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neeti2711: Master | Next Rank: 500 Posts; Posts: 116; Joined: Sat Sep 22, 2012 9:48 pm; Thanked: 3 times

by neeti2711 » Mon Oct 22, 2012 5:02 am

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

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Source: Beat The GMAT — Problem Solving | Mon Oct 22, 2012 5:02 am

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Mon Oct 22, 2012 5:11 am

neeti2711 wrote:When the integer n is divided by 17, the quotient is x and the remainder 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

Dividend = Quotient * Divisor + Remainder
n = 17x + 5 ... Equation 1
n = 23y + 14 ... Equation 2

Equating the value of n from the 2 equations above,
17x + 5 = 23y + 14
17x - 23y = 9

The correct answer is B.

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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 » Mon Oct 22, 2012 5:12 am

neeti2711 wrote:When the integer n is divided by 17, the quotient is x and the remainder 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 choice B)

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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