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21 Dec 2018, 06:01
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
69% (01:23) correct
31%
(01:33)
wrong
based on 300
sessions
History
Date
Time
Result
Not Attempted Yet
If a, b, and c are positive integers, what is the greatest common divisor of a, b and c?
(1) The greatest common divisor of a and b is 3
(2) The greatest common divisor of b and c is 4
M36-46
(1) The greatest common divisor of a and b is 3
(2) The greatest common divisor of b and c is 4
M36-46
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08 Nov 2021, 02:33
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Bunuel
If a, b, and c are positive integers, what is the greatest common divisor of a, b and c?
(1) The greatest common divisor of a and b is 3
(2) The greatest common divisor of b and c is 4
(1) The greatest common divisor of a and b is 3
(2) The greatest common divisor of b and c is 4
Official Solution:
If \(a\), \(b\), and \(c\) are positive integers, what is the greatest common divisor of \(a\), \(b\) and \(c\)?
(1) The greatest common divisor of \(a\) and \(b\) is 3
If the third unknown, \(c\), is also divisible by 3, then the greatest common divisor of \(a\), \(b\) and \(c\) will be 3 (it cannot be more than 3, since 3 is the GCD of \(a\) and \(b\)) but if \(c\) is NOT divisible by 3, then the greatest common divisor of \(a\), \(b\) and \(c\) will be 1. Not sufficient.
(2) The greatest common divisor of \(b\) and \(c\) is 4
If the third unknown, \(a\), is also divisible by 4, then the greatest common divisor of \(a\), \(b\) and \(c\) will be 4 (it cannot be more than 4, since 4 is the GCD of \(b\) and \(c\)) but if \(a\) is NOT divisible by 4, then the greatest common divisor of \(a\), \(b\) and \(c\) will be 1. Not sufficient.
(1)+(2) From (1) we know that \(b\) is divisible by 3 and if \(c\) were also divisible by 3, then the greatest common divisor of \(b\) and \(c\) would be 12, not 4, as given in (2). Thus, \(c\) is NOT divisible by 3, and as we deduced in (1), if \(c\) is NOT divisible by 3, then the greatest common divisor of \(a\), \(b\) and \(c\) will be 1. Sufficient.
Answer: C
General Discussion
aru010
Joined: 19 Nov 2017
Last visit: 17 Feb 2025
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Location: Singapore
Concentration: Technology, Entrepreneurship
Schools: Duke '22 (D) Kellogg '22 (D) Melbourne '21 (A$) Owen '22 (A$) Cornell Tech "21 (A$) Rotman '22 (A$) Schulich(Jan) '22 (A)
GMAT 1: 590 Q45 V27
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Schools: Duke '22 (D) Kellogg '22 (D) Melbourne '21 (A$) Owen '22 (A$) Cornell Tech "21 (A$) Rotman '22 (A$) Schulich(Jan) '22 (A)
GMAT 2: 700 Q48 V37
Posts: 11
23 Dec 2018, 04:19
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I got E.
Since by St#2 : b = 4x , c = 4y , not enough
And by St#1 : a = 3z , b = 3x , not enough
Combining ,in (c)
a= 3z
b = 3*4*x
c = 4*y
We cannot get common factor from here, hence (e)
Since by St#2 : b = 4x , c = 4y , not enough
And by St#1 : a = 3z , b = 3x , not enough
Combining ,in (c)
a= 3z
b = 3*4*x
c = 4*y
We cannot get common factor from here, hence (e)
