• 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 and b are two positive numbers, what is the product of

This topic has 2 expert replies and 2 member replies

If a and b are two positive numbers, what is the product of

Post

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

Difficult



If a and b are two positive numbers, what is the product of a and b?

1) The LCM of a and b is 16
2) The GCD of a and b is 4

OA C

Source: e-GMAT

  • +1 Upvote Post
  • Quote
  • Flag
Top Reply
Post
Product of numbers =product of L.C.M * product of GCD/H.C.F
$$Statement\ 1=LCM\ of\ a\ and\ b\ =16$$
$$Given\ that\ L.C.M\ of\ a\ and\ b=16$$
1 and 16; product will be 16
2 and 16; product will be 32
4 and 16; product will be 64
This product doesn't give a unique answer hence it is INSUFFICIENT
$$statement2\ =\ GCD\ a\ and\ \ b\ =4$$
a and b could be =
4 and 8 ; product will be 32
4 and 12 ; product will be 48
4 and 16 ; product will be 64
There are more that 1 possible combination and statement doesn't give a unique answer hence statement 2 is INSUFFICIENT.
statement 1 and 2 together
product of numbers =LCM *GCD
=16*4
=64
Both statements together are SUFFICIENT
$$answer=option\ C$$

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Top Reply
Post
BTGmoderatorDC wrote:
If a and b are two positive numbers, what is the product of a and b?

1) The LCM of a and b is 16
2) The GCD of a and b is 4
Target question: What is the value of ab?

Statement 1: The LCM of a and b is 16
Let's TEST some values.
There are several values of a and b that satisfy statement 1. Here are two:
Case a: a = 1 and b = 16 (the LCM of 1 and 16 is 16). In this case, the answer to the target question is ab = (1)(16) = 16
Case b: a = 2 and b = 16 (the LCM of 2 and 16 is 16). In this case, the answer to the target question is ab = (2)(16) = 32
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: The GCD of a and b is 4
Let's TEST some more values.
Case a: a = 4 and b = 4 (the GCD of 4 and 4 is 16). In this case, the answer to the target question is ab = (4)(4) = 16
Case b: a = 4 and b = 12 (the GCD of 4 and 12 is 16). In this case, the answer to the target question is ab = (4)(12) = 48
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
--------ASIDE----------------------
There's a nice rule that says:
(greatest common divisor of x and y)(least common multiple of x and y) = xy
Example: x = 10 and y = 15
Greatest common divisor of 10 and 15 = 5
Least common multiple of 10 and 15 = 30
Notice that these values satisfy the above rule, since (5)(30) = (10)(15)
--------BACK TO THE QUESTION! ----------------------

Statement 1 tells us that the LCM of a and b is 16
Statement 2 tells us that the GCD of a and b is 4
So, the product ab = (16)(4) = 64
So, the answer to the target question is ab = 64
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent

_________________
Brent Hanneson – Creator of GMATPrepNow.com
Use my video course along with Beat The GMAT's free 60-Day Study Guide

Sign up for free Question of the Day emails
And check out all of these free resources

  • +1 Upvote Post
  • Quote
  • Flag
GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months!
Post
BTGmoderatorDC wrote:
If a and b are two positive numbers, what is the product of a and b?

1) The LCM of a and b is 16
2) The GCD of a and b is 4

OA C

Source: e-GMAT
Note that the product of two numbers equals the product of their LCM and GCD. Thus, we need both the statements.

The correct answer: C

Hope this helps!

-Jay
_________________
Manhattan Review GMAT Prep

Locations: Hyderabad | Kukatpally | Bangalore | Anna Nagar | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.

  • +1 Upvote Post
  • Quote
  • Flag
Newbie | Next Rank: 10 Posts
Joined
17 Aug 2018
Posted:
9 messages
Post
Hi,

This question tests the basic rule of L.C.M and H.C.F

Rule:

If “x” and “y” are two numbers, then

Product of two numbers = Product of their L.C.M and H.C.F

i.e.,

(x*y) = (L.C.M(x,y) * H.C.F(x,y)).

Given in this question,

Two numbers are “a” and “b”.

Statement I insufficient:

The LCM of a and b is 16

If a = 4 and b = 16, then LCM is 16 but the product of ab is 64

If a = 2 and b = 16, then LCM is 16 but the product of ab is 32.

So not sufficient.

Statement II insufficient:

The GCD of a and b is 4

If a = 4 and b = 16, then GCD is 4 but the product of ab is 64

If a = 4 and b = 8, then GCD is 4 but the product of ab is 32.

So not sufficient.

Together it is sufficient.

According to the rule,

Product of two numbers = Product of their L.C.M and H.C.F

So, Product of two numbers = 16*4 = 64

So the answer is C.

  • +1 Upvote Post
  • Quote
  • Flag
  • Economist Test Prep
    Free Trial & Practice Exam
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

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

    Available with Beat the GMAT members only code

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

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh
  • 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

Top First Responders*

1 Brent@GMATPrepNow 39 first replies
2 Ian Stewart 37 first replies
3 Jay@ManhattanReview 32 first replies
4 GMATGuruNY 26 first replies
5 Scott@TargetTestPrep 17 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

188 posts
2 image description Max@Math Revolution

Math Revolution

84 posts
3 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

71 posts
4 image description Ian Stewart

GMATiX Teacher

45 posts
5 image description GMATGuruNY

The Princeton Review Teacher

45 posts
See More Top Beat The GMAT Experts