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# In the equation y = 36.12x, x and y are integers. If yx leaves a remai

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Math Expert
Joined: 02 Sep 2009
Posts: 50711
In the equation y = 36.12x, x and y are integers. If yx leaves a remai  [#permalink]

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29 Apr 2016, 15:03
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Difficulty:

55% (hard)

Question Stats:

61% (01:48) correct 39% (01:54) wrong based on 150 sessions

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In the equation y = 36.12x, x and y are integers. If y/x leaves a remainder of r, which of the following must divide into r?

A. 2
B. 3
C. 4
D. 6
E. 12

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Math Expert
Joined: 02 Aug 2009
Posts: 7040
In the equation y = 36.12x, x and y are integers. If yx leaves a remai  [#permalink]

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30 Apr 2016, 01:21
1
4
Bunuel wrote:
In the equation y = 36.12x, x and y are integers. If y/x leaves a remainder of r, which of the following must divide into r?

A. 2
B. 3
C. 4
D. 6
E. 12

HI,
y = 36.12x.. it surely MEANS $$y=36.12*x$$
or $$\frac{y}{x}= 36.12 = 36 +0.12$$..

since both x and y are integers, 0.12*x is also an integer and = r...
so 0.12 * x= r..
or $$\frac{12x}{100}$$ = r..
12x = 100r..
3x = 25r...
so x has to be a multiple of 25 .......and r, a multiple of 3..
ans B
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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##### General Discussion
Manager
Joined: 08 Oct 2015
Posts: 241
Re: In the equation y = 36.12x, x and y are integers. If yx leaves a remai  [#permalink]

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30 Apr 2016, 08:17
chetan2u
How can u assume that y/x =36.12?

This is akin to saying y=36.125
And y/5=36.12

Posted from my mobile device
Math Expert
Joined: 02 Aug 2009
Posts: 7040
Re: In the equation y = 36.12x, x and y are integers. If yx leaves a remai  [#permalink]

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30 Apr 2016, 08:29
1
rahulkashyap wrote:
chetan2u
How can u assume that y/x =36.12?

This is akin to saying y=36.125
And y/5=36.12

Posted from my mobile device

hi,

I have taken it because the sentence reads -
Quote:
In the equation y = 36.12x, x and y are integers..

1) It says it is a equation, so y=36.12x should be 36.12 * x..
2) It says x is an integer, again it means 36.12 * x..
Otherwise x would be just a digit and it would be mentioned..

Although not clearly mentioned that 36.12x is actually 36.12 * x, BUT entire info points towards that..
and that is why I have taken y/x = 36.12
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

GMAT online Tutor

Intern
Joined: 30 Apr 2018
Posts: 19
Re: In the equation y = 36.12x, x and y are integers. If yx leaves a remai  [#permalink]

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06 Sep 2018, 06:17
chetan2u wrote:
Bunuel wrote:
In the equation y = 36.12x, x and y are integers. If y/x leaves a remainder of r, which of the following must divide into r?

A. 2
B. 3
C. 4
D. 6
E. 12

HI,
y = 36.12x.. it surely MEANS $$y=36.12*x$$
or $$\frac{y}{x}= 36.12 = 36 +0.12$$..

since both x and y are integers, 0.12*x is also an integer and = r...
so 0.12 * x= r..
or $$\frac{12x}{100}$$ = r..
12x = 100r..
3x = 25r...
so x has to be a multiple of 25 .......and r, a multiple of 3..
ans B

Hi chetan2u

slightly silly doubt , but arn't all 3, 6, 12 multiples of 3? then why did you just pick 3 as an answer? i actually got stuck with answer options - B, D and E
Math Expert
Joined: 02 Aug 2009
Posts: 7040
Re: In the equation y = 36.12x, x and y are integers. If yx leaves a remai  [#permalink]

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06 Sep 2018, 08:11
1
NidSha wrote:
chetan2u wrote:
Bunuel wrote:
In the equation y = 36.12x, x and y are integers. If y/x leaves a remainder of r, which of the following must divide into r?

A. 2
B. 3
C. 4
D. 6
E. 12

HI,
y = 36.12x.. it surely MEANS $$y=36.12*x$$
or $$\frac{y}{x}= 36.12 = 36 +0.12$$..

since both x and y are integers, 0.12*x is also an integer and = r...
so 0.12 * x= r..
or $$\frac{12x}{100}$$ = r..
12x = 100r..
3x = 25r...
so x has to be a multiple of 25 .......and r, a multiple of 3..
ans B

Hi chetan2u

slightly silly doubt , but arn't all 3, 6, 12 multiples of 3? then why did you just pick 3 as an answer? i actually got stuck with answer options - B, D and E

When we say r is multiple of 3, all other mutiple of 3 are also taken in that, so 6 and 12 are also in that.
But if I say it is multiple of 6, then I would mean, it is not necessarily a multiple of 3..
So r as a multiple of 6 excludes all values like 3,9,15 etc
So if r is 3, the value picked as r to be multiple of 6 doesn't stand.
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

GMAT online Tutor

Re: In the equation y = 36.12x, x and y are integers. If yx leaves a remai &nbs [#permalink] 06 Sep 2018, 08:11
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