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## Remainder Problem

tagged by: Brent@GMATPrepNow

This topic has 7 expert replies and 10 member replies
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gmat009 Master | Next Rank: 500 Posts
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#### Remainder Problem

Tue Oct 07, 2008 11:08 am

00:00

A

B

C

D

E

# Global Stats

Difficult

When positive integer x is divided by positive integer y, the remainder is 9. If x/y = 96.12, what is the value of y?

A. 96
B. 75
C. 48
D. 25
E. 12

OA is B
Plz. explain

PussInBoots Master | Next Rank: 500 Posts
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Tue Oct 07, 2008 11:24 am
So x = y * A + 9 (A is integer quotient we get when we perform x / y).
x / y = 96.12 <=> x = y * 96.12 <=> x = y * 96 + .12 * y
A = 96 and 9 = .12 * y <=> y = 9 / .12 <=> y = 75

Remember this: When dividing X by Y, a is the quotient and b is the remainder, we get X = a * Y + b

gmat009 Master | Next Rank: 500 Posts
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Tue Oct 07, 2008 11:33 am
PussInBoots wrote:
So x = y * A + 9 (A is integer quotient we get when we perform x / y).
x / y = 96.12 <=> x = y * 96.12 <=> x = y * 96 + .12 * y
A = 96 and 9 = .12 * y <=> y = 9 / .12 <=> y = 75

Remember this: When dividing X by Y, a is the quotient and b is the remainder, we get X = a * Y + b
Thanks...

4meonly Legendary Member
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Tue Oct 07, 2008 11:42 am
Ian's post for similar problem

http://www.beatthegmat.com/difficult-t15709.html#65825

gmat2010 Junior | Next Rank: 30 Posts
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Tue Oct 07, 2008 12:49 pm
gmat009 wrote:
When positive integer x is divided by positive integer y, the remainder is 9. If x/y = 96.12, what is the value of y?

A. 96
B. 75
C. 48
D. 25
E. 12

OA is B
Plz. explain
x/y = 96.12

x/y = 96 + 12/100

r/y = 12/100

9/y = 12/100

900 = 12y

y=75

apoorva.srivastva Master | Next Rank: 500 Posts
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Tue May 19, 2009 6:41 am
[quote="gmat2010"][quote="gmat009"]When positive integer x is divided by positive integer y, the remainder is 9. If x/y = 96.12, what is the value of y?

A. 96
B. 75
C. 48
D. 25
E. 12

OA is[spoiler] B[/spoiler]
Plz. explain[/quote]

GREAT EXPLANATION..THANNXXXX

x/y = 96.12

x/y = 96 + 12/100

r/y = 12/100

9/y = 12/100

900 = 12y

y=75

abhinav85 Master | Next Rank: 500 Posts
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Tue May 19, 2009 7:58 am
So x = y * A + 9 (A is integer quotient we get when we perform x / y).
x / y = 96.12 <=> x = y * 96.12 <=> x = y * 96 + .12 * y
A = 96 and 9 = .12 * y <=> y = 9 / .12 <=> y = 75

Remember this: When dividing X by Y, a is the quotient and b is the remainder, we get X = a * Y + b

Hey Pussinboots

can u explain in this formula x = y * A + 9
how did u get 9 = .12 * y??
I mean why u seperated .12 from 96??

may be i am missing something!!

p2pg Senior | Next Rank: 100 Posts
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Tue May 19, 2009 11:41 am
Since the remainder is 9 and the decimal portion says .12, the divisor has to be less than 90, but greater than 45. So that eliminates A,D,E. Since hundreth digit is 2, it should be slightly lower than 90, that leaves with only option "B".

p2pg Senior | Next Rank: 100 Posts
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Tue May 19, 2009 11:42 am
Since the remainder is 9 and the decimal portion says .12, the divisor has to be less than 90, but greater than 45. So that eliminates A,D,E. Since hundreth digit is 2, it should be slightly lower than 90, that leaves with only option "B".

OneTwoThreeFour Senior | Next Rank: 100 Posts
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Thu Jan 27, 2011 11:59 am
Even better:

Once you get down to 96 + 3/25, realize that the remainder is 9. So multiply the numerator and denominator by 3 to get 9/75. Thus y = 75.

