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

 It is currently 17 Jun 2019, 08:13 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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  M04-31

Author Message
TAGS:

Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 55635

Show Tags

2
5 00:00

Difficulty:   25% (medium)

Question Stats: 71% (01:11) correct 29% (01:19) wrong based on 196 sessions

HideShow timer Statistics

A perfect number is defined as one for which the sum of all the unique factors less the number itself is equal to the number. For instance, 6 is a perfect number, because the factors of 6 (apart from 6 itself) are 1, 2 and 3, and $$1 + 2 + 3 = 6$$. Which of the following is also a perfect number?

A. 12
B. 20
C. 28
D. 48
E. 60

_________________
Math Expert V
Joined: 02 Sep 2009
Posts: 55635

Show Tags

Official Solution:

A perfect number is defined as one for which the sum of all the unique factors less the number itself is equal to the number. For instance, 6 is a perfect number, because the factors of 6 (apart from 6 itself) are 1, 2 and 3, and $$1 + 2 + 3 = 6$$. Which of the following is also a perfect number?

A. 12
B. 20
C. 28
D. 48
E. 60

$$28 = 1+2+4+7+14$$

_________________
Intern  Joined: 27 Jun 2014
Posts: 1

Show Tags

How we have calculated Factor of 28 ? 4 and 14 are not prime .. is it correct to show factor as non prime number ?
Math Expert V
Joined: 02 Sep 2009
Posts: 55635

Show Tags

2
4
rahulgmat2014 wrote:
How we have calculated Factor of 28 ? 4 and 14 are not prime .. is it correct to show factor as non prime number ?

Factor of an integer is not necessarily a prime number.

A divisor of an integer $$n$$, also called a factor of $$n$$, is an integer which evenly divides $$n$$ without leaving a remainder. In general, it is said $$m$$ is a factor of $$n$$, for non-zero integers $$m$$ and $$n$$, if there exists an integer $$k$$ such that $$n = km$$.

So, the factors of 28 are 1, 2, 4, 7, 14, and 28.

Theory on Number Properties: math-number-theory-88376.html
Divisibility tips: divisibility-multiples-factors-tips-and-hints-174998.html?hilit=divisibility%20tips

DS Divisibility/Multiples/Factors questions to practice: search.php?search_id=tag&tag_id=354
PS Divisibility/Multiples/Factors questions to practice: search.php?search_id=tag&tag_id=185[/textarea]

Hope it helps.
_________________
Intern  Joined: 11 Mar 2014
Posts: 16

Show Tags

So when it says "unique factors' - that does not equal prime?
Math Expert V
Joined: 02 Sep 2009
Posts: 55635

Show Tags

1
phferr1984 wrote:
So when it says "unique factors' - that does not equal prime?

No, Unique factors = different factors.
_________________
Intern  B
Joined: 25 Jan 2013
Posts: 28
Location: United States
Concentration: General Management, Entrepreneurship
Schools: Johnson '21

Show Tags

Bunuel wrote:
Official Solution:

$$28 = 1+2+4+7+14$$

Why 12 is incorrect 1+2+3+6 = 12
Math Expert V
Joined: 02 Sep 2009
Posts: 55635

Show Tags

vs224 wrote:
Bunuel wrote:
Official Solution:

$$28 = 1+2+4+7+14$$

Why 12 is incorrect 1+2+3+6 = 12

4 is also a factor of 12.
_________________
Intern  B
Joined: 03 Sep 2017
Posts: 18
Location: Brazil
GMAT 1: 730 Q49 V41 Show Tags

Bunuel, any way to narrow down some options, so it wont be 100% try and error?
Intern  B
Joined: 17 Apr 2018
Posts: 3
Location: India
GMAT 1: 640 Q42 V35 GPA: 3.4

Show Tags

Is there a faster way to find ALL the factors of a number?
Math Expert V
Joined: 02 Sep 2009
Posts: 55635

Show Tags

1
imran1994 wrote:
Is there a faster way to find ALL the factors of a number?

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.

2. Properties of Integers

5. Divisibility/Multiples/Factors

For other subjects:
ALL YOU NEED FOR QUANT ! ! !
_________________
Manager  S
Joined: 25 Mar 2018
Posts: 65
Location: India
Schools: ISB '21, IIMA , IIMB
GMAT 1: 650 Q50 V28 GPA: 4
WE: Analyst (Manufacturing)

Show Tags

Bunuel wrote:
A perfect number is defined as one for which the sum of all the unique factors less the number itself is equal to the number. For instance, 6 is a perfect number, because the factors of 6 (apart from 6 itself) are 1, 2 and 3, and $$1 + 2 + 3 = 6$$. Which of the following is also a perfect number?

A. 12
B. 20
C. 28
D. 48
E. 60

This is question is simple to calculate for all , To calculate sum of factors except the number , we calculate sum of all factors - the number.

Sum of all factors of a number is given by if a number is P= a^n * b^m * c^k. Sum of all factors of P = (1 + a ..... a^n) (1+b+b^2 .... b^m )(1+c + c^2+....c^k)

so 28 will have (1+ 2 + 4) (1+ 7) = 56 sum of factors ,excluding number will be 28, so the perfect number.
_________________
Please give me +1 kudos if my post helps you a little. It will help me unlock tests. Thanks Re: M04-31   [#permalink] 30 Nov 2018, 08:23
Display posts from previous: Sort by

M04-31

Moderators: chetan2u, Bunuel  