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

 It is currently 18 Oct 2018, 15:24

### 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

# How many positive distinct prime factors does 5^20 + 5^17 have?

Author Message
TAGS:

### Hide Tags

Intern
Joined: 26 Aug 2014
Posts: 3
How many positive distinct prime factors does 5^20 + 5^17 have?  [#permalink]

### Show Tags

04 Dec 2014, 01:32
2
13
00:00

Difficulty:

35% (medium)

Question Stats:

62% (01:01) correct 38% (01:05) wrong based on 250 sessions

### HideShow timer Statistics

How many positive distinct prime factors does 5^20 + 5^17 have?

A) One
B) Two
C) Three
D) Four
E) Five
Senior Manager
Joined: 13 Jun 2013
Posts: 276
Re: How many positive distinct prime factors does 5^20 + 5^17 have?  [#permalink]

### Show Tags

04 Dec 2014, 01:43
1
3
pbarrocas wrote:
How many positive distinct prime factors does 5^20 + 5^17 have?

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

$$5^{20} + 5^{17}$$ = $$5^{17}(5^3+1)$$

=$$5^{17}(125+1)$$
=$$5^{17} (126)$$
=$$5^{17} .2.7.3^2$$
thus total number of distinct prime factors are 4 (2,3,5,7)
Intern
Joined: 23 Jul 2013
Posts: 15
Re: How many positive distinct prime factors does 5^20 + 5^17 have?  [#permalink]

### Show Tags

31 Jan 2016, 18:59
manpreetsingh86 wrote:
pbarrocas wrote:
How many positive distinct prime factors does 5^20 + 5^17 have?

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

$$5^{20} + 5^{17}$$ = $$5^{17}(5^3+1)$$

=$$5^{17}(125+1)$$
=$$5^{17} (126)$$
=$$5^{17} .2.7.3^2$$
thus total number of distinct prime factors are 4 (2,3,5,7)

Hi,

Shouldn't it be 1, 2, 3, 5 and 7? Please confirm. Thanks.
Math Expert
Joined: 02 Sep 2009
Posts: 50000
Re: How many positive distinct prime factors does 5^20 + 5^17 have?  [#permalink]

### Show Tags

31 Jan 2016, 22:17
Meetup wrote:
manpreetsingh86 wrote:
pbarrocas wrote:
How many positive distinct prime factors does 5^20 + 5^17 have?

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

$$5^{20} + 5^{17}$$ = $$5^{17}(5^3+1)$$

=$$5^{17}(125+1)$$
=$$5^{17} (126)$$
=$$5^{17} .2.7.3^2$$
thus total number of distinct prime factors are 4 (2,3,5,7)

Hi,

Shouldn't it be 1, 2, 3, 5 and 7? Please confirm. Thanks.

1 is NOT a prime number.

Check here for more: math-number-theory-88376.html

Hope it helps.
_________________
Current Student
Joined: 12 Aug 2015
Posts: 2638
Schools: Boston U '20 (M)
GRE 1: Q169 V154
Re: How many positive distinct prime factors does 5^20 + 5^17 have?  [#permalink]

### Show Tags

07 Jan 2017, 19:20
BSchool Forum Moderator
Joined: 07 Jan 2016
Posts: 761
Location: India
Schools: ISB '20 (II)
GMAT 1: 710 Q49 V36
Re: How many positive distinct prime factors does 5^20 + 5^17 have?  [#permalink]

### Show Tags

09 Feb 2018, 03:29
pbarrocas wrote:
How many positive distinct prime factors does 5^20 + 5^17 have?

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

5^20 + 5^ 17

take 5^17 common on both sides of the sign = 5^17( 5^3 + 1) = 5^17( 125+1) = 5^17 (126)

14 x 9 = 126 so prime are 2,3,7
5^17 prime is 5

prime factors are 5, 2, 3, 7

1 is not prime
Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2830
Re: How many positive distinct prime factors does 5^20 + 5^17 have?  [#permalink]

### Show Tags

12 Feb 2018, 17:32
pbarrocas wrote:
How many positive distinct prime factors does 5^20 + 5^17 have?

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

We can simplify the given expression by first factoring 5^17 as a common factor:

5^17(5^3 + 1)

5^17(126)

5^17 x 2 x 63

5^17 x 2 x 3^2 x 7

Thus, 5^20 + 5^17 has 4 distinct prime factors.

_________________

Jeffery Miller

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

Senior Manager
Joined: 22 Feb 2018
Posts: 354
Re: How many positive distinct prime factors does 5^20 + 5^17 have?  [#permalink]

### Show Tags

22 Aug 2018, 08:11
pbarrocas wrote:
How many positive distinct prime factors does 5^20 + 5^17 have?

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

OA:D
$$5^{20} + 5^{17} = 5^{17}(5^3+1)=5^{17}(2*3^2*7)$$
Number of positive distinct prime factors$$=4 (2,3,5,7)$$
_________________

Good, good Let the kudos flow through you

Senior Manager
Joined: 12 Feb 2015
Posts: 493
Re: How many positive distinct prime factors does 5^20 + 5^17 have?  [#permalink]

### Show Tags

24 Aug 2018, 11:54
Four factors - 2,3,5 & 7. Take out 5^17 (5^3+1) ...do the prime factorization.
_________________

"Please hit +1 Kudos if you like this post"

_________________
Manish

"Only I can change my life. No one can do it for me"

Re: How many positive distinct prime factors does 5^20 + 5^17 have? &nbs [#permalink] 24 Aug 2018, 11:54
Display posts from previous: Sort by