A number when divided by a certain divisor left...

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

Redeem

This topic has expert replies

Post new topic Post Reply

Previous Topic Next Topic

swerve: Legendary Member; Posts: 2499; Joined: Sun Oct 29, 2017 2:04 pm; Followed by:6 members

A number when divided by a certain divisor left...

by swerve » Mon Jan 08, 2018 6:36 am

A number when divided by a certain divsor left remainder 241, when twice the number was divided by the same divisor, the remainder was 112. Find the divisor?

A. 370
B. 365
C. 380
D. 456
E. 460

The OA is A.

Please, can any expert explain this PS question for me? I tried to solve it but I can't get the correct answer. I need your help. Thanks.

Quote

Source: Beat The GMAT — Problem Solving | Mon Jan 08, 2018 6:36 am

GMAT/MBA Expert

ErikaPrepScholar: Legendary Member; Posts: 503; Joined: Thu Jul 20, 2017 9:03 am; Thanked: 86 times; Followed by:15 members; GMAT Score:770

by ErikaPrepScholar » Mon Jan 08, 2018 7:11 am

We can express any division problem as:

Dividend = Divisor * Quotient + Remainder

We can use this to build equations based on what we know.

We have a number that we are dividing by other numbers - that's our dividend. We'll call it X. When we divide by some other number (our divisor) we're left with a remainder of 241. So we can write this as:

X = DQ+ 241

If we multiply both sides by 2, we get:

2X = 2DQ + 482

We know that when twice our dividend (2X, which we already have in our equation) is divided by the same divisor, we're left with a remainder of 112 (but a different quotient). So we can rewrite our equation as:

2X = 2DQ + 370 + 112

So here, 2X is our dividend, 112 is our remainder, and 2DQ + 370 equals our divisor times our quotient. We know that 2DQ + 370 must be divisible by our divisor, which means both 2DQ and 370 must be divisible by our divisor. So we can check to see which of our answer choices can be divided into 370. Only 370 can be divided into 370 without creating a remainder, so the correct answer is A.

Erika John - Content Manager/Lead Instructor
https://gmat.prepscholar.com/gmat/s/

Get tutoring from me or another PrepScholar GMAT expert: https://gmat.prepscholar.com/gmat/s/tutoring/

Learn about our exclusive savings for BTG members (up to 25% off) and our 5 day free trial

Check out our PrepScholar GMAT YouTube channel, and read our expert guides on the PrepScholar GMAT blog

Quote

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pm; Location: New York, NY; Thanked: 13060 times; Followed by:1906 members; GMAT Score:790

divisor

by GMATGuruNY » Mon Jan 08, 2018 7:44 am

swerve wrote:A number when divided by a certain divisor left remainder 241, . Find the divisor?

A. 370
B. 365
C. 380
D. 456
E. 460

A number when divided by a certain divisor left remainder 241.
In other words, the number x is a multiple of divisor d plus 241:
x = ad + 241.

When twice the number was divided by the same divisor, the remainder was 112.
In other words, twice number x is a multiple of divisor d plus 112:
2x = bd + 112.

Doubling the first equation, we get:
2x = 2ad + 482.

The blue expressions above are both equal to 2x and thus are equal:
bd + 112 = 2ad + 482
bd - 2ad = 370
d(b - 2a) = 370.

The resulting equation implies that d is a factor of 370.
Of the five answer choices, only A is a factor of 370.

The correct answer is A.

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

Quote

GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8085; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Mon Aug 12, 2019 10:42 am

swerve wrote:A number when divided by a certain divsor left remainder 241, when twice the number was divided by the same divisor, the remainder was 112. Find the divisor?

A. 370
B. 365
C. 380
D. 456
E. 460

We can let the number = n and the divisor = d.

Since the remainder is 214 when n is divided by d, we can say:

n/d = q + 241/d

Multiplying both sides by d, we have:

n = qd + 241 [Eq. 1]

Also, since the remainder is 112 when twice n is divided by d, we can say:

2n/d = p + 112/d

Multiplying both sides by d, we have:

2n = pd + 112 [Eq. 2]

Multiplying Eq. 1 by 2, we have:

2n = 2qd + 482

Substituting 2n into Eq. 2 as 2qd + 482, we can say:

2qd + 482 = pd + 112

370 = pd - 2qd

d(p - 2q) = 370

Since (p - 2q) is an integer, d must be a factor of 370. The only number in the answer choices that is a factor of 370 is 370 itself. Thus, answer choice A is correct.

Answer: A

Scott Woodbury-Stewart
Founder and CEO
[email protected]