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If c and d are positive integers and m is the greatest common factor

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If c and d are positive integers and m is the greatest common factor  [#permalink]

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New post 03 Jun 2018, 10:59
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A
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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
Spoiler: OA

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Re: If c and d are positive integers and m is the greatest common factor  [#permalink]

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New post 03 Jun 2018, 22:16
Bunuel wrote:
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


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
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If c and d are positive integers and m is the greatest common factor  [#permalink]

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New post 04 Jun 2018, 00:18
Bunuel wrote:
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


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)
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Re: If c and d are positive integers and m is the greatest common factor  [#permalink]

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New post 05 Jun 2018, 14:36
If m is a factor of c and d, then m must be a factor of (c+d) and (c-d).

Ans A

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Re: If c and d are positive integers and m is the greatest common factor  [#permalink]

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New post 11 Jun 2018, 07:23
Answer is A and here is why.
Assume c and d be 6 and 15, respectively. M would be 3, and checking answer choices we are left with either A or E, because B is 17, gcf is 1 and 17; C is 90 (2*3^2*5), gcf is 2; D is 30 (2*3*5), gcf is 2. I was between A and E and picked A. Maybe someone knows how to check further?
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Re: If c and d are positive integers and m is the greatest common factor  [#permalink]

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New post 13 Jun 2018, 15:22
Bunuel wrote:
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


Let’s let c = 4 and d = 6, so m = GCF(4, 6) = 2. Let’s analyze each choice.

A. c + d = 10, and GCF(4, 10) = 2, so A could be the answer.

B. 2 + d = 8, and GCF(4, 8) = 4, so B could not be the answer.

C. cd = 24, and GCF(4, 24) = 4, so C could not be the answer.

D. 2d = 12, and GCF(4, 12) = 4, so D could not be the answer.

E. d^2 = 36, and GCF(4, 36) = 4, so E could not be the answer.

Answer: A
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Re: If c and d are positive integers and m is the greatest common factor  [#permalink]

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New post 29 Mar 2020, 06:05
Bunuel wrote:
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


Asked: 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?
gcd(c, d)= m

Let us take (c,d) = (12,30); gcd(12,30) = 6
A. c + d
gcd(12,42) = 6: TRUE
B. 2 + d
gcd(12,32) = 4: FALSE
C. cd
gcd(12,12*42) = 12: FALSE
D. 2d
gcd(12,60) = 12: FALSE
E. d^2
gcd(12,900) = 12: FALSE

IMO A
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Re: If c and d are positive integers and m is the greatest common factor   [#permalink] 29 Mar 2020, 06:05
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