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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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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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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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