BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Target Test Prep · GMAT

Choose how you want to prepare

Learn live with an expert or move at your own pace. Every option includes the complete TTP study system.

★★★★★5.0559 reviews
GMATLiveTeach 7 seats left
Chris Peckover
NEXT LIVE COHORT

Oct 13 to Jan 7, 2027

with Chris Peckover

Schedule
Tue, Thu · 8:00 to 10:00 PM ET
Included
40 live hours + 6 months of GMAT OnDemand
  • Live instruction and real-time questions
  • Class recordings and assigned practice
View class & enroll
Limited cohort · enrollment openTarget Test Prep
EALiveTeach 5 seats left
Logan Thompson
EXECUTIVE ASSESSMENT

Sep 6 to Dec 6, 2026

with Logan Thompson

Schedule
Sun · 9:30 AM to 12:30 PM ET
Included
40 hours of live online classes plus six months of access to the complete TTP EA OnDemand course.
  • 165+ EA Score Guarantee
  • 4,100+ Quant, Verbal, and Integrated Reasoning practice questions
  • 400+ hours of in-depth video lessons
  • 3,000+ step-by-step video solutions
View EA class & enroll
Limited cohort · enrollment openTarget Test Prep
GMATOnDemand Start anytime
SELF-PACED MASTERCLASS

Target Test Prep GMAT OnDemand

Complete access from day one. Study on your schedule.

715+ score guarantee
$0to start then $127/mo
  • Personalized study plan and analytics
  • Thousands of lessons and practice questions
Start free 5-day trial
Read 559 reviewsTarget Test Prep

Compare the format, schedule, and included access before enrolling. Prices and seat counts shown reflect the supplied offer details.

Divisible

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Data Sufficiency |

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10392
Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members
Location: Palo Alto, CA
Thanked: 2867 times
GMAT Score:800

by [email protected] » Wed Nov 19, 2014 1:03 pm
Hi akhilsuhag,

This question is perfect for TESTing VALUES.

We're told that A, B and C are INTEGERS. We're asked if (A)(B) is a multiple of 18? This is a YES/NO question.

Fact 1: 2A = 3B

If...
A = 3
B = 2
AB = 6 and the answer to the question is NO

A = 9
B = 6
AB = 54 and the answer to the question is YES
Fact 1 is INSUFFICIENT

Fact 2: 2B = 3C

We know NOTHING about A, so this Fact is likely to be INSUFFICIENT, but here's how you can prove it:

If...
B = 3
C = 2
A = 1
AB = 3 and the answer to the question is NO

B = 3
C = 2
A = 6
AB = 18 and the answer to the question is YES
Fact 2 is INSUFFICIENT

Combined, we know...
2A = 3B
2B = 3C

This tells us that B MUST be a multiple of 2 (from Fact 1) AND a multiple of 3 (From Fact 2), so B MUST be a multiple of 6...By extension, this means that A MUST be a multiple of 3. TESTing VALUES proves it:

If....
B = 6
A = 9
AB = 54 and the answer to the question is YES

B = 12
A = 18
AB = (18)(12) and the answer to the question is YES
Combined, SUFFICIENT

Final Answer: C

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Master | Next Rank: 500 Posts
Posts: 447
Joined: Fri Nov 08, 2013 7:25 amFollowed by: 1 member
Thanked: 25 times

by Mathsbuddy » Thu Nov 20, 2014 5:28 am
If ab is a multiple of 18, then 18 is a factor of ab.
To be such, then ab = 2 x 3 x 3 x n, where n is a non-negative integer

Using Statement 1 we know a = 3b/2, which does not necessarily satisfy ab = 3b^2/2 = 2 x 3 x 3 x n
In fact, the factor of 3 is guaranteed only once. NOT SUFFICIENT

Using Statement 2 we know b = 3c/2, which does not necessarily satisfy ab = 3ac/2 = 2 x 3 x 3 x n
In fact, the factor of 3 is guaranteed only once. NOT SUFFICIENT

Combined: (2) ab = 3b/2 x 3c/2 = 9bc/4. Three is 2 of the factors here. In addition, the fact that a = 3b/2 means that for a to be an integer, then 3b must be a multiple of 2. Hence factors 2, 3 and 3 are guaranteed. This suggests: SUFFICIENT

However, do not ignore what happens if a and/or b equal zero (because zero is a multiple of all numbers). Quick test: if a and or b = 0, then ab = 0. Also SUFFICIENT.

ANSWER = C
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members
Location: Vancouver, BC
Thanked: 5254 times
GMAT Score:770

by Brent@GMATPrepNow » Sat Nov 22, 2014 7:13 am
akhilsuhag wrote:If a, b and c are integers, is ab a multiple of 18?

