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Updated on: 10 Mar 2024, 09:12
Originally posted by EgmatQuantExpert on 28 Feb 2018, 03:08.
Last edited by Bunuel on 10 Mar 2024, 09:12, edited 4 times in total.
Last edited by Bunuel on 10 Mar 2024, 09:12, edited 4 times in total.
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
35% (02:17) correct
65%
(02:06)
wrong
based on 353
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If \(x\) is a positive integer, is the GCD of \(x+3\) and \(x+5\) more than \(1\)?
(1) \(3x\) is the common factor of \(12\) and \(6\).
(2) \(2x^n\) has \(1\) prime factor.
This is
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(1) \(3x\) is the common factor of \(12\) and \(6\).
(2) \(2x^n\) has \(1\) prime factor.
- A) Statement (1) ALONE is sufficient, but statement (2) ALONE is not sufficient.
B) Statement (2) ALONE is sufficient, but statement (1) ALONE is not sufficient.
C) Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D) EACH statement ALONE is sufficient.
E) Statement (1) and (2) TOGETHER are NOT sufficient.
This is
Question 7 of The e-GMAT Number Properties Marathon
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28 Feb 2018, 04:01
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EgmatQuantExpert
we need to find value of x and check if x+3 and x+5 are co-prime together
1) 3x is the common factor of 12 and 6
factors of 12= 1,2,3,4,6,12
factors of 6 = 1,2,3,6
common factor = 1,2,3,6
3x = 3 or 3x=6
x= 1 or x =2
if x=1
x+3 and x+5 are 4 and 6 hcf >1
but if x=2
x+3 and x+5 are 5 and 7 hcf not greater than insufficient
2) 2x^n has 1 prime factor
i.e x^n is a power of 2/x=1
if x=1
2x^n = 2
x=2 n=2
2x^n = 2^3
x=2
similar cases to A
insufficient
combining we get x as 1/2
(E) imo
If common factor = HCF then (A) imo
My understanding of common factor is neccesatrily not the greatest common factor
niks18, pushpitkc and amanvermagmat what do you guys think?
28 Feb 2018, 06:14
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Hey Hatakekakashi
A common factor is not necessarily the HCF.
HCF is the highest common factor and there can be other common factors for two numbers as well.
Consider the numbers 4 and 12. The HCF is 4, but 2 is also a common factor.
As per my understanding, the solution you have given is perfect and the OA must be E!
A common factor is not necessarily the HCF.
HCF is the highest common factor and there can be other common factors for two numbers as well.
Consider the numbers 4 and 12. The HCF is 4, but 2 is also a common factor.
As per my understanding, the solution you have given is perfect and the OA must be E!
