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

Redeem
TTP OnDemand GMAT Video Course
Featured Course

Target Test Prep GMAT OnDemand

Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.

  • 715+ score guarantee — highest in the industry (99th percentile)
  • 52 chapters · 1,500+ lessons · 4,000+ practice questions
  • 400 hours of video · 1,500+ instructor-led HD smartboard lessons
  • 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
  • 24/7 live support + weekly Zoom office hours with GMAT instructors
  • TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
  • 1,200+ flashcards + AI-powered study assistant & daily calendar
  • OnDemand, LiveTeach & GMAT Bootcamp formats available
  • Also: GRE, SAT Math & Executive Assessment courses
  • MBA Admissions Consulting now available
  • 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
  • 200,000+ students served
  • 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★ 5.0 (559 reviews)
130-pt guarantee
$0 to start then $127/mo
Start Free 5-Day Trial Read 559 Reviews →

The integer x is positive. What is the remainder when x is d

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Data Sufficiency |
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members
Location: New York, NY
Thanked: 13060 times
GMAT Score:790

by GMATGuruNY » Sat Jan 30, 2016 8:18 am
eitijan wrote:The integer x is positive. What is the remainder when the x is divided by 14?

(1) The remainder when 4x is divided by 28 is 12.
(2) The remainder when x is divided by 21 is 3.
Statement 1:
In other words, 4x is equal to 12 more than a multiple of 28.
In math terms:
4x = 28a + 12, whether a is a nonnegative integer.

Dividing the equation above by 4, we get:
x = 7a + 3.

Options for x:
3, 10, 17, 24, 31...

If x=3, then x/14 = 3/14 = 0 R3.
If x=10, then x/14 = 10/14 = 0 R10.
Since the remainder can be different values, INSUFFICIENT.

Statement 2:
In other words, x is equal to 3 more than a multiple of 21.
In math terms:
x = 21b + 3, whether b is a nonnegative integer.

Options for x:
3, 24, 45...

If x=3, then x/14 = 3/14 = 0 R3.
If x=24, then x/14 =24/14 = 1 R10.
Since the remainder can be different values, INSUFFICIENT.

Statements combined:
Option for x yielded by Statement 1: 3, 10, 17, 24, 31...
Option for x yielded by Statement 2: 3, 24, 45..
Values common to both lists: 3, 24...

If x=3, then x/14 = 3/14 = 0 R3.
If x=24, then x/14 = 24/14 = 1 R10.
Since the remainder can be different values, INSUFFICIENT.

The correct answer is E.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Master | Next Rank: 500 Posts
Posts: 157
Joined: Sat Jan 30, 2016 5:55 am
Thanked: 1 times

by eitijan » Sat Jan 30, 2016 8:24 am
If we solve above question as:

St1: 4x/28 or 2x/14 gives 6 as remainder. Now, if dividend decreases, remainder also decreases in same proportion. Eg: x= 20 => so (2 * 20)/14 gives 6 as remainder and 20/14 will give 3(12/2) as remainder. So as per this,statement1 can find out what will be the remainder.

Please tell me the error in my approach.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

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] » Sat Jan 30, 2016 9:06 am
Hi eitijian,

When a question deals with 'remainders', you CANNOT 'reduce' the given fraction because that changes what the remainders could be.

Here, with 4X/28, and the restriction that X is an positive integer, we have the following possible remainders:

X = 1 --> 4/28 = 0r4
X = 2 --> 8/28 = 0r8
X = 3 --> 12/28 = 0r12
X = 4 --> 16/28 = 0r16
X = 5 --> 20/28 = 0r20
X = 6 --> 24/28 = 0r24
X = 7 --> 28/28 = 1r0
X = 8 --> 32/28 = 1r4
Etc.

By reducing the fraction to 2X/14, you CHANGE the possible values of the remainder....

X = 1 --> 2/14 = 0r2
X = 2 --> 4/14 = 0r4
X = 3 --> 6/14 = 0r6
X = 4 --> 8/14 = 0r8
X = 5 --> 10/14 = 0r10
X = 6 --> 12/14 = 0r12
X = 7 --> 14/14 = 1r0
Etc.

In real basic terms, by doing that math, you are NOT answering the question that is asked.

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
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members
Location: New York, NY
Thanked: 13060 times
GMAT Score:790

by GMATGuruNY » Sat Jan 30, 2016 3:40 pm
eitijan wrote:If we solve above question as:

St1: 4x/28 or 2x/14 gives 6 as remainder. Now, if dividend decreases, remainder also decreases in same proportion. Eg: x= 20 => so (2 * 20)/14 gives 6 as remainder and 20/14 will give 3(12/2) as remainder. So as per this,statement1 can find out what will be the remainder.

Please tell me the error in my approach.
The statement in red is not true in every case.

Consider the following:
If x=10, then dividing by 2 yields a remainder of 0:
10/2 = 5 R0.
If x=5, then dividing by 2 yields a remainder of 1:
5/2 = 2 R1.
Here, the dividend DECREASES from x=10 to x=5, while the remainder INCREASES from 0 to 1.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Master | Next Rank: 500 Posts
Posts: 157
Joined: Sat Jan 30, 2016 5:55 am
Thanked: 1 times

by eitijan » Sun Jan 31, 2016 10:21 am
Thank you Rich and Mitch.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
GMAT Instructor
Posts: 2630
Joined: Wed Sep 12, 2012 3:32 pmFollowed by: 119 members
Location: East Bay all the way
Thanked: 625 times
GMAT Score:780

by Matt@VeritasPrep » Sun Jan 31, 2016 7:09 pm
You could also use:

S1:
4x = 28*something + 12
x = 7*something + 3

S2:
x = 21*something + 3

Taking the two together, we see that the second case is a subset of the first one: in the first case, x could be 3, 10, 17, 24, ...., but in the second, x can only be 3, 24, ...

Luckily for us, the first two values (3 and 24) give contradictory results, so we're done!
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1