For positive integers x and y, x = 16.375y. What is the remainder when

Question

For positive integers x and y, x = 16.375y. What is the remainder when x is divided by y?

(1) y < 12

(2) y > 6

chetan2u · Accepted Answer

x=16.375y=(16+0.375)*y=16y+0.375y...
This should be an integer so 0.375*y should be an integer & the remainder..
It will be integer only when y is a multiple of 8...
So remainder will depend on y and will be 0.375*8 or 0.375*8*2 or 0.375*8*3 and so on..

Let's see the statements 
(1) y<12...
y is positive and a multiple of 8..
ONLY possible value is 8..
So remainder is 0.375*8=3
Sufficient

(2) y>6..
y can be 8,16,24.....
Insuff

A

yezz · Answer

from stem x= 16y+ 375/1000y, y>0 .......... = 16y+3/8y and since 3/8y has to be an integer thus y is a multiple of 8 from 1 00 giving different remainders .......insuff A

abhikdas2512 · Answer

But 3 won't be the answer rather, multiples of 3 can be answers. e.g. 3,6,9,12..... which is why, <12 &>6 narrow the choice to 9. Hence, C is correct.

rajendra00 · Answer

Option A
X= 16.375y.. Can be written as ----> X/Y = 16 + 0.375----> Further can be written as X/Y = 16 + 3/8

So, Y is greater than or equal to 8 & Multiples of 8( 8, 16, 24). Statement 1: Sufficient.

Statement 2: Since y> 6 , different values are possible -- NS

Jelita · Answer

Both are positive integers, and x = 16,375y -> x/y = 16,375. For any Y that's multiple of 8 the conditions are fulfilled and the division will result in 16,375. Dosn't matter if Y is 8, 16, 24... The remainder is always the same => Either statement is sufficient I'm going against the flow of other responses on this one :D If I am indeed right, please share some KUDOS (need them for access to the extra CATs. Thanks!

)

BillyZ · Answer

Official solution from Veritas Prep.

When dealing with quotient/remainder problems involving decimals, it is critical to recognize that the portion of the result after the decimal point (in this case the 0.375 that follows the 16) comes from the remainder being divided by the divisor. While this concept is abstract when written out in words, you can somewhat quickly prove it to yourself by testing small numbers to remind yourself how division with remainders and decimals works. If you had 12 divided by 5, 5 would go into 12 twice (5x2 = 10) with 2 left over. What do you do with that 2? You divide it by 5 to get 0.4, so that your answer is 2.4.

So in this case, before you even look at the statements, you should unpack the given information. Since they're asking about x divided by y, quickly divide both sides of the given equation by y to get x/y = 16.375. Then recognize that the 0.375 after the decimal point will come from the remainder divided by y.

The 0.375 value should jump out at you as equaling 3/8. That means that the remainder divided by y must be a fraction that can be reduced to 3/8. It could be 3/8, or 6/16,or 30/80, but it must remain in that ratio. That means that the remainder must be a multiple of 3, and that y must be a multiple of 8. And so when you get to the statements, you should see that statement 1 provides an ever-important restriction. y must be a multiple of 8, and since it's defined as positive it must be greater than 0. So with statement 1 you know that y is a multiple of 8 between 0 and 12, which means it can only be 8. In turn, that guarantees that the remainder is 3, so statement 1 is sufficient.

Statement 2 is not sufficient because it allows for multiple pairings of remainder and y. y could be 8, meaning that the remainder is 3, but it could also be 16 meaning that the remainder is 6. And with no upper limit on y, statement 2 allows for infinite pairings of remainder/y = 3/8, so statement 2 is not sufficient. The correct answer is A.

pranjal123 · Answer

Question stem is bit confusing. I thought "y" is the last digit but after checking the solution it seems "Y" part of product .

Is question format correct as per GMAT standard. ? I think the question should be formatted something like x = (16.375)y

sleepynut · Answer

Hi,I think we have nothing to do with the value of y.
We don't have to worry about zero dividing as both x and y are positive integer.
Since we have x=16.375y and are asked to find the remainder of x when it is divided by y.Basically the result is 16.375,which is  \frac{131}{8} .
Hence,both is sufficient in itself.

What did I miss?
Thanks

bumpbot · Answer

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For positive integers x and y, x = 16.375y. What is the remainder when

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For positive integers x and y, x = 16.375y. What is the remainder when

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