When positive integer x is divided by 11, the quotient is y and the re

Question

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

AmoyV · Accepted Answer

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 · Answer

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 · Answer

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

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

answer D

OptimusPrepJanielle · Answer

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). -- Optimus Prep's GMAT On Demand course for only $299 covers all verbal and quant. concepts in detail. Visit the following link to get your 7 days free trial account: https://www.optimus-prep.com/gmat-on-demand-course

lipsi18 · Answer

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

Bunuel · Answer

MAGOOSH OFFICIAL SOLUTION: remainders13yminusx_text.PNG

evdo · Answer

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

Ans = D

forrgrav · Answer

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?

nkme2007 · Answer

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

pxion00p · Answer

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

KarishmaB · Answer

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.

Abhishek009 · Answer

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)

luisdicampo · Answer

Deconstructing the Question

From the first condition,

x = 11y + 4

From the second condition,

2x = 8(3y) + 2

We solve the system to find   x   and   y  .

Step-by-step

Simplify the second equation:

2x = 24y + 2

Divide by 2:

x = 12y + 1

Now set equal to the first expression for   x  :

11y + 4 = 12y + 1

Solve:

4 = y + 1

y = 3

Find   x  :

x = 11\cdot 3 + 4 = 37

Compute:

13y - x = 13\cdot 3 - 37 = 2

Answer: D

When positive integer x is divided by 11, the quotient is y and the re

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When positive integer x is divided by 11, the quotient is y and the re

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