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

It is currently 22 Oct 2018, 15:55

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

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

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

Hide Tags

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50042
If P is the product of all of the positive multiples of 11 less than 1  [#permalink]

Show Tags

New post 05 Nov 2017, 02:36
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

79% (01:38) correct 21% (01:46) wrong based on 138 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

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Manager
Manager
avatar
S
Joined: 18 May 2016
Posts: 182
Location: India
GMAT 1: 710 Q48 V40
WE: Marketing (Education)
GMAT ToolKit User Reviews Badge
Re: If P is the product of all of the positive multiples of 11 less than 1  [#permalink]

Show Tags

New post 05 Nov 2017, 03:03
1
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
Senior SC Moderator
avatar
V
Joined: 22 May 2016
Posts: 2040
Premium Member CAT Tests
If P is the product of all of the positive multiples of 11 less than 1  [#permalink]

Show Tags

New post 05 Nov 2017, 11:10
1
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

Answer B
_________________

___________________________________________________________________
For what are we born if not to aid one another?
-- Ernest Hemingway

Manager
Manager
avatar
B
Joined: 06 Aug 2017
Posts: 88
GMAT 1: 570 Q50 V18
GMAT 2: 610 Q49 V24
GMAT 3: 640 Q48 V29
Re: If P is the product of all of the positive multiples of 11 less than 1  [#permalink]

Show Tags

New post 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


Answer is B as follows
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

B is the answer.
_________________

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

GMAT PREP 1: Q50 V34 - 700

Veritas Test 1: Q43 V34 - 630
Veritas Test 2: Q46 V30 - 620
Veritas Test 3: Q45 V29 - 610
Veritas Test 4: Q49 V30 - 650

GMAT PREP 2: Q50 V34 - 700

Veritas Test 5: Q47 V33 - 650
Veritas Test 5: Q46 V33 - 650

Target Test Prep Representative
User avatar
G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2830
Re: If P is the product of all of the positive multiples of 11 less than 1  [#permalink]

Show Tags

New post 08 Nov 2017, 17:36
1
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.

Answer: B
_________________

Jeffery Miller
Head of GMAT Instruction

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

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

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

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


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| 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®.