It is currently 11 Dec 2017, 12:16

### 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 June
Open Detailed Calendar

# If P is the product of all of the positive multiples of 11 less than 1

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 42544

Kudos [?]: 135256 [0], given: 12679

If P is the product of all of the positive multiples of 11 less than 1 [#permalink]

### Show Tags

05 Nov 2017, 02:36
00:00

Difficulty:

45% (medium)

Question Stats:

80% (00:57) correct 20% (01:29) wrong based on 81 sessions

### HideShow timer Statistics

If P is the product of all of the positive multiples of 11 less than 100, then what is the sum of the distinct primes of P?

(A) 22

(B) 28

(C) 45

(D) 49

(E) 89
[Reveal] Spoiler: OA

_________________

Kudos [?]: 135256 [0], given: 12679

Manager
Joined: 18 May 2016
Posts: 152

Kudos [?]: 33 [0], given: 106

Location: India
Schools: ISB '19 (I), IIMA (I)
GMAT 1: 710 Q48 V40
WE: Marketing (Other)
Re: If P is the product of all of the positive multiples of 11 less than 1 [#permalink]

### Show Tags

05 Nov 2017, 03:03
1
This post was
BOOKMARKED
P= 11^9 * (1*2*3*4*5*6*7*8*9)

Sum of distinct primes= 2+3+5+7+11 = 28

Option B

Sent from my A0001 using GMAT Club Forum mobile app

Kudos [?]: 33 [0], given: 106

VP
Joined: 22 May 2016
Posts: 1106

Kudos [?]: 396 [0], given: 640

If P is the product of all of the positive multiples of 11 less than 1 [#permalink]

### Show Tags

05 Nov 2017, 11:10
1
This post was
BOOKMARKED
Bunuel wrote:
If P is the product of all of the positive multiples of 11 less than 100, then what is the sum of the distinct primes of P?

(A) 22

(B) 28

(C) 45

(D) 49

(E) 89

Positive multiples of 11 less than 100:
11, 22, 33, 44, 55, 66, 77, 88, 99

P = the product of all these numbers. So each factor in each multiple will be a factor of P. No need to worry about the actual product; factors are the key.

Multiples of 11 whose other factor is a prime number:

22 = 2 * 11
33 = 3 * 11
55 = 5 * 11
77 = 7 * 11

Other multiples of 11? Except for 11 (which = 11 * 1, where 1 is not prime), their other factors are already-used single-digit primes:

11 = 11 * 1, 1 is not prime
44 = 11 * 2$$^2$$
66 = 11 * 2 * 3
88 = 11 * 2$$^3$$
99 = 11 * 3$$^2$$
Prime factors 2 and 3 have already been "used" in 22 and 33. Not distinct.

Sum of P's distinct prime factors?
11 + 2 + 3 + 5 + 7 = 28

Kudos [?]: 396 [0], given: 640

Manager
Joined: 06 Aug 2017
Posts: 74

Kudos [?]: 14 [0], given: 29

GMAT 1: 610 Q48 V24
Re: If P is the product of all of the positive multiples of 11 less than 1 [#permalink]

### Show Tags

05 Nov 2017, 12:05
Bunuel wrote:
If P is the product of all of the positive multiples of 11 less than 100, then what is the sum of the distinct primes of P?

(A) 22

(B) 28

(C) 45

(D) 49

(E) 89

Positive multiple of 11 less than 100 are 11,22,33,44,55,66,77,88,99
These numbers can be written as
11
22=2*11
33=3*11
44=4*11 = $$2^2$$*11
55=5*11
66=6*11 = 2*3*11
77=7*11
88=8*11 = $$2^3$$*11
99=9*11 = $$3^2$$*11

P = 11*22*33*44*55*66*77*88*99 = 11*(2*11)*(3*11)*($$2^2$$*11)*(5*11)*(2*3*11)*(7*11)*($$2^3$$*11)*($$3^2$$*11) = $$2^7*3^4*5*7*11^9$$
Prime factors are 2,3,5,7,11
Sum of these prime factors are 2+3+5+7+11 = 28

_________________

-------------------------------------------------------------------------------
Kudos are the only way to tell whether my post is useful.

GMATPREP1: Q47 V36 - 680
Veritas Test 1: Q43 V34 - 630
Veritas Test 2: Q46 V30 - 620

Kudos [?]: 14 [0], given: 29

Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 1788

Kudos [?]: 978 [1], given: 5

Re: If P is the product of all of the positive multiples of 11 less than 1 [#permalink]

### Show Tags

08 Nov 2017, 17:36
1
KUDOS
Expert's post
Bunuel wrote:
If P is the product of all of the positive multiples of 11 less than 100, then what is the sum of the distinct primes of P?

(A) 22

(B) 28

(C) 45

(D) 49

(E) 89

We can create the following expression:

11 x 2(11) x 3(11) x 4(11) x 5(11) x 6(11) x 7(11) x 8(11) x 9(11)

We see that the prime factors of P are 2, 3, 5, 7, and 11. So, the sum of those distinct primes is 2 + 3 + 5 + 7 + 11 = 28.

_________________

Jeffery Miller

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

Kudos [?]: 978 [1], given: 5

Re: If P is the product of all of the positive multiples of 11 less than 1   [#permalink] 08 Nov 2017, 17:36
Display posts from previous: Sort by