When positive integer x is divided by 11, the quotient is y and the re : Problem Solving (PS)

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Bunuel

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When positive integer x is divided by 11, the quotient is y and the re [#permalink]

31 Mar 2015, 05:45

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When positive integer x is divided by 11, the quotient is y and the remainder is 4. When 2x is divided by 8, the quotient is 3y and the remainder is 2. What is the value of 13y – x ?

A. -4
B. -2
C. 0
D. 2
E. 4

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AmoyV

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Re: When positive integer x is divided by 11, the quotient is y and the re [#permalink]

31 Mar 2015, 06:21

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Bunuel wrote:

When positive integer x is divided by 11, the quotient is y and the remainder is 4. When 2x is divided by 8, the quotient is 3y and the remainder is 2. What is the value of 13y – x ?

A. -4
B. -2
C. 0
D. 2
E. 4

Kudos for a correct solution.

x=11y+4; 2x=22y+8....(1)
2x=8*3y+2
2x=24y+2....(2)

(1) and (2)

22y+8=24y+2
y=3

Therefore x=11*3+4=37

13y-x=39-37=2

Answer : D

cherryli2015

Intern

Joined: 15 Feb 2015

Posts: 11

Re: When positive integer x is divided by 11, the quotient is y and the re [#permalink]

31 Mar 2015, 07:44

2

Kudos

My solution comes here:

X = 11Y + 4
2X = 8*3Y + 2
3x - Y = ?

1 -> 2X = 22Y + 8
2X = 24 Y + 2
-> 22Y + 8 = 24Y + 2
-> 2Y = 6
-> Y = 3

-> X = 37
-> 3X - Y = 3*37 - 3 = 101 - 3 = 98

Lucky2783

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Re: When positive integer x is divided by 11, the quotient is y and the re [#permalink]

31 Mar 2015, 08:53

1

Kudos

Bunuel wrote:

When positive integer x is divided by 11, the quotient is y and the remainder is 4. When 2x is divided by 8, the quotient is 3y and the remainder is 2. What is the value of 13y – x ?

A. -4
B. -2
C. 0
D. 2
E. 4

Kudos for a correct solution.

X= 11*Y + 4 --------1st
2X= 8*3Y + 2 -------2nd

2nd - 1st
X= 13Y -2
so 13Y - X = 2

answer D

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OptimusPrepJanielle

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Joined: 06 Nov 2014

Posts: 1799

Re: When positive integer x is divided by 11, the quotient is y and the re [#permalink]

31 Mar 2015, 11:28

3

Kudos

Expert Reply

Bunuel wrote:

When positive integer x is divided by 11, the quotient is y and the remainder is 4. When 2x is divided by 8, the quotient is 3y and the remainder is 2. What is the value of 13y – x ?

A. -4
B. -2
C. 0
D. 2
E. 4

Kudos for a correct solution.

Number = Quotient * Divisor + Remainder
So, x = 11y + 4
And, 2x = 24y + 2
Solve these 2, we get,
x = 37 and y = 3.
So, 13y - x = 2
Hence option (D).

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lipsi18

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Re: When positive integer x is divided by 11, the quotient is y and the re [#permalink]

03 Apr 2015, 14:08

2

Kudos

Equation 1: x=11y+4
Equation 2: x=12y+11
from equation 1& 2 we know y=3; putting this value to find out x=37
Hence 13y-x=39-37=2

Hence answer is D

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Bunuel

Math Expert

Joined: 02 Sep 2009

Posts: 92698

Re: When positive integer x is divided by 11, the quotient is y and the re [#permalink]

06 Apr 2015, 05:48

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Expert Reply

Bunuel wrote:

When positive integer x is divided by 11, the quotient is y and the remainder is 4. When 2x is divided by 8, the quotient is 3y and the remainder is 2. What is the value of 13y – x ?

A. -4
B. -2
C. 0
D. 2
E. 4

Kudos for a correct solution.

MAGOOSH OFFICIAL SOLUTION:

Attachment:

remainders13yminusx_text.PNG [ 15.77 KiB | Viewed 11837 times ]

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Re: When positive integer x is divided by 11, the quotient is y and the re [#permalink]

31 Jul 2015, 08:24

x = 11y + 4
2x = 24y + 2 (-)
-x = -13y + 2
13y - x = 2

Ans = D

forrgrav

Intern

Joined: 16 Apr 2019

Posts: 3

Re: When positive integer x is divided by 11, the quotient is y and the re [#permalink]

28 Jul 2019, 09:43

Sorry but how are you getting the equations that are being used to solve? There seems to be no explanation of how you get from x/11=yR4 to x=11y+4?

Can someone please explain?

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nkme2007

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Re: When positive integer x is divided by 11, the quotient is y and the re [#permalink]

10 Jul 2020, 00:05

Bunuel wrote:

When positive integer x is divided by 11, the quotient is y and the remainder is 4. When 2x is divided by 8, the quotient is 3y and the remainder is 2. What is the value of 13y – x ?

A. -4
B. -2
C. 0
D. 2
E. 4

Kudos for a correct solution.

From the question stem, we can get two equations as below:

x=11y+4
2x=8(3y)+2

Solving both

x=37 and y=3

So, 13y-x = 13(3)-37 = 2

OA: D
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pxion00p

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Joined: 14 Jul 2020

Posts: 1

Re: When positive integer x is divided by 11, the quotient is y and the re [#permalink]

03 Aug 2020, 13:42

forrgrav wrote:

Sorry but how are you getting the equations that are being used to solve? There seems to be no explanation of how you get from x/11=yR4 to x=11y+4?

Can someone please explain?

The equation is really X/11 = y+4/11 since Remainder for written out is 4/11 so when you multiply both sides by 11 the 4/11 goes to 4. Equation becomes X = 11y+4

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KarishmaB

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Joined: 16 Oct 2010

Posts: 14804

Location: Pune, India

Re: When positive integer x is divided by 11, the quotient is y and the re [#permalink]

15 Feb 2021, 04:48

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Kudos

Expert Reply

Bunuel wrote:

When positive integer x is divided by 11, the quotient is y and the remainder is 4. When 2x is divided by 8, the quotient is 3y and the remainder is 2. What is the value of 13y – x ?

A. -4
B. -2
C. 0
D. 2
E. 4

Kudos for a correct solution.

x = 11y + 4 ....... (I)
2x = 8*3y + 2 = 24y + 2 ..... (II)

(II) - (I)

x = 13y - 2
13y - x = 2

Answer (D)

This is not a remainders question. It is just algebraic manipulation.
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Abhishek009

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Re: When positive integer x is divided by 11, the quotient is y and the re [#permalink]

19 Feb 2024, 08:20

Bunuel wrote:

When positive integer x is divided by 11, the quotient is y and the remainder is 4. When 2x is divided by 8, the quotient is 3y and the remainder is 2. What is the value of 13y – x ?

A. -4
B. -2
C. 0
D. 2
E. 4

$x = 11y + 4$----------(I)
$2x = 8*3y + 2$----------(II)

$(I)*2 = (II)$

$24y + 2 = 22y + 8$

So, $y = 3$

From (I)

$x = 33 + 4 => 37$

Now, $13y – x = 13*3 - 37 => 2$, Answer must be (D)

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Re: When positive integer x is divided by 11, the quotient is y and the re [#permalink]

19 Feb 2024, 08:20

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