(1) 2a = 3b
(2) 2b = 3c
Target question: Is ab a multiple of 18?

Given: a, b and c are INTEGERS

Statement 1: 2a = 3b
This statement doesn't FEEL sufficient, so I'm going to test some values.

Aside: For more on this idea of plugging in values when a statement doesn't feel sufficient, you can read my article: https://www.beatthegmat.com/mba/2013/10/ ... -in-values

There are several values of a and b that satisfy this condition. Here are two:
Case a: a = 3 and b = 2, in which case ab = 6, and 6 is NOT a multiple of 18
Case b: a = 9 and b = 6, in which case ab = 54, and 54 IS a multiple of 18
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: 2b = 3c
There's no information about the variable a, so a can have ANY value. So, this statement SEEMS/FEELS insufficient. Let's test some values.
There are several values of a, b and c that satisfy this condition (keeping in mind that variable a can have ANY value). Here are two possible cases:
Case a: a = 1, b = 3 and c = 2, in which case ab = 3, and 3 is NOT a multiple of 18
Case b: a = 6, b = 3 and c = 2, in which case ab = 18, and 18 IS a multiple of 18
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that 2a = 3b
Divide both sides by 2 to get: a = 3b/2
Since a is an INTEGER, we know that 3b/2 is an INTEGER
If 3b/2 is an INTEGER, then b must be divisible by 2

Statement 2 tells us that 2b = 3c
Divide both sides by 3 to get: c = 2b/3
Rewrite as c = (2/3)b
Let's also take the statement 1 equation (2a = 3b) and divide both sides by 3 to get: b = 2a/3
Now take c = (2/3)b and replace b with 2a/3
We get: c = (2/3)(2a/3)
Simplify to get: c = 4a/9
Since c is an INTEGER, we know that 4a/9 is an INTEGER
If 4a/9 is an INTEGER then a must be divisible by 9

We now know that b must be divisible by 2 and a must be divisible by 9.
So, we can conclude that ab is divisible by (2)(9)
In other words, ab is a multiple of 18
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer = C

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Senior | Next Rank: 100 Posts
Posts: 38
Joined: Thu Apr 28, 2016 7:17 pm
Thanked: 1 times

by Gurpreet singh » Sun Jun 19, 2016 10:29 pm
Having knowledge is one thing but putting it in a language which can be understood by all is another skill.
I was lost in this question
Brilliant explanation Brent.
Regards

Brent@GMATPrepNow wrote:
akhilsuhag wrote:If a, b and c are integers, is ab a multiple of 18?

(1) 2a = 3b
(2) 2b = 3c
Target question: Is ab a multiple of 18?

Given: a, b and c are INTEGERS

Statement 1: 2a = 3b
This statement doesn't FEEL sufficient, so I'm going to test some values.

Aside: For more on this idea of plugging in values when a statement doesn't feel sufficient, you can read my article: https://www.beatthegmat.com/mba/2013/10/ ... -in-values

There are several values of a and b that satisfy this condition. Here are two:
Case a: a = 3 and b = 2, in which case ab = 6, and 6 is NOT a multiple of 18
Case b: a = 9 and b = 6, in which case ab = 54, and 54 IS a multiple of 18
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: 2b = 3c
There's no information about the variable a, so a can have ANY value. So, this statement SEEMS/FEELS insufficient. Let's test some values.
There are several values of a, b and c that satisfy this condition (keeping in mind that variable a can have ANY value). Here are two possible cases:
Case a: a = 1, b = 3 and c = 2, in which case ab = 3, and 3 is NOT a multiple of 18
Case b: a = 6, b = 3 and c = 2, in which case ab = 18, and 18 IS a multiple of 18
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that 2a = 3b
Divide both sides by 2 to get: a = 3b/2
Since a is an INTEGER, we know that 3b/2 is an INTEGER
If 3b/2 is an INTEGER, then b must be divisible by 2

Statement 2 tells us that 2b = 3c
Divide both sides by 3 to get: c = 2b/3
Rewrite as c = (2/3)b
Let's also take the statement 1 equation (2a = 3b) and divide both sides by 3 to get: b = 2a/3
Now take c = (2/3)b and replace b with 2a/3
We get: c = (2/3)(2a/3)
Simplify to get: c = 4a/9
Since c is an INTEGER, we know that 4a/9 is an INTEGER
If 4a/9 is an INTEGER then a must be divisible by 9

We now know that b must be divisible by 2 and a must be divisible by 9.
So, we can conclude that ab is divisible by (2)(9)
In other words, ab is a multiple of 18
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer = C

Cheers,
Brent
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1