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![If the expression [m]x^2 + 9[/m] and x + 5 are to have a common odd f](/forum/styles/gmatclub_light/imageset/icon_post_target_unread.svg "If the expression [m]x^2 + 9[/m] and x + 5 are to have a common odd f"){kind=icon}
26 May 2019, 17:37
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Difficulty:
95%
(hard)
Question Stats:
26% (01:44) correct
74%
(02:39)
wrong
based on 88
sessions
History
Date
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If the expression \(x^2 + 9\) and x + 5 have a common odd factor other than 1 such that x is a natural number less than 100, then how many values of x are possible.
A. 0
B. 4
C. 6
D. 8
E. 10
A. 0
B. 4
C. 6
D. 8
E. 10
Let k is the common odd factor
\(x^2+9= (x+5)^2 -(10x+16)\)
if k is the factor of x+5 and \(x^2+9\), then 'k' must be the factor of 10x+16
10x+16= 10(x+5)-34
if k is the factor of x+5 and 10x+16, then 'k' must be the factor of (34)
There are 2 odd factors of 34= 1 and 17
k can't be 1, hence k=17
x+5=17m where m is a natural number
x can be 12, 29, 46, 63, 80 or 97
Hence x can take 6 values.
\(x^2+9= (x+5)^2 -(10x+16)\)
if k is the factor of x+5 and \(x^2+9\), then 'k' must be the factor of 10x+16
10x+16= 10(x+5)-34
if k is the factor of x+5 and 10x+16, then 'k' must be the factor of (34)
There are 2 odd factors of 34= 1 and 17
k can't be 1, hence k=17
x+5=17m where m is a natural number
x can be 12, 29, 46, 63, 80 or 97
Hence x can take 6 values.
nick1816
ayushkumar22941
Joined: 26 Apr 2019
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Location: India
Concentration: Finance, Leadership
Schools: ISB '21 (II) Schulich(Jan) '22 Marshall'23 Broad (A) Tepper '23 IIMA PGPX'22 (I) Rotman '23 Said '22 Kelley '23 (WL)
GMAT 1: 690 Q49 V34
GMAT 2: 700 Q49 V36
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GMAT 4: 740 Q50 V40
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Schools: ISB '21 (II) Schulich(Jan) '22 Marshall'23 Broad (A) Tepper '23 IIMA PGPX'22 (I) Rotman '23 Said '22 Kelley '23 (WL)
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27 May 2019, 12:22
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tough problem , you cant solve such question unless you have practiced such questions.
