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

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Joined: 03 Dec 2010
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When the integer n is divided by 17, the quotient is x and the remaind  [#permalink]

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Updated on: 21 Sep 2019, 13:31
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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

Originally posted by Acer86 on 03 Apr 2011, 04:45.
Last edited by Bunuel on 21 Sep 2019, 13:31, 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]

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03 Apr 2011, 04:54
7
From the problem it follows:
n=17x+5
n=23y+14

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

##### General Discussion
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Joined: 03 Dec 2010
Posts: 30
Re: When the integer n is divided by 17, the quotient is x and the remaind  [#permalink]

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03 Apr 2011, 05:01
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]

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03 Apr 2011, 05:03
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]

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03 Apr 2011, 05:07
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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]

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03 Apr 2011, 06:57
n = 17x+5
n = 23y+14

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

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Re: When the integer n is divided by 17, the quotient is x and the remaind  [#permalink]

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03 Apr 2011, 18:17
n = 17x + 5

n = 23y + 14

So 17x + 5 = 23y + 14

=> 17x –23y = 9

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Re: When the integer n is divided by 17, the quotient is x and the remaind  [#permalink]

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03 Apr 2011, 21:05
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]

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17 Nov 2013, 11:59
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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Re: When the integer n is divided by 17, the quotient is x and the remaind  [#permalink]

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04 Jun 2018, 10:03
Top Contributor
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

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Re: When the integer n is divided by 17, the quotient is x and the remaind  [#permalink]

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09 Jan 2019, 02:04
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

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Re: When the integer n is divided by 17, the quotient is x and the remaind  [#permalink]

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09 Jan 2019, 03:45
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

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Re: When the integer n is divided by 17, the quotient is x and the remaind  [#permalink]

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08 Jan 2020, 19:42
1
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

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Re: When the integer n is divided by 17, the quotient is x and the remaind   [#permalink] 08 Jan 2020, 19:42