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Retired Moderator
Joined: 19 Nov 2020
Posts: 326
Given Kudos: 64
GRE 1: Q160 V152
A difference between the numbers of odd ...
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Updated on: 28 Jul 2021, 01:30
Updated on: 28 Jul 2021, 01:30
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Question Stats:
75% (02:34) correct
25% (00:59) wrong based on 4 sessions
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A difference between the numbers of positive odd and even factors of 344 when multipled by \(\frac{1}{2}\) is equal to which value
A) -3
B) -2
C) 1
D) 2
E) 3
A) -3
B) -2
C) 1
D) 2
E) 3
Originally posted by motion2020 on 27 Jul 2021, 17:34.
Last edited by motion2020 on 28 Jul 2021, 01:30, edited 1 time in total.
Last edited by motion2020 on 28 Jul 2021, 01:30, edited 1 time in total.
Re: A difference between the numbers of odd ...
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28 Jul 2021, 00:19
28 Jul 2021, 00:19
1
Factors of \(344 ( 2 * 2 * 2 * 43 ) = 1 , 2 , 4 , 8 , 43 , 86 , 172 , 344\)
No of odd factors : \(2\) & no of even factors : \(6\)
A difference between the numbers of odd and even factors \(= 2 - 6 = -4\)
Multiply by \(\frac{1}{2}\) \(= \frac{-4}{2} = -2\)
Answer B
No of odd factors : \(2\) & no of even factors : \(6\)
A difference between the numbers of odd and even factors \(= 2 - 6 = -4\)
Multiply by \(\frac{1}{2}\) \(= \frac{-4}{2} = -2\)
Answer B
Retired Moderator
Joined: 19 Nov 2020
Posts: 326
Given Kudos: 64
GRE 1: Q160 V152
A difference between the numbers of odd ...
[#permalink]
28 Jul 2021, 01:29
28 Jul 2021, 01:29
rx10 wrote:
Factors of \(344 ( 2 * 2 * 2 * 43 ) = 1 , 2 , 4 , 8 , 43 , 86 , 172 , 344\)
No of odd factors : \(2\) & no of even factors : \(6\)
A difference between the numbers of odd and even factors \(= 2 - 6 = -4\)
Multiply by \(\frac{1}{2}\) \(= \frac{-4}{2} = -2\)
Answer B
No of odd factors : \(2\) & no of even factors : \(6\)
A difference between the numbers of odd and even factors \(= 2 - 6 = -4\)
Multiply by \(\frac{1}{2}\) \(= \frac{-4}{2} = -2\)
Answer B
Great, thanks for solution. My only worry is that with bigger number, say not 344 but 687 or something different, listing the odd and the even may be time consuming. Therefore, I offer to separate these two categories such as \(2^3 * 43\) and the number of positive factors will be \((3+1)*(1+1)\). While the number of odd factors is simply \((1+1)\), the remaining will be even factors \(8-2=6\).
I have also updated the question's prompt as factors sought here are positive only. This is my made question. I have GRE in less than 10 days (6th August). Fingers crossed, as I hope to attain at least Q160
