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For nonnegative integers x and y, what is the remainder when

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For nonnegative integers x and y, what is the remainder when [#permalink] New post 15 Dec 2012, 10:35
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For nonnegative integers x and y, what is the remainder when x is divided by y?

(1) x/y = 13.8
(2) The numbers x and y have a combined total of less than 5 digits
[Reveal] Spoiler: OA

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Re: For nonnegative integers x and y, what is the remainder when [#permalink] New post 15 Dec 2012, 14:53
good one... do you know the explanation?
given x,y \geq 0; what is R in x = Qy + R
1) x=13y + 0.8y
in this case we need value of 0.8y but we don't know values of x,y; Not Sufficient
2) x+y < 10^4; Not Sufficient

1+2
from 1) x=13.8y so from 2) 14.8y < 10^4
so y < \frac{10^4}{14.8}
there exists multiple integer values of y less than 10^4/14.8 for which x is integer... So my answer is E.... Since OA is different, i think my thinking in the last part is wrong....
Not sure how to proceed from here....

Last edited by Amateur on 15 Dec 2012, 17:12, edited 1 time in total.
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Re: For nonnegative integers x and y, what is the remainder when [#permalink] New post 15 Dec 2012, 17:08
Bunuel.... I need your presence here..... I am becoming reckless to get a solution for this.....
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Re: For nonnegative integers x and y, what is the remainder when [#permalink] New post 16 Dec 2012, 02:12
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Amateur wrote:
Bunuel.... I need your presence here..... I am becoming reckless to get a solution for this.....



Let me try

X/Y = 13+ .8
X/Y = 13 + 4/5

X and Y are integers...
Possibilities of Remainder/Divisor = 4/5, 8/10, 12/15
if 4/5
X = 69 Y = 5
If 8/10
X=138 Y =10
If 12/15
X= 207 Y =15


B says we should have the total digits of X and Y less than 5
only 4/5 suffice.
Hence OA.
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Re: For nonnegative integers x and y, what is the remainder when [#permalink] New post 16 Dec 2012, 03:07
BangOn wrote:
Amateur wrote:
Bunuel.... I need your presence here..... I am becoming reckless to get a solution for this.....



Let me try

X/Y = 13+ .8
X/Y = 13 + 4/5

X and Y are integers...
Possibilities of Remainder/Divisor = 4/5, 8/10, 12/15
if 4/5
X = 69 Y = 5
If 8/10
X=138 Y =10
If 12/15
X= 207 Y =15


B says we should have the total digits of X and Y less than 5
only 4/5 suffice.
Hence OA.



B says we should have the total digits of X and Y less than 5
only 4/5 suffice.


Didnt this mean total no of digits less than 5?
Can u explain ur soln Bangon
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Re: For nonnegative integers x and y, what is the remainder when [#permalink] New post 16 Dec 2012, 05:57
shanmugamgsn wrote:
BangOn wrote:
Amateur wrote:
Bunuel.... I need your presence here..... I am becoming reckless to get a solution for this.....



Let me try

X/Y = 13+ .8
X/Y = 13 + 4/5

X and Y are integers...
Possibilities of Remainder/Divisor = 4/5, 8/10, 12/15
if 4/5
X = 69 Y = 5
If 8/10
X=138 Y =10
If 12/15
X= 207 Y =15


B says we should have the total digits of X and Y less than 5
only 4/5 suffice.
Hence OA.



B says we should have the total digits of X and Y less than 5
only 4/5 suffice.


Didnt this mean total no of digits less than 5?
Can u explain ur soln Bangon



Yeah Sure. Total Digits in both X and Y should be less than 5.
if 4/5
X = 69 Y = 5
No. Of digits in X and Y is 3
If 8/10
X=138 Y =10
No. Of digits in X and Y is 5
If 12/15
X= 207 Y =15
No. Of digits in X and Y is 5

So from C, we have only one possible solution X = 69 Y = 5
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Re: For nonnegative integers x and y, what is the remainder when [#permalink] New post 16 Dec 2012, 08:37
BangOn wrote:
Amateur wrote:
Bunuel.... I need your presence here..... I am becoming reckless to get a solution for this.....



