## When the integer n is divided by 17, the quotient is x and the remainder is 5.

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### When the integer n is divided by 17, the quotient is x and the remainder is 5.

by BTGModeratorVI » Sun Jul 19, 2020 1:35 pm

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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 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

Source: Official guide

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### Re: When the integer n is divided by 17, the quotient is x and the remainder is 5.

by [email protected] » Mon Jul 20, 2020 1:00 am
BTGModeratorVI wrote:
Sun Jul 19, 2020 1:35 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

Source: Official guide
From the information that the integer n is divided by 17, the quotient is x and the remainder is 5, we have n = 17x + 5 and from the information that n is divided by 23, the quotient is y and the remainder is 14, we have n = 23y + 14

=> 17x + 5 = 23y + 14

17 – 23y = 9

Hope this helps!

-Jay
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### Re: When the integer n is divided by 17, the quotient is x and the remainder is 5.

by [email protected] » Mon Jul 20, 2020 8:46 am
BTGModeratorVI wrote:
Sun Jul 19, 2020 1:35 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

Source: Official guide
\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

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### Re: When the integer n is divided by 17, the quotient is x and the remainder is 5.

by [email protected] » Sat Jul 24, 2021 3:44 am
BTGModeratorVI wrote:
Sun Jul 19, 2020 1:35 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

Source: Official guide
Solution:

We can create the equations:

n/17 = x + 5/17 and n/23 = y + 14/23

Simplifying the equations, we have:

n = 17x + 5 and n = 23y + 14

Now equating the right hand side of both equations (since they both equal n), we have:

17x + 5 = 23y + 14

17x - 23y = 9