### GMAT/MBA Expert

GMATGuruNY GMAT Instructor
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Thu Jan 27, 2011 1:08 pm
gmat009 wrote:
When positive integer x is divided by positive integer y, the remainder is 9. If x/y = 96.12, what is the value of y?

A. 96
B. 75
C. 48
D. 25
E. 12

OA is B
Plz. explain
When one positive integer doesn't divide evenly into another positive integer, we can represent what's left over as a decimal (5/2 = 2.5) or as a remainder (5/2 = 2 R 1). The problem above is testing the relationship between the decimal representation and the remainder representation. Here's the relationship:

decimal * divisor = remainder

Let's revisit 5/2 = 2.5. If we multiply the decimal (.5) by the divisor (2), we get .5 * 2 = 1, which is the remainder if we represent the division as 5/2 = 2 R1.

In the problem above. the decimal is .12, the divisor is y, and the remainder is 9. Thus:
.12y = 9
y = 9/.12 = 900/12 = 75.

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John Faber Newbie | Next Rank: 10 Posts
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Mon Feb 21, 2011 8:34 am
thanks lots, this is the first time I understood a remainder question ...
Wonder why they ask you to know that anyway, you reckon anybody would ever use that concept in a business school?

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Rich.C@EMPOWERgmat.com Elite Legendary Member
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Sat Jan 14, 2017 2:51 pm
Hi All,

Many Test Takers will approach this question algebraically. Here's a way to use Number Properties, the answer choices and "brute force" to find the solution.

In this prompt, we're told that X and Y are INTEGERS.

X/Y = 96.12 can be written as....

X = 96.12(Y)

The Y has to "multiply out" the .12 so that X becomes an integer. Since .12 is such a weird value, there can't be that many numbers that X and Y could be. Since none of the answers ends in 00, we need to find another way to multiply out the .12 - the only way to do it is with a multiple of 25. Eliminate A, C and E.

Between B and D, we just need to find the one that matches the rest of the info in the prompt (X/Y = 96.12 and X/Y has a remainder of 9)

Answer B: If Y = 75, then X = 7209

7209/75 gives a remainder of 9 THIS IS A MATCH

GMAT assassins aren't born, they're made,
Rich

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Brent@GMATPrepNow GMAT Instructor
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Sat Jan 14, 2017 2:56 pm
Quote:
When positive integer x is divided by positive integer y, the remainder is 9. If x/y = 96.12, what is the value of y?

A. 96
B. 75
C. 48
D. 25
E. 12

There are a few ways to tackle this question.

One way is to examine a few other fractions.
7/2 = 3 with remainder 1.
7/2 = 3 1/2 = 3.5
Notice that 0.5 = 1/2

Another example:
11/4 = 2 with remainder 3.
11/4 = 2 3/4 = 2.75
Notice that 0.75 = 3/4

Now onto the question....

So, we know that x/y = some value with remainder 9
If x/y = 96.12, we can conclude that 0.12 = 9/y
Now solve for y.
0.12 = 9/y
12/100 = 9/y [rewrite 0.12 as 12/100]
Simplify to get: 3/25 = 9/y
At this point, we might already see that y = 75. If we don't spot this, we can always cross-multiply.
We get: 3y = (25)(9)
Solve to get y = 75

Cheers,
Brent

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GMATGuruNY GMAT Instructor
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Sat Jan 14, 2017 3:20 pm
gmat009 wrote:
When positive integer x is divided by positive integer y, the remainder is 9. If x/y = 96.12, what is the value of y?

A. 96
B. 75
C. 48
D. 25
E. 12
One more approach:

x/y = 96.12 = 9612/100 = 4806/50 = 2403/25.
The resulting fraction -- x/y = 2403/25 -- indicates that x must be a multiple of 2403 and that y must be a multiple of 25.
Eliminate A, C and E.

D: y=25
Since x/y = 2403/25, y=25 implies that x=2403.
Check whether 2403/25 will leave a remainder of 9.
Since 2400 is divisible by 25 -- and 2403 is 3 more than 2400 -- dividing 2403 by 25 will leave a remainder of 3.
Eliminate D.

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GMATGuruNY@gmail.com
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