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

Question

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

chetan2u · Accepted Answer

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

rahulkashyap · Answer

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

chetan2u · Answer

hi,

I have taken it because the sentence reads - 
 
 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

NidSha · Answer

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
TIA for your help

chetan2u · Answer

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.

Fdambro294 · Answer

Concept: Given ONLY the Decimal Form of the REMAINDER after we Divide 2 Integers, we can NOT Find the Actual Value of the Divisor ---

BUT, after Converting the Decimal Form to the Fractional Form of the Remainder and then Canceling this Fraction to its Most Fully Reduced Form ----

we can Infer what the Remainder and Divisor must be Evenly Divisible by

Rebuilding the Dividend Formula:

(Dividend)/ (Divisor) = Quotient + (Remainder) / (Divisor)

or

Dividend = (Divisor) * (Quotient) + Remainder

Given:

Y = 36.12X

----Where Y and X are Both Integers----

Y = (36.12) * (X)

(Y) / (X) = 36.12

(Y) / (X) = 36 + 12/100

----Reducing the Fractional Remainder Part to its most Fully Reduced Form-----

(Y) / (X) = 36 + 3 / 25

Following the Rebuilding the Dividend Formula, where X and Y are Integers and the Quotient = 36

(Dividend-Y) / (Divisor-X) = (Quotient-36) + (Remainder = 3k) / (Divisor = 25k)

2 Inferences can be pulled out:

Divisor X must be a Multiple of 25

and

when Integer Y is Divided by Integer X ------>the Remainder = r must be a Multiple of 3

-B-

aarnavn · Answer

HI,  
  y = 36.12x.. it surely MEANS   
   y=36.12∗xy=36.12∗x

or   
   yx=36.12=36+0.12yx=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   
   12x10012x100   
  = r.. 
 12x = 100r.. 
 3x = 25r... 
  so x has to be a multiple of 25 .......and r, a multiple of 3..  
 ans B

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

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

Prep Toolkit

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