When the integer n is divided by 17, the quotient is x and

Expert replies

BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pmFollowed by: 23 members

by BTGmoderatorDC » Sat Dec 28, 2019 6:05 pm

When the integer n is divided by 17, the quotient is x and the remainder is 5. When n is divided by 23, the quotient is y and the remainder is 14. Which of the following is true?

(A) 23x + 17y =19
(B) 17x -23y = 9
(C) 17x +23y =19
(D) 14x + 5y = 6
(E) 5x - 14y = -6

OA B

Source: Official Guide

Like this post

Source: Beat The GMAT — Problem Solving | Sat Dec 28, 2019 6:05 pm

GMAT/MBA Expert

Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 amFollowed by: 34 members; Location: Grand Central / New York; Thanked: 470 times

by Jay@ManhattanReview » Mon Dec 30, 2019 9:39 pm

BTGmoderatorDC wrote:When the integer n is divided by 17, the quotient is x and the remainder is 5. When n is divided by 23, the quotient is y and the remainder is 14. Which of the following is true?

(A) 23x + 17y =19
(B) 17x -23y = 9
(C) 17x +23y =19
(D) 14x + 5y = 6
(E) 5x - 14y = -6

Given that when the integer n is divided by 17, the quotient is x and the remainder is 5, we have n = 17x + 5;
Also, given that when the integer n is divided by 23, the quotient is y and the remainder is 14, we have n = 23y + 14;

Thus, 17x + 5 = 23y + 14

=> 17x - 23y = 9

The correct answer: B

Hope this helps!

-Jay
_________________
Manhattan Review GRE Prep

Locations: GMAT Classes San Francisco | GRE Prep Course DC | GRE Prep Houston | SAT Prep Classes NYC | and many more...

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

OA B

Source: Official Guide

Like this post

GMAT/MBA Expert

Brent@GMATPrepNow: 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 » Tue Dec 31, 2019 3:17 am

BTGmoderatorDC wrote:When the integer n is divided by 17, the quotient is x and the remainder is 5. When n is divided by 23, the quotient is y and the remainder is 14. Which of the following is true?

(A) 23x + 17y =19
(B) 17x -23y = 9
(C) 17x +23y =19
(D) 14x + 5y = 6
(E) 5x - 14y = -6

Here's a useful rule:
If A divided by B equals C with remainder D, then it's also true that BC + D = A (this is an important GMAT concept)
Example: Since 32 divided by 5 equals 6 with remainder 2, then it's also true that (5)(6) + 2 = 32

Now onto the question:
We're told that "when n is divided by 17, the quotient is x and the remainder is 5," which means 17x + 5 = n

We're also told that "when n is divided by 23, the quotient is y and the remainder is 14," which means that 23y + 14 = n

Now, if 17x + 5 equals n AND 23y + 14 also equals n, it must be true that 17x + 5 = 23y + 14

If we rearrange the terms of this equation, we get 17x - 23y = 9

Answer: B

Brent Hanneson - Creator of GMATPrepNow.com

Like this post

GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8157; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Fri Jan 10, 2020 8:30 am

BTGmoderatorDC wrote:When the integer n is divided by 17, the quotient is x and the remainder is 5. When n is divided by 23, the quotient is y and the remainder is 14. Which of the following is true?

(A) 23x + 17y =19
(B) 17x -23y = 9
(C) 17x +23y =19
(D) 14x + 5y = 6
(E) 5x - 14y = -6

OA B

Source: Official Guide

We can create two equations:

n = 17x + 5

and

n = 23y + 14

Thus:

17x + 5 = 23y + 14

17x - 23y = 9

Answer: B

Scott Woodbury-Stewart
Founder and CEO
[email protected]

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

560 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review