BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

the greatest prime factor of n t

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
GMAT Instructor
Posts: 3650
Joined: Wed Jan 21, 2009 4:27 am
Location: India
Thanked: 267 times
Followed by:80 members
GMAT Score:760

the greatest prime factor of n t

by sanju09 » Wed Apr 08, 2009 4:57 am
If n and t are positive integers, what is the greatest prime factor of n t?

(1) The greatest common factor of n and t is 5.

(2) The least common multiple of n and t is 105.



OA B
The mind is everything. What you think you become. -Lord Buddha



Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com
Top
Source: — Data Sufficiency |
Master | Next Rank: 500 Posts
Posts: 418
Joined: Wed Jun 11, 2008 5:29 am
Thanked: 65 times

by bluementor » Thu Apr 09, 2009 4:43 am
Statement 1: GCF(n,t) = 5

if n=15, t=10, greatest prime factor of nt = 5
if n=21, t=15, greatest prime factor of nt = 7. Hence insufficient.

Statement 2: LCM(n,t) = 105 = 3x5x7

7 is the greatest prime factor for 105.

either n or t or both must contain 7 as a factor. Therefore 7 is the greatest prime factor of nt. Sufficient.

Choose B.

-BM-
Top
Newbie | Next Rank: 10 Posts
Posts: 1
Joined: Wed Aug 18, 2010 4:05 pm
Thanked: 1 times

by TheDeliveryGuy » Mon Aug 23, 2010 4:15 pm
Bluementor, I think you overlooked an important fact in statement 1:

(1) The greatest common factor of n and t is 5.

Although your answer is correct and your though process is aligned with what the question intends. The statement specifies that both n and t have 5 as GCF. N=21 (1*3*7) does not have 5 as a factor and can't be used in this case. An alternative example (and easier to compute mentally) would be n=5 and t=5 versus n=35 (equivalent to 7*5) and t=5. The GCF would indeed be 5 for both, but the product of n and t in the second case would yield 175, which is divisible by 1, 5, 7, and 7 being the largest prime factor. Therefore insufficient.

Notice that we could have used the next highest prime factor, in this case 11. We would have obtained n=55 (5*11) and t=5. The GCF is 5, but the greatest prime of their product is now 11. When confronted with these type of questions that involve prime, common, and least common factors, it is almost always easier to visualize and decompose the numbers in terms of factors. Instead of thinking about 4 (visualize 2*2) or instead of 12 (visualize 1*2*3). This enables you to see the big picture and prevents you from committing "silly" mistakes.

(2) The least common multiple of n and t is 105.

Assume n=105 (3,5,7) and lets say we double this and use t=210 (2,3,5,7) as well. 7 remains the largest prime factor. We could even use n=105 (3,5,7) and t=1155 (3,5,7,11), but still 7 will be largest prime in common. Hence sufficient.
Top
Post new topic Post Reply
• Page 1 of 1