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When the integer n is divided by 17, the quotient is x and the remaind

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Acer86
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When the integer n is divided by 17, the quotient is x and the remaind [#permalink] New post   Updated on: 21 Sep 2019, 14:31
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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

PS66402.01
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B

Originally posted by Acer86 on 03 Apr 2011, 05:45.
Last edited by Bunuel on 21 Sep 2019, 14:31, edited 3 times in total.
Renamed the topic and edited the question.
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Re: When the integer n is divided by 17, the quotient is x and the remaind [#permalink] New post   03 Apr 2011, 05:54
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From the problem it follows:
n=17x+5
n=23y+14

So, 17x+5=23y+14
17x-23y=9

The answer is B
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Acer86
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Re: When the integer n is divided by 17, the quotient is x and the remaind [#permalink] New post   03 Apr 2011, 06:01
Thank you. One

quick question...shouldnt the equation be n/17 = X + 5 ?? why dont we multiply 5 by 17?
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Re: When the integer n is divided by 17, the quotient is x and the remaind [#permalink] New post   03 Apr 2011, 06:03
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Acer86 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 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 = Divisor*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

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

Ans: "B"
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Re: When the integer n is divided by 17, the quotient is x and the remaind [#permalink] New post   03 Apr 2011, 06:07
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Acer86 wrote:
Thank you. One

quick question...shouldnt the equation be n/17 = X + 5 ?? why dont we multiply 5 by 17?


Also,
\(\frac{Dividend}{Divisor}=Quotient+\frac{Remainder}{Divisor}\)

\(\frac{n}{17}=x+\frac{5}{17}\)

After multiplying entire equation by 17
\(n=17x+5\)
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Re: When the integer n is divided by 17, the quotient is x and the remaind [#permalink] New post   03 Apr 2011, 07:57
n = 17x+5
n = 23y+14

17x+5 = 23y+14 => 17x-23y =9

Answer B.
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Re: When the integer n is divided by 17, the quotient is x and the remaind [#permalink] New post   03 Apr 2011, 19:17
n = 17x + 5

n = 23y + 14

So 17x + 5 = 23y + 14

=> 17x –23y = 9


Answer - B
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Re: When the integer n is divided by 17, the quotient is x and the remaind [#permalink] New post   03 Apr 2011, 22:05
Dividend Divisor Quotient Remainder
n 17 x 5 n = 17x + 5
n 23 y 14 n = 23y+14

17x + 5 = 23y + 14

On solving, we get option B
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Re: When the integer n is divided by 17, the quotient is x and the remaind [#permalink] New post   17 Nov 2013, 12:59
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


n = 17x+5 ------------ (1)
n = 23y+14 ------------(2)

By soving equation (1) & (2),we get the following answer

17x+5=23y+14
ie 17x-23y=9

So.Option (b) is correct.
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When the integer n is divided by 17, the quotient is x and the remaind [#permalink] New post   Updated on: 17 May 2021, 08:32
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Acer86 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 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: B

RELATED VIDEO

Originally posted by BrentGMATPrepNow on 04 Jun 2018, 11:03.
Last edited by BrentGMATPrepNow on 17 May 2021, 08:32, edited 2 times in total.
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Re: When the integer n is divided by 17, the quotient is x and the remaind [#permalink] New post   09 Jan 2019, 03:04
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Bunuel 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 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


"When the integer n is divided by 17, the quotient is x and the remainder is 5"
n = 17x + 5

"When n is divided by 23, the quotient is y and the remainder is 14"
n = 23y + 14

17x + 5 = 23y + 14 = n
17x - 23y = 9

Answer (B)
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Re: When the integer n is divided by 17, the quotient is x and the remaind [#permalink] New post   09 Jan 2019, 04:45
Bunuel 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 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


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

When n is divided by 23, the quotient is y and the remainder is 14
n = 23y +14

On comparing both sides
23y +14 = 17x + 5
17x – 23y = 9

IMO Answer is B.
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Re: When the integer n is divided by 17, the quotient is x and the remaind [#permalink] New post   08 Jan 2020, 20:42
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Acer86 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 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

PS66402.01


We see that n/17 = x + 5/17 → n = 17x + 5 and n/23 = y + 14/23 → n = 23y + 14. Therefore, we have:

17x + 5 = 23y + 14

17x - 23y = 9

Answer: B
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Re: When the integer n is divided by 17, the quotient is x and the remaind [#permalink] New post   14 Nov 2020, 09:40
n/17 = x + 5
n = 17x + 5

n/23 = y + 14
n = 23y + 14

17x + 5 = 23y + 14
17x - 23y = 9

Answer is B.
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Re: When the integer n is divided by 17, the quotient is x and the remaind [#permalink] New post   07 Dec 2020, 13:11
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Acer86 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 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

PS66402.01


\((i) n=17x+5\)

\((ii) n=23y+14\)

Deducting (ii) from (i):


\(0=17x-23y-9\)

\(9=17x-23y\)

\(17x-23y=9\)

The answer is \(B\)
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Re: When the integer n is divided by 17, the quotient is x and the remaind [#permalink] New post   25 Sep 2022, 05:01
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When the integer n is divided by 17, the quotient is x and the remainder is 5

Theory: Dividend = Divisor*Quotient + Remainder

n -> Dividend
17 -> Divisor
x -> Quotient
5 -> Remainder
=> n = 17*x + 5 = 17x + 5 ..(1)

When n is divided by 23, the quotient is y and remainder is 14

=> n = 23y + 14 ..(2)

From (1) and (2) we get
n = 17x + 5 = 23y + 14

=> 17x - 23y = 14 - 5 = 9

So, Answer will be B
Hope it helps!

Watch the following video to learn the Basics of Remainders

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Re: When the integer n is divided by 17, the quotient is x and the remaind [#permalink] New post   29 Sep 2023, 07:49
Acer86 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 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

PS66402.01

\(17x + 5 = 23y + 14\)

Or, \(17x –23y = 9\), Answer will be (B)
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Re: When the integer n is divided by 17, the quotient is x and the remaind [#permalink]
29 Sep 2023, 07:49
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