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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

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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

by BTGModeratorVI » Wed Dec 16, 2020 12:33 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

Answer: B
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. When n is divided by 23, the quotient

by Brent@GMATPrepNow » Mon Dec 28, 2020 8:18 am
BTGModeratorVI wrote: ↑
Wed Dec 16, 2020 12:33 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

Answer: B
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

Answer: B
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Re: 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

by swerve » Mon Dec 28, 2020 4:37 pm
BTGModeratorVI wrote: ↑
Wed Dec 16, 2020 12:33 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

Answer: B
Source: official guide
Dividend \(=\) Divisor\(\cdot\) Quotient \(+\) Remainder

When the integer \(n\) is divided by \(17\), the quotient is \(x\) and the remainder is \(5\)
Dividend\(=n\)
Divisor\(=17\)
Quotient\(=x\)
Remainder\(=5\)

\(n = 17x+5\)

Likewise;
\(n\) is divided by \(23\), the quotient is \(y\) and the remainder is \(14\)
\(n = 23y+14\)

\(n=n\)
\(17x+5=23y+14\)
\(17x−23y=9\)

Therefore, B
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Re: 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

by Scott@TargetTestPrep » Fri Jan 01, 2021 5:10 am
BTGModeratorVI wrote: ↑
Wed Dec 16, 2020 12:33 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

Answer: B
Source: official guide
Solution:

We can create two equations:

n = 17x + 5

and

n = 23y + 14

Thus:

17x + 5 = 23y + 14

17x - 23y = 9

Answer: B

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