Let me try

X/Y = 13+ .8
X/Y = 13 + 4/5

X and Y are integers...
Possibilities of Remainder/Divisor = 4/5, 8/10, 12/15
if 4/5
X = 69 Y = 5
If 8/10
X=138 Y =10
If 12/15
X= 207 Y =15


B says we should have the total digits of X and Y less than 5
only 4/5 suffice.
Hence OA.


thank you for the explanation, statement B makes sense now. one thing- how did you get the possibilities of remainder/divisor?
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Re: For nonnegative integers x and y, what is the remainder when [#permalink] New post 16 Dec 2012, 09:47
[/quote] thank you for the explanation, statement B makes sense now. one thing- how did you get the possibilities of remainder/divisor?[/quote]

Possibilities by just multiplying the fraction .8 = 4/5
1) 4/5*1/1 = 4/5
2) 4/5 * 2/2 = 8/10
.
.
similarly
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Re: For nonnegative integers x and y, what is the remainder when [#permalink] New post 16 Dec 2012, 13:42
JJ2014 wrote:
For nonnegative integers x and y, what is the remainder when x is divided by y?

(1) x/y = 13.8
(2) The numbers x and y have a combined total of less than 5 digits

BangOn wrote:
Amateur wrote:
Bunuel.... I need your presence here..... I am becoming reckless to get a solution for this.....

B says we should have the total digitsof X and Y less than 5
only 4/5 suffice.
Hence OA.

BangOn wrote:
thank you for the explanation, statement B makes sense now. one thing- how did you get the possibilities of remainder/divisor?[/quote]

Possibilities by just multiplying the fraction .8 = 4/5
1) 4/5*1/1 = 4/5
2) 4/5 * 2/2 = 8/10
.
.
similarly[/quote]
estimating reminders is fine.... but calculating x and y values when you have remainders, I think it is time consuming process for a 600-700 problem.....
Also, B didnot say we should have total digits less than 5, b said x and y have a combined total of less than 5 digits.... if it did say the number of digits of x and y have a combined total of less than 5 you must have been correct.... but since it said less than 5 digits.... the equation will be x+y<10^4
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Re: For nonnegative integers x and y, what is the remainder when [#permalink] New post 16 Dec 2012, 19:12
Statement -1 :
X= 13 Y + .8 Y
As X & Y are Non negative integers ,hence .8Y integer
Possible values of Y for which R =.8 Y is an integers : 5,10,15,...
As there are multiple values of Y for which R is an integers- Not sufficient


Statement 2 : Insufficient

Together :
As ,Total digits ( X & Y ) less than 5 : this implies Y cant be in double digit ,so Y=5
Hence C is sufficient
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Re: For nonnegative integers x and y, what is the remainder when [#permalink] New post 10 Aug 2013, 06:51
Not a good question from veritas .

As I saw the explanations and the question stem, it revealed two flaws.

(1).Non - negative integer x,y '0' is also non-negative integer.

(2). Combined total of digits of x,y mean the sum total of x and y or as stated in the explanation

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Re: For nonnegative integers x and y, what is the remainder when [#permalink] New post 10 Aug 2013, 06:57
Could somebody help with this tough question:-

If zt < -3, is z < 4? E
a. z < 9
b. t < -4

thanks
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Re: For nonnegative integers x and y, what is the remainder when [#permalink] New post 10 Aug 2013, 07:00
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semwal wrote:
Could somebody help with this tough question:-

If zt < -3, is z < 4? E
a. z < 9
b. t < -4

thanks



From your post I perceive that you are a new bee in this forum.You have to post your question at the right place and in a right way where in you provide OA/source/difficulty level.

PS: Rules of posting

rules-for-posting-please-read-this-before-posting-133935.html
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Re: For nonnegative integers x and y, what is the remainder when [#permalink] New post 17 Jun 2014, 00:27
what does combined total mean? That is a redundant usage...question not well formed

Source please
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Re: For nonnegative integers x and y, what is the remainder when [#permalink] New post 17 Jun 2014, 02:45
I was having a lot of trouble with this one.

I could cross of the first statement as both 138/10 and 1380/10 would give the same answer, but the remainder would've been different.

For the second one I got that we have a max of 4 numbers. I could not really solve it, but I figured it was possible given the information so I picked C. (However, it was impossible with just the information from B, I sometimes just jump ahead of time-.-)
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Re: For nonnegative integers x and y, what is the remainder when [#permalink] New post 18 Jun 2014, 05:01
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sayansarkar wrote:
what does combined total mean? That is a redundant usage...question not well formed

Source please


This means that the number of digits in x plus the number of digits in y is less than 5.

For nonnegative integers x and y, what is the remainder when x is divided by y?

(1) x/y = 13.8 --> x/y = 69/5 = 138/10 = 207/15 = ... You'll get different remainders for different x and y. Not sufficient.

(2) The numbers x and y have a combined total of less than 5 digits. Clearly insufficient.

(1)+(2) From (2) we know that the number of digits in x plus the number of digits in y is less than 5, so x and y could only be 69 and 5 (combined total of 3 digits). Sufficient.

Answer: C.

Hope it's clear.
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Re: For nonnegative integers x and y, what is the remainder when   [#permalink] 18 Jun 2014, 05:01
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