Remainder Problem

[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 B
Plz. explain

[PussInBoots]

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]

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]

Ian's post for similar problem
May be helpful

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

[gmat2010]

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

ANSWER B.

[apoorva.srivastva]

[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

ANSWER B.[/quote]

[abhinav85]

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]

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]

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]

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.

[GMATGuruNY]

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.

The correct answer is B.

[John Faber]

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?

[[email protected]]

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

Final Answer: B

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

[Brent@GMATPrepNow]

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

[GMATGuruNY]

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.

Test answer choice D.

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.

The correct answer is B.