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Manager  P
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x, y are positive integers. When x is divided by y, the remainder is 6  [#permalink]

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x, y are positive integers. When x is divided by y, the remainder is 6 and x/y=6.12, what is the value of x?

A. 6
B. 50
C. 206
D. 306
E. 336
Intern  Joined: 24 Sep 2016
Posts: 17
Re: x, y are positive integers. When x is divided by y, the remainder is 6  [#permalink]

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Ans :D

0,12y =6
y=50
x=6y +6=306

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Re: x, y are positive integers. When x is divided by y, the remainder is 6  [#permalink]

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haardiksharma wrote:
x, y are positive integers. When x is divided by y, the remainder is 6 and x/y=6.12, what is the value of x?

A. 6
B. 50
C. 206
D. 306
E. 336

$$\frac{x}{y} = 6.12$$

Or, $$\frac{x}{y} = \frac{612}{100}$$

Or, $$x = 306$$ & $$y = 50$$ ( Here we have x is divided by y, the remainder is 6 and x/y=6.12 )

Thus, the answer must be (D) 306
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x, y are positive integers. When x is divided by y, the remainder is 6  [#permalink]

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haardiksharma wrote:
x, y are positive integers. When x is divided by y, the remainder is 6 and x/y=6.12, what is the value of x?

A. 6
B. 50
C. 206
D. 306
E. 336

x/y=6.12
(x-6)/y=6
subtracting,
6/y=.12
y=50
50*6.12=x=306
D
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Re: x, y are positive integers. When x is divided by y, the remainder is 6  [#permalink]

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x, y are positive integers. When x is divided by y, the remainder is 6 and x/y=6.12, what is the value of x?

$$\frac{x}{y}$$ = k + $$\frac{6}{y}$$ = 6 + 0.12

so k = 6 & $$\frac{6}{y}$$ = 0.12
so y = 50m ( m is a factor )

let's say m = 1 ; y = 50 ; x = 50 + 6 = 56 ; $$\frac{x}{y}$$ = $$\frac{56}{50}$$ <> 6.12
let's say m = 2 ; y = 50 ; x = 100 + 6 = 106 ; $$\frac{x}{y}$$ = $$\frac{106}{50}$$ <> 6.12
let's say m = 3 ; y = 50 ; x = 150 + 6 = 156 ; $$\frac{x}{y}$$ = $$\frac{156}{50}$$ <> 6.12
let's say m = 4 ; y = 50 ; x = 200 + 6 = 206 ; $$\frac{x}{y}$$ = $$\frac{206}{50}$$ <> 6.12
let's say m = 5 ; y = 50 ; x = 250 + 6 = 256 ; $$\frac{x}{y}$$ = $$\frac{256}{50}$$ <> 6.12

let's say m = 6 ; y = 50 ; x = 300 + 6 = 306 ; $$\frac{x}{y}$$ = $$\frac{306}{50}$$ = 6.12
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x, y are positive integers. When x is divided by y, the remainder is 6  [#permalink]

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since the remainder is 6 and the decimal part of the quotient is .12

0.12 * y = 6 {decimal part of quotient * divisor = remainder}

therefore y = 6/0.12 = 50
and x = 6y +6 = 6(50)+6 = 306

Option D
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x, y are positive integers. When x is divided by y, the remainder is 6  [#permalink]

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haardiksharma wrote:
x, y are positive integers. When x is divided by y, the remainder is 6 and x/y=6.12, what is the value of x?

A. 6
B. 50
C. 206
D. 306
E. 336

1. $$\frac{x}{y}$$ = 6.12 = 6 + $$\frac{12}{100}$$, or + $$\frac{3}{25}$$

2. $$\frac{x}{y}$$ = a + $$\frac{6}{y}$$, where latter = $$\frac{r}{y}$$ from remainder formula

3. Set $$\frac{r}{y}$$ equal to the decimal part of the decimal quotient from #1, and solve for y:

$$\frac{6}{y}$$ = $$\frac{3}{25}$$ --> y = 50

4. Rebuild the dividend x:

$$\frac{x}{y}$$ = a + $$\frac{6}{y}$$ --> x = (a)(y) + 6

From the quotient 6.12, we know a = 6 (the integer part of the quotient in decimal form = the integer quotient)

5. x = (6)(50) + 6 = 306, Answer D

An exceptionally clear explanation for problems like this one is from Mike McGarry, here:
https://magoosh.com/gmat/2012/gmat-quant-thoughts-on-remainders
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Re: x, y are positive integers. When x is divided by y, the remainder is 6  [#permalink]

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haardiksharma wrote:
x, y are positive integers. When x is divided by y, the remainder is 6 and x/y=6.12, what is the value of x?

A. 6
B. 50
C. 206
D. 306
E. 336

We must remember that the remainder formula is:

x/y = Q + r/y

Substituting values into the equation, we have:

x/y = 6 + 12/100

x/y = 6 + 3/25

Thus, we see that 3/25 represents r/y, and since we are told that r = 6 we have:

3/25 = 6/y

3y = 6(25)

y = 2(25) = 50

Since y is 50, we see that x = 6.12y = 6.12(50) = 306.

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