 It is currently 28 Sep 2020, 01:33 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. # If c and d are positive integers and m is the greatest comm  Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:
Founder  Joined: 18 Apr 2015
Posts: 13371
Followers: 291

Kudos [?]: 3402 , given: 12227

If c and d are positive integers and m is the greatest comm [#permalink]
Expert's post 00:00

Question Stats: 36% (01:16) correct 63% (01:17) wrong based on 79 sessions
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 $$d^2$$

Kudos to the right solution and explanation
[Reveal] Spoiler: OA

_________________

Need Practice? 20 Free GRE Quant Tests available for free with 20 Kudos
GRE Prep Club Members of the Month: Each member of the month will get three months free access of GRE Prep Club tests. Sherpa Prep Representative Joined: 15 Jan 2018
Posts: 147
GMAT 1: Q V
Followers: 7

Kudos [?]: 240  , given: 0

Re: If c and d are positive integers and m is the greatest comm [#permalink]
2
KUDOS
Expert's post
We can solve this problem using either logic or just picking numbers. I'll use a combination of both.

If we call c 15, and d 21, then the greatest common factor, m, is 3. Let's look at the answer choices:

A) c + d = 36, and the greatest common factor of c and c + d is 3, which is m. So using the numbers we've chose this appears to work. Logic is a bit more airtight, but tougher. But if you factor out the greatest common factor from c + d, you'd get m(leftovers of c + leftovers of d). We know that there are no factors in common in the leftovers of c and d since if there were, it would be included in m, so we therefore know that m is the GCF of c and c + d. So it's A.

B) Using our picked numbers, 2 + d = 23, which is a prime number and has no common factors with 15, so B is out. Logically, there's no reason to think that adding two to D will allow it to have a common factor with C.

C) cd = 15x21 = 315. The GCF of 15 and 315 is 15 itself. Logically, that makes sense: cd is simply some multiple of c, so c has to be the GCF of the two of them.

D) 2d = 42, and the GCF of 15 and 42 is 3, or m. But does it have to be? We've just put in an extra 2. What if c had had a 2 in it? For example, if we'd picked c = 6 and d = 21, their GCF is still 3, but the GCF of 6 and 2d, or 42, is now 6. So this one's out.

E) d^2 = 21^2 which is 441. (This should be on your list of things to memorize, but if you haven't, you could always just make it a smaller number that you do know the square of.) The GCF of 15 and 441 is 3, or m, so this looks good. But again, it doesn't have to work. What if c had had a square in it that d didn't have, but when you squared d it did have it? Let's say c = 45 and d = 21. So m is still 3 and d^2 is still 441. But now we know d^2 has 9 as a factor, and so does 45. Since 9 isn't m, E is out.

So it's A.
_________________

-
-
-
-
-

Need help with GRE math? Check out our ground-breaking books and app. Target Test Prep Representative Affiliations: Target Test Prep
Joined: 09 May 2016
Posts: 161
Location: United States
Followers: 8

Kudos [?]: 195  , given: 0

Re: If c and d are positive integers and m is the greatest comm [#permalink]
2
KUDOS
Expert's post
Carcass 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.

_________________

# Jeffrey Miller

Jeff@TargetTestPrep.com

See why Target Test Prep is the top rated GRE quant course on GRE Prep Club. Read Our Reviews

Manager Joined: 08 Dec 2018
Posts: 94
Followers: 0

Kudos [?]: 44 , given: 30

Re: If c and d are positive integers and m is the greatest comm [#permalink]
Can C in the above math equal M- where M is the greatest common factor?
Can we assume that C=2, D=8, M=2, or C and M are different integers ?
Founder  Joined: 18 Apr 2015
Posts: 13371
Followers: 291

Kudos [?]: 3402 , given: 12227

Re: If c and d are positive integers and m is the greatest comm [#permalink]
Expert's post
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)

It is assumed that the two numbers are different
_________________

Need Practice? 20 Free GRE Quant Tests available for free with 20 Kudos
GRE Prep Club Members of the Month: Each member of the month will get three months free access of GRE Prep Club tests.

Intern Joined: 23 Sep 2019
Posts: 1
Followers: 0

Kudos [?]: 0 , given: 0

Re: If c and d are positive integers and m is the greatest comm [#permalink]
can someone prove this question for the pair (6,8). If not, why? GRE Instructor Joined: 10 Apr 2015
Posts: 3838
Followers: 149

Kudos [?]: 4499  , given: 69

Re: If c and d are positive integers and m is the greatest comm [#permalink]
1
KUDOS
Expert's post
ANKITDROCH1995 wrote:
can someone prove this question for the pair (6,8). If not, why?

If c = 6 and d = 8, then we find that answer choices A, B, D and E all work.
That is, we can only eliminate C when we test c = 6 and d = 8
This means we have to now test another pair of values.

Likewise, if we use c = 2 and d = 2, then we find that EVERY answer choice works.

Cheers,
Brent
_________________

Brent Hanneson – Creator of greenlighttestprep.com
If you enjoy my solutions, you'll like my GRE prep course.  Re: If c and d are positive integers and m is the greatest comm   [#permalink] 24 Sep 2019, 06:18
Display posts from previous: Sort by

# If c and d are positive integers and m is the greatest comm  Question banks Downloads My Bookmarks Reviews Important topics  Powered by phpBB © phpBB Group Kindly note that the GRE® test is a registered trademark of the Educational Testing Service®, and this site has neither been reviewed nor endorsed by ETS®.