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Updated on: 25 Jun 2017, 00:31
Originally posted by GMATinsight on 24 Jun 2017, 20:55.
Last edited by GMATinsight on 25 Jun 2017, 00:31, edited 1 time in total.
Last edited by GMATinsight on 25 Jun 2017, 00:31, edited 1 time in total.
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
55% (02:02) correct
45%
(01:52)
wrong
based on 137
sessions
History
Date
Time
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Not Attempted Yet
Is n a multiple of 6?
1) 3n has twice as many factors as n has
2) 2n has twice as many factors as n has
Source: https://www.GMATinsight.com
1) 3n has twice as many factors as n has
2) 2n has twice as many factors as n has
Source: https://www.GMATinsight.com
24 Jun 2017, 22:29
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I chose D.
Here is my approach
For n to be a multiple of 6, it has to be a multiple of 3 and 2 both.
Statement 1
3n has twice as many factors as n.
Let the highest power of 3 in n be a
this means that number of factors of n= (a+1)*y
now 3n will have (a+2)*y factors=2*(a+1)*y
a+2=2a+2
a=0
thus n is not a multiple of 3 and thus not a multiple of 6
similarly for statement 2
n is not a multiple of 2.
Thus both the statements individually are sufficient.
Where did I go wrong?
Here is my approach
For n to be a multiple of 6, it has to be a multiple of 3 and 2 both.
Statement 1
3n has twice as many factors as n.
Let the highest power of 3 in n be a
this means that number of factors of n= (a+1)*y
now 3n will have (a+2)*y factors=2*(a+1)*y
a+2=2a+2
a=0
thus n is not a multiple of 3 and thus not a multiple of 6
similarly for statement 2
n is not a multiple of 2.
Thus both the statements individually are sufficient.
Where did I go wrong?
24 Jun 2017, 23:35
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GMATinsight
Hi,
Since we are saying n has factors so n is a positive integer.
For n to be a multiple of 6, n has to be multiple of both 2 and 3...
Let's see the statements..
1) 3n has twice as many factors as n has..
This is possible ONLY when n is not a multiple of 3.
Factors become two times, as when 3 is added..
The factors of n will get multiplied by (1+1) from 3^1.
So n is not a multiple of 3 and thus of 6
Sufficient
2) 2n has twice as many factors as n has
Same logic as above.
n is not a multiple of 2, and thus of 6
Sufficient
D
GMATinsight, pl relook into your Q
