GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 17 Jul 2018, 16:27

### 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

# If n and t are positive integers, what is the greatest prime

Author Message
TAGS:

### Hide Tags

Director
Status: Finally Done. Admitted in Kellogg for 2015 intake
Joined: 25 Jun 2011
Posts: 511
Location: United Kingdom
GMAT 1: 730 Q49 V45
GPA: 2.9
WE: Information Technology (Consulting)
If n and t are positive integers, what is the greatest prime [#permalink]

### Show Tags

29 Jan 2012, 17:24
5
39
00:00

Difficulty:

55% (hard)

Question Stats:

56% (00:43) correct 44% (00:49) wrong based on 662 sessions

### HideShow timer Statistics

If n and t are positive integers, what is the greatest prime factor of nt?

(1) The greatest common factor of n and t is 5
(2) The least common multiple of n and t is 105

Ok - I have got the correct answer B, but it was a guess work on statement 1.

Considering statement 1

n and t can have several values for example n = 25, t = 105. GCF will be 5 but the greatest Prime factor will be 7. However if n and t both equals 5 then GCF will be 5 but greatest prime factor will be 5. Therefore this statement is insufficient. Am I right or wrong?

Considering statement 2

It means that greatest value of n & t is 105 and prime factors of 105 are 1,3,5 and 7. Therefore 7 is the greatest Prime factor. Am I right?

_________________

Best Regards,
E.

MGMAT 1 --> 530
MGMAT 2--> 640
MGMAT 3 ---> 610
GMAT ==> 730

Math Expert
Joined: 02 Sep 2009
Posts: 47037
Re: Greatest Prime Factor of nt [#permalink]

### Show Tags

29 Jan 2012, 17:40
17
16
If n and t are positive integers, what is the greatest prime factor of nt?

(1) The greatest common factor of n and t is 5 --> if n and t does not have any prime greater than 5 then the greatest prime factor of nt will be 5 (example: n=5 and t=5 or n=10 and t=15) BUT if n and/or t have some primes more than 5 then the greatest prime factor of nt will be more than 5 (example: n=35 and t=5 --> the greatest prime of nt is 7 or n=5 and t=55 --> the greatest prime of nt is 11)

(2) The least common multiple of n and t is 105 --> the least common multiple of two integers contains all common primes of these integers, thus 105 has all the primes which appear in both n and t --> the greatest prime factor of 105 is 7, hence it's the the greatest prime factor of nt (no greater factor can "appear" in nt if it's not in either of them). Sufficient.

Hope it's clear.
_________________
##### General Discussion
Intern
Joined: 25 Jan 2014
Posts: 45
GMAT 1: 600 Q44 V29
GMAT 2: 710 Q48 V38
GPA: 3.35
WE: Analyst (Computer Software)
Re: If n and t are positive integers, what is the greatest prime [#permalink]

### Show Tags

14 May 2014, 04:51
Bunuel

It is quite agreed that LCM of two integers will contain all the primes of these integers, does the same hold true for GCF of two numbers as well?
Math Expert
Joined: 02 Sep 2009
Posts: 47037
Re: If n and t are positive integers, what is the greatest prime [#permalink]

### Show Tags

14 May 2014, 06:50
gaurav1418z wrote:
Bunuel

It is quite agreed that LCM of two integers will contain all the primes of these integers, does the same hold true for GCF of two numbers as well?

The greatest common divisor (gcd), also known as the greatest common factor (gcf), or highest common factor (hcf), of two or more non-zero integers, is the largest positive integer that divides the numbers without a remainder.

To find the GCF, you will need to do prime-factorization. Then, multiply the common factors (pick the lowest power of the common factors).

Hence the GCF will contain only the common primes of two number. For example, the GCF of 36=2^2*3^2 and 100=2^2*5^2 is 4=2^2.

Theory on Number Properties: math-number-theory-88376.html

All DS Number Properties Problems to practice: search.php?search_id=tag&tag_id=38
All PS Number Properties Problems to practice: search.php?search_id=tag&tag_id=59

_________________
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 1755
Re: If n and t are positive integers, what is the greatest prime [#permalink]

### Show Tags

26 May 2015, 23:17
Hi All,

Prime factorization is a very strong tool while solving LCM-GCD questions. This question directly tests the process knowledge of prime factorization method of finding LCM-GCD.

For further refinement of your approach in LCM-GCD questions and avoiding fatal mistakes please go through the below article on mistakes committed by students in LCM-GCD questions.

3 Deadly Mistakes you must avoid in LCM-GCD questions

Hope this helps

Regards
Harsh
_________________

Ace GMAT quant
Articles and Question to reach Q51 | Question of the week

Number Properties – Even Odd | LCM GCD
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line

Practice Questions
Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets

| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Director
Joined: 26 Oct 2016
Posts: 664
Location: United States
Schools: HBS '19
GMAT 1: 770 Q51 V44
GPA: 4
WE: Education (Education)
Re: If n and t are positive integers, what is the greatest prime [#permalink]

### Show Tags

31 Jan 2017, 22:18
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.
_________________

Thanks & Regards,
Anaira Mitch

Intern
Joined: 08 Feb 2017
Posts: 6
Re: If n and t are positive integers, what is the greatest prime [#permalink]

### Show Tags

16 Feb 2017, 06:13
Hi guys, I got quite confused after seeing this question in my practice test.

There are no sets of numbers for n and t in whichh the GCF and 5 AND the LCM is 105. Sentences 1 and 2 therefore appear to be inconsistent.

My question is - for data sufficiency questions, aren't the 2 sentences supposed to be consistent with each other and the initial question? Or am I missing something here?

