• NEW! FREE Beat The GMAT Quizzes
    NEW! FREE Beat The GMAT Quizzes
    NEW! FREE Beat The GMAT Quizzes
    Hundreds of Questions Highly Detailed Reporting Expert Explanations TAKE A FREE GMAT QUIZ
  • 7 CATs FREE!
    If you earn 100 Forum Points

    Engage in the Beat The GMAT forums to earn
    100 points for $49 worth of Veritas practice GMATs FREE

    Veritas Prep
    VERITAS PRACTICE GMAT EXAMS
    Earn 10 Points Per Post
    Earn 10 Points Per Thanks
    Earn 10 Points Per Upvote
    REDEEM NOW

If A = 10! + 12! + 14! + 16! +..........+100!...

This topic has 1 expert reply and 0 member replies

If A = 10! + 12! + 14! + 16! +..........+100!...

Post
If A = 10! + 12! + 14! + 16! +..........+100!, then the highest power of 2 in A is

A. 7
B. 8
C. 9
D. 10
E. 11

The OA is B.

I don't understand this PS question. Can any expert explain it for me, please? Thanks.

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Legendary Member
Joined
14 Jan 2015
Posted:
2667 messages
Followed by:
122 members
Upvotes:
1153
GMAT Score:
770
Post
LUANDATO wrote:
If A = 10! + 12! + 14! + 16! +..........+100!, then the highest power of 2 in A is

A. 7
B. 8
C. 9
D. 10
E. 11

The OA is B.

I don't understand this PS question. Can any expert explain it for me, please? Thanks.
This question isn't terribly well-worded, but the gist seems to ask, if 2^n is a factor of the sum, what is the greatest possible value of n?

First, we know that every term in the series contains 10! for example: 12! = 12*11*10!, and 14! = 14*13*12*11*10!, etc.

So we can re-write the sum as 10!(1 + 12*11 + 14*13*12*11 ... + 100*99*98...) Notice that inside the parentheses, every number will be even, aside from '1.' So we know that this enormous sum will be ODD, as EVEN + 1 = ODD.) Now all we have to do is count the 2's in the prime factorization of 10!

10/2 = 5 terms with at least one 2.
10/(2^2) = 10/4 = 2.5 -->2 terms with at least two 2's.
10/(2^3) = 10/8 = 1.25 --> 1 term with at least three 2's.

5 + 2 + 1 = 8. The answer is B

_________________
Veritas Prep | GMAT Instructor

Veritas Prep Reviews
Save $100 off any live Veritas Prep GMAT Course

  • +1 Upvote Post
  • Quote
  • Flag
Enroll in a Veritas Prep GMAT class completely for FREE. Wondering if a GMAT course is right for you? Attend the first class session of an actual GMAT course, either in-person or live online, and see for yourself why so many students choose to work with Veritas Prep. Find a class now!
  • Economist Test Prep
    Free Trial & Practice Exam
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep
  • The Princeton Review
    FREE GMAT Exam
    Know how you'd score today for $0

    Available with Beat the GMAT members only code

    MORE DETAILS
    The Princeton Review
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider
  • Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT
  • Target Test Prep
    5-Day Free Trial
    5-day free, full-access trial TTP Quant

    Available with Beat the GMAT members only code

    MORE DETAILS
    Target Test Prep
  • Kaplan Test Prep
    Free Practice Test & Review
    How would you score if you took the GMAT

    Available with Beat the GMAT members only code

    MORE DETAILS
    Kaplan Test Prep
  • Varsity Tutors
    Award-winning private GMAT tutoring
    Register now and save up to $200

    Available with Beat the GMAT members only code

    MORE DETAILS
    Varsity Tutors
  • e-gmat Exclusive Offer
    Get 300+ Practice Questions
    25 Video lessons and 6 Webinars for FREE

    Available with Beat the GMAT members only code

    MORE DETAILS
    e-gmat Exclusive Offer

Top First Responders*

1 Ian Stewart 53 first replies
2 Brent@GMATPrepNow 36 first replies
3 Jay@ManhattanReview 29 first replies
4 GMATGuruNY 25 first replies
5 ceilidh.erickson 15 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

Most Active Experts

1 image description Scott@TargetTestPrep

Target Test Prep

199 posts
2 image description Max@Math Revolution

Math Revolution

90 posts
3 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

76 posts
4 image description Ian Stewart

GMATiX Teacher

62 posts
5 image description GMATGuruNY

The Princeton Review Teacher

44 posts
See More Top Beat The GMAT Experts