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03 Jun 2018, 11:59
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If c and d are positive integers and m is the greatest common factor of c and d, then m must be the greatest common factor of c and which of the following integers?
A. c + d
B. 2 + d
C. cd
D. 2d
E. d^2
A. c + d
B. 2 + d
C. cd
D. 2d
E. d^2
03 Jun 2018, 23:16
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Bunuel
If c and d are positive integers and m is the greatest common factor of c and d, then m must be the greatest common factor of c and which of the following integers?
A. c + d
B. 2 + d
C. cd
D. 2d
E. d^2
A. c + d
B. 2 + d
C. cd
D. 2d
E. d^2
IMO - E
Only Option E is always true, as we already know GCF(C , D) = M
Therefore the greatest common factor of GCF(C , D*D) = M
04 Jun 2018, 01:18
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Bunuel
If c and d are positive integers and m is the greatest common factor of c and d, then m must be the greatest common factor of c and which of the following integers?
A. c + d
B. 2 + d
C. cd
D. 2d
E. d^2
A. c + d
B. 2 + d
C. cd
D. 2d
E. d^2
Assume c=6,d=3 (GCF = 3) as GCF of c and d is m
Now, evaluating the answer options and finding the GCF along with c=6
A. c + d = 9 (GCF remains 3)
B. 2 + d = 5 (GCF becomes 1)
C. cd = 18 (GCF becomes 6)
D. 2d = 6 (GCF becomes 6)
E. d^2 = 9 (GCF remains 3)
To eliminate between A and E, let c=12,d=6 (GCF = 6)
A. c + d = 18 (GCF remains 6)
E. d^2 = 36 (GCF becomes 12) (Option A)