Thanks!

Posted from my mobile device
Math Expert
Joined: 02 Sep 2009
Posts: 47037
Re: If n and t are positive integers, what is the greatest prime [#permalink]

### Show Tags

16 Feb 2017, 06:30
1
bigbanana14 wrote:
Hi guys, I got quite confused after seeing this question in my practice test.

There are no sets of numbers for n and t in whichh the GCF and 5 AND the LCM is 105. Sentences 1 and 2 therefore appear to be inconsistent.

My question is - for data sufficiency questions, aren't the 2 sentences supposed to be consistent with each other and the initial question? Or am I missing something here?

Thanks!

Posted from my mobile device

On the GMAT, two data sufficiency statements always provide TRUE information and these statements NEVER contradict each other or the stem.

But the statements in the original questions does not contradict. Consider
n = 5 and t = 105
n = 15 and t = 35

The greatest common factor of n and t is 5 and the least common multiple of n and t is 105.
_________________
Intern
Joined: 16 Nov 2016
Posts: 3
Re: If n and t are positive integers, what is the greatest prime [#permalink]

### Show Tags

19 Aug 2017, 09:25
I keep stumbling wrt statement 2 here. What if n is 11x7x5x3 and t is 7x5x3. Then the LCM is still 7x5x3=105 but the greatest prime factor of nt is 11?
Math Expert
Joined: 02 Sep 2009
Posts: 47037
Re: If n and t are positive integers, what is the greatest prime [#permalink]

### Show Tags

19 Aug 2017, 09:32
1
shahidkhan42 wrote:
I keep stumbling wrt statement 2 here. What if n is 11x7x5x3 and t is 7x5x3. Then the LCM is still 7x5x3=105 but the greatest prime factor of nt is 11?

You are mixing the least common multiple and the greatest common factor. 105 is the greatest common factor (GCF) of 11*7*5*3 and 7*5*3, not the least common multiple (LCM).
_________________
Intern
Joined: 16 Nov 2016
Posts: 3
Re: If n and t are positive integers, what is the greatest prime [#permalink]

### Show Tags

19 Aug 2017, 09:49
Bunuel wrote:
shahidkhan42 wrote:
I keep stumbling wrt statement 2 here. What if n is 11x7x5x3 and t is 7x5x3. Then the LCM is still 7x5x3=105 but the greatest prime factor of nt is 11?

You are mixing the least common multiple and the greatest common factor. 105 is the greatest common factor (GCF) of 11*7*5*3 and 7*5*3, not the least common multiple (LCM).

Got it. I knew I was messing up something. Thanks.
SVP
Joined: 26 Mar 2013
Posts: 1719
Re: If n and t are positive integers, what is the greatest prime [#permalink]

### Show Tags

20 Aug 2017, 02:25
Bunuel wrote:
If n and t are positive integers, what is the greatest prime factor of nt?

(1) The greatest common factor of n and t is 5 --> if n and t does not have any prime greater than 5 then the greatest prime factor of nt will be 5 (example: n=5 and t=5 or n=10 and t=15) BUT if n and/or t have some primes more than 5 then the greatest prime factor of nt will be more than 5 (example: n=35 and t=5 --> the greatest prime of nt is 7 or n=5 and t=55 --> the greatest prime of nt is 11)

Dear Bunuel,

In Statement 1:

If n = 5 & t =45....then GCF =5 but what is the greatest prime factor of nt?? Is it 3^2 or 5?? When used term greatest, should we include power or ignore it?

Thanks
Math Expert
Joined: 02 Sep 2009
Posts: 47037
Re: If n and t are positive integers, what is the greatest prime [#permalink]

### Show Tags

20 Aug 2017, 02:30
Mo2men wrote:
Bunuel wrote:
If n and t are positive integers, what is the greatest prime factor of nt?

(1) The greatest common factor of n and t is 5 --> if n and t does not have any prime greater than 5 then the greatest prime factor of nt will be 5 (example: n=5 and t=5 or n=10 and t=15) BUT if n and/or t have some primes more than 5 then the greatest prime factor of nt will be more than 5 (example: n=35 and t=5 --> the greatest prime of nt is 7 or n=5 and t=55 --> the greatest prime of nt is 11)

Dear Bunuel,

In Statement 1:

If n = 5 & t =45....then GCF =5 but what is the greatest prime factor of nt?? Is it 3^2 or 5?? When used term greatest, should we include power or ignore it?

Thanks

3^2 = 9 and it's not prime, so you should not consider it.

If n = 5 and t = 45, then $$nt = 5*45 = 3^2*5^2$$. So, the greatest common factor of nt is 5.
_________________
Intern
Joined: 19 Jul 2017
Posts: 19
Re: If n and t are positive integers, what is the greatest prime [#permalink]

### Show Tags

29 Jun 2018, 09:10
[quote="enigma123"]If n and t are positive integers, what is the greatest prime factor of nt?

(1) The greatest common factor of n and t is 5
(2) The least common multiple of n and t is 105

1- it's possible that n = t = 5. then the greatest prime factor of nt is 5.
- it's possible that n = 5 and t = 35. then the greatest prime factor of nt is 7.
insufficient.

2- the least common multiple contains every factor of t or n at least once. (it has to; if, say, t had a factor that wasn't contained in it, then it would fail to be a multiple of t.) so, the biggest prime factor of this # will also be the biggest prime factor of the product nt.
sufficient.
Re: If n and t are positive integers, what is the greatest prime   [#permalink] 29 Jun 2018, 09:10
Display posts from previous: Sort by

# Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.