
Then, y= 2x, this implies y is divisible by 2
Therefore x is even
Sufficient

St2: x is div by 3
X can be 3,6,9,12
Not sufficient

Option A
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Re: Is a single digit integer x even? 1) Sum of all the factors of x is e  [#permalink]

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30 Jun 2017, 21:30
RaguramanS wrote:
Is a single digit integer x even?

1) Sum of all the factors of x is equal to twice the number
2) x is divisible by 3

X = 2k ?

St1: factors of x = 2* x
Let sum of factors of x= y
Then, y= 2x, this implies y is divisible by 2
Therefore x is even
Sufficient

St2: x is div by 3
X can be 3,6,9,12
Not sufficient

Option A

Reasoning of statement 1 is incorrect in the above mentioned solution

CORRECT REASONING
from 1 to 9 there is only one number (which is 6) for which sum of all he factors = 2*Number

Factors of 6 = 1, 2, 3, 6
and 1+2+3+6 = 12 = 2*6

hence, SUFFICIENT
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Re: Is a single digit integer x even? 1) Sum of all the factors of x is e  [#permalink]

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30 Jun 2017, 22:39
GMATinsight wrote:

CORRECT REASONING
from 1 to 9 there is only one number (which is 6) for which sum of all he factors = 2*Number

Factors of 6 = 1, 2, 3, 6
and 1+2+3+6 = 12 = 2*6

hence, SUFFICIENT

Thanks for the clarification.
So checking every number from 1 to 9 is the only way to solve the problem.?
Can you please elaborate on why my above reasoning is wrong. I have generalized the statement to save time.
The actual number as per my analysis is also an even number.
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Re: Is a single digit integer x even? 1) Sum of all the factors of x is e   [#permalink] 30 Jun 2017, 22:39
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