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

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

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

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

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

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

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
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OA B

Source: Official Guide

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; 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

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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