It is currently 17 Nov 2017, 10:31

Close

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
Your Progress

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.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If a three digit number ‘xyz’ has 2 factors, how many factors does the

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

1 KUDOS received
CR Forum Moderator
avatar
P
Status: The best is yet to come.....
Joined: 10 Mar 2013
Posts: 471

Kudos [?]: 198 [1], given: 191

GMAT ToolKit User CAT Tests
If a three digit number ‘xyz’ has 2 factors, how many factors does the [#permalink]

Show Tags

New post 20 Oct 2017, 10:05
1
This post received
KUDOS
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

73% (01:47) correct 27% (01:40) wrong based on 33 sessions

HideShow timer Statistics

If a three digit number ‘xyz’ has 2 factors, how many factors does the 6-digit number ‘xyzxyz’ have?

A. 16
B. 18
C. 20
D. 24
E. 30
[Reveal] Spoiler: OA

_________________

Hasan Mahmud

Kudos [?]: 198 [1], given: 191

BSchool Forum Moderator
User avatar
D
Joined: 26 Feb 2016
Posts: 1594

Kudos [?]: 667 [0], given: 17

Location: India
Concentration: General Management, Leadership
WE: Sales (Retail)
Premium Member CAT Tests
If a three digit number ‘xyz’ has 2 factors, how many factors does the [#permalink]

Show Tags

New post 20 Oct 2017, 10:40
The best way to solve this question is to find a number xyz which has 2 factors.
Only prime numbers have only 2 factors. Let the prime number be 101

If a number(N) can be prime factorized to give \(a^m*b^n*c^o\),
the total number of factors are \((m+1)(n+1)(o+1)\)


101101 is the 6 digit prime number, which when prime factorized gives 7*11*13*101
Therefore, the total number of factors are 2*2*2*2 = 16 factors(Option A)
_________________

Stay hungry, Stay foolish

2017-2018 MBA Deadlines

Class of 2020: Rotman Thread | Schulich Thread
Class of 2019: Sauder Thread

Kudos [?]: 667 [0], given: 17

Senior Manager
Senior Manager
avatar
S
Joined: 22 Aug 2013
Posts: 469

Kudos [?]: 153 [0], given: 265

Location: India
Re: If a three digit number ‘xyz’ has 2 factors, how many factors does the [#permalink]

Show Tags

New post 20 Oct 2017, 10:54
Any six digit number xyzxyz can be re-written as: xyz*1001 or xyz * 7 * 11 * 13 (since 1001 is product of 7, 11, 13)

Now xyz is prime (its given that it has 2 factors only) so this number xyz * 7 * 11 * 13 is now the product of 4 distinct prime numbers. Hence its number of factors = 2*2*2*2 = 16

Hence A answer

Kudos [?]: 153 [0], given: 265

Manager
Manager
User avatar
B
Joined: 22 May 2017
Posts: 90

Kudos [?]: 7 [0], given: 221

GMAT 1: 580 Q41 V29
GMAT 2: 580 Q43 V27
Re: If a three digit number ‘xyz’ has 2 factors, how many factors does the [#permalink]

Show Tags

New post 21 Oct 2017, 15:02
Mahmud6 wrote:
If a three digit number ‘xyz’ has 2 factors, how many factors does the 6-digit number ‘xyzxyz’ have?

A. 16
B. 18
C. 20
D. 24
E. 30


A six digit number xyzxyz can be re-written as: xyz*1001
or
xyz * 7 * 11 * 13

number of factors = 2*2*2*2 = 16

Hence A answer

Kudos [?]: 7 [0], given: 221

1 KUDOS received
Intern
Intern
avatar
B
Joined: 12 Oct 2017
Posts: 24

Kudos [?]: 17 [1], given: 9

If a three digit number ‘xyz’ has 2 factors, how many factors does the [#permalink]

Show Tags

New post 21 Oct 2017, 19:27
1
This post received
KUDOS
1
This post was
BOOKMARKED
We have the formula to find the number of factors of an integer n (include 1 and n itself):

First make prime factorization of an integer n=a^p * b^q * c^r (where a,b,c are prime factors of n and p,q,r are their powers)
Then, the number of factors of n will be expressed by the formula: (p+1)(q+1)(r+1)

Here we have xyzxyz = xyz * 1001 = xyz^1 * 7^1 * 11^1 *13^1
Since xyz has 2 factors => xyz is a prime number.
=> total number of factors of xyzxyz = 2*2*2*2 = 16 factors.

Hence the answer is A.
-----
Kindly press Kudos if the explanation is clear. :-)
Thank you

Kudos [?]: 17 [1], given: 9

If a three digit number ‘xyz’ has 2 factors, how many factors does the   [#permalink] 21 Oct 2017, 19:27
Display posts from previous: Sort by

If a three digit number ‘xyz’ has 2 factors, how many factors does the

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

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®.