If X and Y are nonzero integers

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madhur_ahuja: Master | Next Rank: 500 Posts; Posts: 435; Joined: Sat May 02, 2009 3:55 am; Thanked: 17 times

by madhur_ahuja » Fri Jul 17, 2009 10:19 pm

If X and Y are nonzero integers, what is the remainder when X is divided by Y?

(1) When X is divided by 2Y, the remainder is 4
(2) When X+Y is divided by Y, the remainder is 4

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Source: Beat The GMAT — Data Sufficiency | Fri Jul 17, 2009 10:19 pm

vittalgmat: Legendary Member; Posts: 621; Joined: Wed Apr 09, 2008 7:13 pmFollowed by: 4 members; Thanked: 33 times

by vittalgmat » Fri Jul 17, 2009 11:50 pm

I am not 100% sure of the answer.
I get D. What is the OA?

Here is my approach.

"When x is divided by y, we get a remainder of 4 " can be algebraically written as
x = Ay + 4, for some integer constant A.

Similarly lets write stmt 1 and 2.

stmt 1:
x = 2yA + 4
=> x = y (2A) +4
Now 2A is a constant and let us call it B
So we have x = yB +4

This is same as the general formula.. ie
x/y leaves a remainder of 4.

Sufficient.

Stmt 2:
again we rewrite as follows
x+y = yA + 4
=> x = yA -y +4
=> x = y(A-1) +4
A-1 is another constant. Let us call it B.

So x = yB +4.
Again this is same as the generaly eqn.
So the remainder is 4 as well.
Sufficient.

So D

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madhur_ahuja: Master | Next Rank: 500 Posts; Posts: 435; Joined: Sat May 02, 2009 3:55 am; Thanked: 17 times

by madhur_ahuja » Sat Jul 18, 2009 5:38 am

vittalgmat wrote:I am not 100% sure of the answer.
I get D. What is the OA?

Here is my approach.

"When x is divided by y, we get a remainder of 4 " can be algebraically written as
x = Ay + 4, for some integer constant A.

Similarly lets write stmt 1 and 2.

stmt 1:
x = 2yA + 4
=> x = y (2A) +4
Now 2A is a constant and let us call it B
So we have x = yB +4

This is same as the general formula.. ie
x/y leaves a remainder of 4.

So D

I am sorry but I do not have OA. We will have to arrive at answer through consensus.

I too went with the above approach.

However, if you take x=22, y=3

You will get different remainders for statement I.

IMO answer is B.

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tohellandback: Legendary Member; Posts: 752; Joined: Sun May 17, 2009 11:04 pm; Location: Tokyo; Thanked: 81 times; GMAT Score:680

by tohellandback » Sat Jul 18, 2009 6:02 am

IMO B
1)2Y gives remainder 4, so 2Y must be >4
so Y>=3
now X=n*2Y+4
X=n1*Y+4
now from this equation, for Y=3 we get remainder 1
for Y=4 we get remainder 0
for Y>4 we get remainder 4

INSUFF

2) X+Y=nY+4
X=(n-1)Y+4
SUFFICIENT

but by plugging in numbers I got the solution faster

The powers of two are bloody impolite!!

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sana.noor: Legendary Member; Posts: 512; Joined: Mon Jun 18, 2012 11:31 pmFollowed by: 20 members; Thanked: 42 times

by sana.noor » Sat Sep 21, 2013 3:13 am

answer must be B
if X is divided by 2y the remainder is 4 thus it means 2y>4. we dont know what is the value of X or y so we cant say what exactly the remainder is
However, statement two says that x+y/y leaves as remainder of 4
x+y/y = x/y +y/y one can see that y is divisible by y and will have 0 remainder; thus the remainder of 4 means that when x is divided by y it leaves remainder 4. sufficient!

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theCodeToGMAT: Legendary Member; Posts: 1556; Joined: Tue Aug 14, 2012 11:18 pmFollowed by: 34 members; Thanked: 448 times; GMAT Score:650

by theCodeToGMAT » Sat Sep 21, 2013 6:05 am

ANSWER [spoiler]{B}[/spoiler]

To find remainder of X/Y

Statement 1:
2yk + 4 = x
Let
y=1, k=1, x==> 6 --> remainder = 0
y=3, k=1, x==> 10 --> remainder = 1
INSUFFICIENT

Statement 2:
(X+Y)/y --> r=4
X/y + Y/Y
X/Y + 0
hence, X/Y --> r=4
SUFFICIENT

R A H U L

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ahmedshafea: Junior | Next Rank: 30 Posts; Posts: 19; Joined: Wed Aug 30, 2017 10:04 am

by ahmedshafea » Wed Aug 30, 2017 12:37 pm

please explain to me the math steps , how you got the Statement 1 is INSUFFICIENT and Statement 2 is SUFFICIENT

theCodeToGMAT wrote:ANSWER [spoiler]{B}[/spoiler]

To find remainder of X/Y

Statement 1:
2yk + 4 = x
Let
y=1, k=1, x==> 6 --> remainder = 0
y=3, k=1, x==> 10 --> remainder = 1
INSUFFICIENT

Statement 2:
(X+Y)/y --> r=4
X/y + Y/Y
X/Y + 0
hence, X/Y --> r=4
SUFFICIENT

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ErikaPrepScholar: Legendary Member; Posts: 503; Joined: Thu Jul 20, 2017 9:03 amFollowed by: 15 members; Thanked: 86 times; GMAT Score:770

by ErikaPrepScholar » Thu Aug 31, 2017 7:09 am

Remainder problems require us to translate words into math. The question asks us to find the remainder when X is divided by Y. So:

X/Y = Z | R: ?

where Z is some whole number variable. We'll start by going through the statements individually.

Statement 1

This statement tells us that

X/2Y = K | R: 4

where K is some whole number variable. We could go ahead and use this to build an equation (dividend = divisor * constant + remainder) ... but we don't really need to if we use small, simple integers.

For example, let's let Y = 2 and K = 1:

X/2(2) = 1 | R: 4
X/4 = 1 | R: 4
X = 4 | R: 4 â†’ X = 8

Then we can plug this into our initial equation:

X/Y = Z | R = ?
8/2 = 4 | R = 0

So X/Y can have a remainder of 0. Let's try a different set of integers, introducing a small change to see if we can create a remainder: maybe Y = 3 and K = 1:

X/2(3) = 1 | R: 4
X/6 = 1 | R: 4
X = 6 | R = 4 â†’ X = 10

Plugging back into our initial equation:

X/Y = Z | R = ?
10/3 = 3 | R = 1
We quickly find that we can have either remainder 0 or remainder 1. Statement 1 is NOT sufficient.

Statement 2

Using N as our whole number variable, this statement tells us that

(X+Y)/Y = N | R: 4

Before we start plugging things in, we should notice that we can rearrange this equation a bit by splitting up the denominator on the left half of the equation:

X/Y + Y/Y = N | R: 4
X/Y + 1 = N | R: 4
X/Y = N + 1 | R: 4

Since N is a variable, we can set N + 1 as a new variable - let's use M.

X/Y = M | R: 4

This means that whenever we divide X by Y, the remainder will always be 4 ... which is exactly what we want to know! No need to plug in numbers here. Statement 2 is sufficient.

The correct answer is B.

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