It is currently 19 Feb 2018, 16:03

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# If a is a positive integer and

Author Message
TAGS:

### Hide Tags

Manager
Joined: 21 Oct 2017
Posts: 66
Concentration: Entrepreneurship, Technology
GMAT 1: 750 Q48 V44
WE: Project Management (Internet and New Media)
If a is a positive integer and [#permalink]

### Show Tags

25 Nov 2017, 14:33
1
KUDOS
00:00

Difficulty:

15% (low)

Question Stats:

79% (01:12) correct 21% (01:34) wrong based on 52 sessions

### HideShow timer Statistics

If a is a positive integer and $$\frac{22a}{210}$$ is also an integer, how many different positive prime factors could a possibly have at most given that a is less than 150?

A) Two
B) Three
C) Four
D) Five
E) Six
[Reveal] Spoiler: OA

_________________

Please Press +1 Kudos if it helps!

October 9th, 2017: Diagnostic Exam - Admit Master (GoGMAT) - 640
November 11th, 2017: CAT 1 - Admit Master (GoGMAT) - 700
November 20th, 2017: CAT 2 - GMATPrep - 700 (Q: 47, V: 40)
November 25th, 2017: CAT 3 - Admit Master (GoGMAT) - 710 (Q: 48, V: 40)
November 27th, 2017: CAT 4 - GMATPrep - 720 (Q: 49, V: 40)

December 4th, 2017: GMAT Exam - 750 (Q: 48, V: 44, IR: 8, AWA: 6)

Intern
Joined: 05 Nov 2017
Posts: 5
Re: If a is a positive integer and [#permalink]

### Show Tags

25 Nov 2017, 19:37
If a is a positive integer and $$\frac{22a}{210}$$ is also an integer, how many different positive prime factors could a possibly have at most given that a is less than 150?

A) Two
B) Three
C) Four
D) Five
E) Six

Ans : B

210 = 2*3*5*7
22a = 2*11*a

For 22a to be perfectly divisible by 210, a should have the missing prime factors 3,5 and 7.
Math Expert
Joined: 02 Sep 2009
Posts: 43810
Re: If a is a positive integer and [#permalink]

### Show Tags

26 Nov 2017, 00:44
1
KUDOS
Expert's post
If a is a positive integer and $$\frac{22a}{210}$$ is also an integer, how many different positive prime factors could a possibly have at most given that a is less than 150?

A) Two
B) Three
C) Four
D) Five
E) Six

Similar question from GMAT Prep: https://gmatclub.com/forum/in-n-is-a-po ... 00763.html
_________________
Intern
Joined: 15 Jan 2017
Posts: 1
Re: If a is a positive integer and [#permalink]

### Show Tags

26 Nov 2017, 17:42
210 = 2x3x5x7
22= 2x11
22a/210 = 11a/3x5x7 is a integer

a must contain 3,5,7
prime factor a= kx3x5x7=kx105 if k=2 therefore a>150
so three prime factors
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 2181
Location: United States (CA)
Re: If a is a positive integer and [#permalink]

### Show Tags

29 Nov 2017, 09:59
If a is a positive integer and $$\frac{22a}{210}$$ is also an integer, how many different positive prime factors could a possibly have at most given that a is less than 150?

A) Two
B) Three
C) Four
D) Five
E) Six

Let’s simplify the given expression:

22a/210 = 11a/105

Thus, we see that a/105 is an integer. In other words, a = 105k for some positive integer k. However, since we are given that a is less than 150, we see that k must be 1 and thus a must be 105.

Since 105 = 7 x 3 x 5, we see that a could have 3 different prime factors.

_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Re: If a is a positive integer and   [#permalink] 29 Nov 2017, 09:59
Display posts from previous: Sort by