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

 It is currently 14 Dec 2018, 16:59

### 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 December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
• ### Typical Day of a UCLA MBA Student - Recording of Webinar with UCLA Adcom and Student

December 14, 2018

December 14, 2018

10:00 PM PST

11:00 PM PST

Carolyn and Brett - nicely explained what is the typical day of a UCLA student. I am posting below recording of the webinar for those who could't attend this session.
• ### Free GMAT Strategy Webinar

December 15, 2018

December 15, 2018

07:00 AM PST

09:00 AM PST

Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.

# Find the number of factors of a three digit even number xyz

Author Message
TAGS:

### Hide Tags

Intern
Joined: 19 Feb 2012
Posts: 4
Find the number of factors of a three digit even number xyz  [#permalink]

### Show Tags

Updated on: 27 May 2013, 03:47
1
5
00:00

Difficulty:

55% (hard)

Question Stats:

62% (01:41) correct 38% (01:38) wrong based on 218 sessions

### HideShow timer Statistics

Find the number of factors of a three digit even number xyz where x, y and z are distinct prime numbers (2, 3 and 5)

A. 8
B. 10
C. 12
D. 16
E. 24

Originally posted by kiran882 on 04 Mar 2012, 03:29.
Last edited by Bunuel on 27 May 2013, 03:47, edited 2 times in total.
Edited the question
Math Expert
Joined: 02 Sep 2009
Posts: 51215
Re: Find the number of factors of a three digit even number xyz  [#permalink]

### Show Tags

04 Mar 2012, 03:57
1
1
kiran882 wrote:
Find the number of factors of a three digit even number xyz where x, y and z are distinct prime numbers (2, 3 and 5)

A. 8
B. 10
C. 12
D. 16
E. 24

Since xyz is an even number then it's $$532=2^2*7*19$$ or $$352=2^5*11$$.

In either case the # of factors is 12:
For $$532=2^2*7*19$$ the # of factors will be $$(2+1)(1+1)(1+1)=12$$;
For $$352=2^5*11$$ the # of factors will be $$(5+1)(1+1)=12$$.

In case one doesn't know.
Finding the Number of Factors of an Integer

First make prime factorization of an integer $$n=a^p*b^q*c^r$$, where $$a$$, $$b$$, and $$c$$ are prime factors of $$n$$ and $$p$$, $$q$$, and $$r$$ are their powers.

The number of factors of $$n$$ will be expressed by the formula $$(p+1)(q+1)(r+1)$$. NOTE: this will include 1 and n itself.

Example: Finding the number of all factors of 450: $$450=2^1*3^2*5^2$$

Total number of factors of 450 including 1 and 450 itself is $$(1+1)*(2+1)*(2+1)=2*3*3=18$$ factors.

For more on number properties check: math-number-theory-88376.html

Hope it helps.
_________________
Manager
Joined: 14 Dec 2011
Posts: 76
Re: Find the number of factors of a three digit even number xyz  [#permalink]

### Show Tags

27 Jan 2017, 08:21
Bunuel wrote:

Since xyz is an even number then it's $$532=2^2*7*19$$ or $$352=2^5*11$$.

In either case the # of factors is 12:
For $$532=2^2*7*19$$ the # of factors will be $$(2+1)(1+1)(1+1)=12$$;
For $$352=2^5*11$$ the # of factors will be $$(5+1)(1+1)=12$$.

Why answer cannot be E-24. We have 2 even numbers 532 and 352. Both are giving 12 as # of factors. Question asks, Find the number of factors of a three digit even number xyz ? So, Can't we consider both the even numbers ?
Math Expert
Joined: 02 Sep 2009
Posts: 51215
Re: Find the number of factors of a three digit even number xyz  [#permalink]

### Show Tags

27 Jan 2017, 08:29
1
vinnik wrote:
Bunuel wrote:

Since xyz is an even number then it's $$532=2^2*7*19$$ or $$352=2^5*11$$.

In either case the # of factors is 12:
For $$532=2^2*7*19$$ the # of factors will be $$(2+1)(1+1)(1+1)=12$$;
For $$352=2^5*11$$ the # of factors will be $$(5+1)(1+1)=12$$.

Why answer cannot be E-24. We have 2 even numbers 532 and 352. Both are giving 12 as # of factors. Question asks, Find the number of factors of a three digit even number xyz ? So, Can't we consider both the even numbers ?

No. Find the number of factors of a three digit even number xyz. xyz is one number.
_________________
Manager
Joined: 14 Dec 2011
Posts: 76
Re: Find the number of factors of a three digit even number xyz  [#permalink]

### Show Tags

27 Jan 2017, 23:32
Bunuel wrote:
No. Find the number of factors of a three digit even number xyz. xyz is one number.

Okay. Got it. Thanks
Current Student
Joined: 12 Aug 2015
Posts: 2627
Schools: Boston U '20 (M)
GRE 1: Q169 V154
Find the number of factors of a three digit even number xyz  [#permalink]

### Show Tags

28 Jan 2017, 03:16
Bunuel wrote:
kiran882 wrote:
Find the number of factors of a three digit even number xyz where x, y and z are distinct prime numbers (2, 3 and 5)

A. 8
B. 10
C. 12
D. 16
E. 24

Since xyz is an even number then it's $$532=2^2*7*19$$ or $$352=2^5*11$$.

In either case the # of factors is 12:
For $$532=2^2*7*19$$ the # of factors will be $$(2+1)(1+1)(1+1)=12$$;
For $$352=2^5*11$$ the # of factors will be $$(5+1)(1+1)=12$$.

In case one doesn't know.
Finding the Number of Factors of an Integer

First make prime factorization of an integer $$n=a^p*b^q*c^r$$, where $$a$$, $$b$$, and $$c$$ are prime factors of $$n$$ and $$p$$, $$q$$, and $$r$$ are their powers.

The number of factors of $$n$$ will be expressed by the formula $$(p+1)(q+1)(r+1)$$. NOTE: this will include 1 and n itself.

Example: Finding the number of all factors of 450: $$450=2^1*3^2*5^2$$

Total number of factors of 450 including 1 and 450 itself is $$(1+1)*(2+1)*(2+1)=2*3*3=18$$ factors.

For more on number properties check: math-number-theory-88376.html

Hope it helps.

Hi Bunuel.
I have a doubt in the highlighted part.

The question says -> x, y and z are distinct prime numbers (2, 3 and 5)
So shouldn't x,y,z be 2,3,5 respectively?
Why would they write x,y,z and then mention 2,3,5 against them.
Wouldn't GMAT specify the same?

Though the answer would not be affected but i guess a clarification would be helpful in similar questions.

Regards
Stone Cold.

_________________

MBA Financing:- INDIAN PUBLIC BANKS vs PRODIGY FINANCE!

Getting into HOLLYWOOD with an MBA!

The MOST AFFORDABLE MBA programs!

STONECOLD's BRUTAL Mock Tests for GMAT-Quant(700+)

AVERAGE GRE Scores At The Top Business Schools!

Non-Human User
Joined: 09 Sep 2013
Posts: 9162
Re: Find the number of factors of a three digit even number xyz  [#permalink]

### Show Tags

23 Nov 2018, 07:53
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: Find the number of factors of a three digit even number xyz &nbs [#permalink] 23 Nov 2018, 07:53
Display posts from previous: Sort by