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when the integer n is divided by 17, the quotient is x and t [#permalink]
03 Jun 2018, 07:47
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Question Stats:
100% (01:29) correct
0% (00:00) wrong based on 26 sessions
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?
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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Expert's post
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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100% (01:29) correct
