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

 It is currently 16 Oct 2019, 02:39 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.  The expression x#y denotes the product of the consecutive multiples of

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

Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 58400
The expression x#y denotes the product of the consecutive multiples of  [#permalink]

Show Tags

2
6 00:00

Difficulty:   45% (medium)

Question Stats: 70% (02:55) correct 30% (02:33) wrong based on 167 sessions

HideShow timer Statistics

The expression x#y denotes the product of the consecutive multiples of 3 between x and y, inclusive. What is the sum of the exponents in the prime factorization of 21#42?

A. 23
B. 24
C. 25
D. 26
E. 27

Kudos for a correct solution.

_________________
Manager  Joined: 18 Mar 2014
Posts: 226
Location: India
Concentration: Operations, Strategy
GMAT 1: 670 Q48 V35 GPA: 3.19
WE: Information Technology (Computer Software)
Re: The expression x#y denotes the product of the consecutive multiples of  [#permalink]

Show Tags

1
1
21#42
= 21*24*27*30*33*36*39*42
= 3^11 * 7^2 * 2^7 * 5^1 * 11^1 * 13^1

so total is = 11+2+7+1+1+1=23

_________________
Press +1 Kudos if you find this Post helpful Manager  Joined: 03 Sep 2014
Posts: 75
Concentration: Marketing, Healthcare
Re: The expression x#y denotes the product of the consecutive multiples of  [#permalink]

Show Tags

1
1
Bunuel wrote:
The expression x#y denotes the product of the consecutive multiples of 3 between x and y, inclusive. What is the sum of the exponents in the prime factorization of 21#42?

A. 23
B. 24
C. 25
D. 26
E. 27

Kudos for a correct solution.

21#42 = 21*24*27*30*33*36*39*42 => 3(7*8*9*10*11*12*13*14) => $$3^{11} * {2^7}* {7^2}*5*11*13$$ => 11+7+2+1+1+1 = 23

Hence, answer is A
Senior Manager  B
Joined: 28 Feb 2014
Posts: 291
Location: United States
Concentration: Strategy, General Management
Re: The expression x#y denotes the product of the consecutive multiples of  [#permalink]

Show Tags

1
The question is basically asking for the total number of factors between 21 and 42, inclusive.
21, 24, 27, 30, 33, 36, 39, 42

2^7 = 7
3^11= 11
5^1= 1
7^2= 2
11^1= 1
13^1= 1

23 is the total

Manager  S
Joined: 24 Jan 2015
Posts: 68
GPA: 4
WE: Consulting (Pharmaceuticals and Biotech)
Re: The expression x#y denotes the product of the consecutive multiples of  [#permalink]

Show Tags

1
The product of the consecutive multiples of 3 between 21 and 42 inclusive
= 21 * 24 * 27 * 30 * 33 * 36 * 39 * 42

Factorize them separately and we get,

= (3 * 7) * (3 * $$2^3$$) * ($$3^3$$) * (3 * 2 * 5) * (3 * 11) * ($$3^2$$ * $$2^2$$) * (3 * 13) * (3 * 2 * 7)

= ($$3^{11}$$) * ($$2^7$$) * ($$5^1$$) * ($$7^2$$) *($$11^1$$) * ($$13^1$$)

Sum of exponents = 11 + 7 + 1 + 2 + 1 + 1 = 23

Correct answer is (A)
Math Expert V
Joined: 02 Sep 2009
Posts: 58400
Re: The expression x#y denotes the product of the consecutive multiples of  [#permalink]

Show Tags

Bunuel wrote:
The expression x#y denotes the product of the consecutive multiples of 3 between x and y, inclusive. What is the sum of the exponents in the prime factorization of 21#42?

A. 23
B. 24
C. 25
D. 26
E. 27

Kudos for a correct solution.

MANHATTAN GMAT OFFICIAL SOLUTION:

First, translate the expression 21#42, using the definition given:

21#42 = 21×24×27×30×33×36×39×42

You need the prime factorization of this enormous product.

Since these are consecutive multiples of 3, a good move is to factor out that 3 from each multiple. You have 8 multiples, all multiplied together, so you get 3^8:

21#42 = 3^8(7×8×9×10×11×12×13×14)

Now replace each consecutive integer with its prime factorization:

21#42 = 3^8(7×2^3×3^2×(2×5)×11×(2^2×3)×13×(2×7))

Group up the prime bases:

21#42 = 2^7×3^11×5×7^2×11×13

Don’t forget to put in an understood 1 for the primes lacking explicit exponents:

21#42 = 2^7×3^11×5^1×7^2×11^1×13^1

Finally, add up the exponents:

7 + 11 + 1 + 2 + 1 + 1 = 23

The correct answer is A.
_________________
Manager  Joined: 27 Apr 2016
Posts: 93
Location: Brazil
GMAT 1: 610 Q37 V36 GPA: 2.7
WE: Information Technology (Education)
Re: The expression x#y denotes the product of the consecutive multiples of  [#permalink]

Show Tags

1
LMAO this should be on the verbal section!!!

Took me 6 minutes to figure out what "product of the consecutive multiples of 3 between x and y" and "sum of the exponents in the prime factorization" meant. Another 3 to actually solve it, but at least I figured it out by myself in the end. I guess the right part of my brain kept spaming messages to the left asking "Why would you wanna do this? Why would you wanna do that? Whats the context? This makes no sense!!".
_________________
The errant cosmos works against me!
Non-Human User Joined: 09 Sep 2013
Posts: 13159
Re: The expression x#y denotes the product of the consecutive multiples of  [#permalink]

Show Tags

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 expression x#y denotes the product of the consecutive multiples of   [#permalink] 11 Apr 2019, 20:07
Display posts from previous: Sort by

The expression x#y denotes the product of the consecutive multiples of

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

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne  