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

Question

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

bagrettin · Accepted Answer

From the problem it follows:
n=17x+5
n=23y+14

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

The answer is B

Acer86 · Answer

Thank you. One

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

fluke · Answer

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"

fluke · Answer

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

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

After multiplying entire equation by 17
 n=17x+5

Spidy001 · Answer

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

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

Answer B.

subhashghosh · Answer

n = 17x + 5

n = 23y + 14

So 17x + 5 = 23y + 14

=> 17x –23y = 9

Answer - B

gmatprep2011 · Answer

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

sumit88 · Answer

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.

BrentGMATPrepNow · Answer

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
 https://www.youtube.com/watch?v=XCxgIR042tE

KarishmaB · Answer

"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)

KanishkM · Answer

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.

ScottTargetTestPrep · Answer

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

Basshead · Answer

n/17 = x + 5
n = 17x + 5

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

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

Answer is B.

MHIKER · Answer

(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

BrushMyQuant · Answer

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

https://www.youtube.com/watch?v=P0S6j2uTaj4

Abhishek009 · Answer

17x + 5 = 23y + 14

Or,  17x –23y = 9 , Answer will be (B)

bumpbot · Answer

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

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

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