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

 It is currently 16 Oct 2019, 01:19

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

The positive integer 200 has how many factors?

Author Message
TAGS:

Hide Tags

Intern
Joined: 24 Jul 2012
Posts: 12
Schools: Schulich '16
GMAT 1: 610 Q49 V26
WE: Consulting (Consulting)
The positive integer 200 has how many factors?  [#permalink]

Show Tags

Updated on: 17 Sep 2012, 07:01
1
5
00:00

Difficulty:

5% (low)

Question Stats:

78% (00:43) correct 22% (01:03) wrong based on 320 sessions

HideShow timer Statistics

The positive integer 200 has how many factors?

A. 2
B. 10
C. 12
D. 15
E. 24

Can someone help me with a formula for such type of questions?

Originally posted by Vamshi8411 on 17 Sep 2012, 06:24.
Last edited by Bunuel on 17 Sep 2012, 07:01, edited 2 times in total.
Edited the question.
Math Expert
Joined: 02 Sep 2009
Posts: 58374
Re: The positive integer 200 has how many factors?  [#permalink]

Show Tags

17 Sep 2012, 07:00
2
6
Vamshi8411 wrote:
The positive integer 200 has how many factors?

A. 2
B. 10
C. 12
D. 15
E. 24

Can someone help me with a formula for such type of questions?

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.

BACK OT THE ORIGINAL QUESTION:

$$200=2^3*5^2$$, so it has (3+1)(2+1)=12 different factors.

For more check Number Theory chapter of Math Book: math-number-theory-88376.html

Hope it helps.
_________________
General Discussion
CEO
Joined: 20 Mar 2014
Posts: 2603
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
Re: The positive integer 200 has how many factors?  [#permalink]

Show Tags

21 Aug 2015, 08:33
kamathimanshu wrote:
The positive number 200 has how many factors?

A: 2
B: 10
C: 12
D: 15
E: 24

The OA can not be E . It should be C

Direct formula for number of factors of a number N = a^p*b^q... = (p+1)(q+1)... And these include 1 and N as well.

Thus for 200= 2^3*5^2 -----> 4*3=12
Intern
Joined: 03 Aug 2015
Posts: 40
Location: India
Concentration: Entrepreneurship, Finance
GMAT 1: 630 Q47 V30
GMAT 2: 610 Q46 V28
GPA: 3.2
WE: Information Technology (Telecommunications)
Re: The positive integer 200 has how many factors?  [#permalink]

Show Tags

21 Aug 2015, 09:24
Bunuel wrote:
kamathimanshu wrote:
The positive number 200 has how many factors?

A: 2
B: 10
C: 12
D: 15
E: 24

Merging topics.

Please refer to the discussion above.

Can negative numbers also be factors.
If so the answer turns out to be 12*2 = 24.

CEO
Joined: 20 Mar 2014
Posts: 2603
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
Re: The positive integer 200 has how many factors?  [#permalink]

Show Tags

21 Aug 2015, 09:41
1
kamathimanshu wrote:
Bunuel wrote:
kamathimanshu wrote:
The positive number 200 has how many factors?

A: 2
B: 10
C: 12
D: 15
E: 24

Merging topics.

Please refer to the discussion above.

Can negative numbers also be factors.
If so the answer turns out to be 12*2 = 24.

As far as I have seen , "factors" in GMAT refers to positive factors only.
Intern
Joined: 27 Aug 2016
Posts: 24
Location: India
Concentration: Entrepreneurship, Marketing
GPA: 3.87
WE: Sales (Internet and New Media)
Re: The positive integer 200 has how many factors?  [#permalink]

Show Tags

14 Dec 2016, 08:45
Bunuel wrote:
Vamshi8411 wrote:
The positive integer 200 has how many factors?

A. 2
B. 10
C. 12
D. 15
E. 24

Can someone help me with a formula for such type of questions?

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.

BACK OT THE ORIGINAL QUESTION:

$$200=2^3*5^2$$, so it has (3+1)(2+1)=12 different factors.

For more check Number Theory chapter of Math Book: math-number-theory-88376.html

Hope it helps.

Hi Bunuel
As of 2016 do we consider negative factors also in the GMAT ,
as in factors of 200=(2)^3*(5)^2-->(3+1)(2+1)positive factors-->2*12(both positive and negative factors)=24?
Math Expert
Joined: 02 Sep 2009
Posts: 58374
Re: The positive integer 200 has how many factors?  [#permalink]

Show Tags

14 Dec 2016, 08:51
4
karanchamp1 wrote:
Bunuel wrote:
Vamshi8411 wrote:
The positive integer 200 has how many factors?

A. 2
B. 10
C. 12
D. 15
E. 24

Can someone help me with a formula for such type of questions?

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.

BACK OT THE ORIGINAL QUESTION:

$$200=2^3*5^2$$, so it has (3+1)(2+1)=12 different factors.

For more check Number Theory chapter of Math Book: math-number-theory-88376.html

Hope it helps.

Hi Bunuel
As of 2016 do we consider negative factors also in the GMAT ,
as in factors of 200=(2)^3*(5)^2-->(3+1)(2+1)positive factors-->2*12(both positive and negative factors)=24?

No. A factor is a positive divisor.
_________________
Intern
Joined: 27 Aug 2016
Posts: 24
Location: India
Concentration: Entrepreneurship, Marketing
GPA: 3.87
WE: Sales (Internet and New Media)
Re: The positive integer 200 has how many factors?  [#permalink]

Show Tags

14 Dec 2016, 08:56
Many many thanks for the lightning fast reply
You're the best
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 4003
Re: The positive integer 200 has how many factors?  [#permalink]

Show Tags

26 Nov 2017, 12:24
1
Top Contributor
Vamshi8411 wrote:
The positive integer 200 has how many factors?

A. 2
B. 10
C. 12
D. 15
E. 24

APPROACH #1 - FORMULA
If the prime factorization of N = (p^a)(q^b)(r^c) . . . (where p, q, r, etc are different prime numbers), then N has a total of (a+1)(b+1)(c+1)(etc) positive divisors.

Example: 14000 = (2^4)(5^3)(7^1)
So, the number of positive divisors of 14000 = (4+1)(3+1)(1+1) =(5)(4)(2) = 40

Now onto the question...
Example: 200 = (2^3)(5^2)
So, the number of positive divisors of 200 = (3+1)(2+1)
= (4)(3)
= 12
= C

APPROACH #2 - LIST
We can quickly list all of the factors of 200
I suggest we do so in PAIRS of values whose product is 200
We get:
1 and 200
2 and 100
4 and 50
5 and 40
8 and 25
10 and 20
DONE!

Total = 12
= C

RELATED VIDEO FROM OUR COURSE

_________________
Test confidently with gmatprepnow.com
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8069
Location: United States (CA)
Re: The positive integer 200 has how many factors?  [#permalink]

Show Tags

29 Nov 2017, 11:15
Vamshi8411 wrote:
The positive integer 200 has how many factors?

A. 2
B. 10
C. 12
D. 15
E. 24

We can break 200 into primes, then add 1 to each exponent and find the product of all the sums. That product will give us the number of total factors.

200 = 20 x 10 = 2^2 x 5^1 x 2^1 x 5^1 = 2^3 x 5^2

Thus, 200 has (3 + 1)(2 + 1) = 4 x 3 = 12 factors.

_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Non-Human User
Joined: 09 Sep 2013
Posts: 13161
Re: The positive integer 200 has how many factors?  [#permalink]

Show Tags

04 Dec 2018, 12:04
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: The positive integer 200 has how many factors?   [#permalink] 04 Dec 2018, 12:04
Display posts from previous: Sort by