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when the integer n is divided by 17, the quotient is x and t

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when the integer n is divided by 17, the quotient is x and t [#permalink] New post 03 Jun 2018, 07:47
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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 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

src: Orbit Test prep
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Re: when the integer n is divided by 17, the quotient is x and t [#permalink] New post 04 Jun 2018, 10:01
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amorphous 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 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

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Re: when the integer n is divided by 17, the quotient is x and t   [#permalink] 04 Jun 2018, 10:01
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when the integer n is divided by 17, the quotient is x and t

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