When positive integer x is divided by positive integer y, the remainde

Think of it this way:
\(\frac{x}{y} = 96.12 = 96 \frac{12}{100}\) (in mixed fraction format)\(= 96 \frac{3}{25}\)
This means when x is divided by y, quotient obtained is 96 and remainder is 3 if y is 25. If remainder is 9, y must be 75.

Given \(\frac{x}{y}=96.12\):

\(x=96.12y\).

Split 96.12y into the integer and the decimal parts:

\(x=96y + 0.12y\).

Also, given that when positive integer x is divided by positive integer y, the remainder is 9:

\(x = qy + 9\).

So, q = 96 and:

\(0.12y=9\);

\(y=75\).

Answer: B.
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Easy it is

x/y = 96 + .12..... (1)

Remember here:

x = yQ + R

Can also be written as

x/y = Q + R/y ..... (2)

Comparing (1) and (2)

Q=96 and
R/y=.12

We know that Remainder is 9 , hence R=9

y=75

As we know, \(Decimal Part\) \(=\) \(\frac{Remainder}{Divisor}\)

Therefore, .12 = \(\frac{x}{y}\)

or \(\frac{12}{100}\) = \(\frac{x}{y}\)

or \(\frac{3}{25}\) = \(\frac{x}{y}\)

or \(\frac{9}{75}\) = \(\frac{x}{y}\)

Hence, 75 ... Hence, B ..........

Hi Galiya,

For this i will give u a example
When 23/2 =11.5 (Q = 11 and Remainder = 1)
Here Quotient = 11 and Remainder = .5 * 2 (Divisor) = 1

Hence in the original problem q = 96
x/y = 96.12-->
X= q *y (divisor) + Remainder (.12* Divisor)

Hope its clear.

Regards,
Rrsnathan.

when you are given a remainder from a fraction, and the remainder is in decimal form, you can solve for like this:

\(\frac{Remainder}{denominator}\)=[decimal of quotient]

So in this case; \(\frac{9}{y}\)=.12
=
\(\frac{9}{y}\)= \(\frac{12}{100}\)
=
\(\frac{9}{y}\)= \(\frac{3}{25}\)
=
3y=225
=
y=75

B

Are there any other questions similar to this one? I just simply cannot seem to wrap my head around the concept, so practicing on more examples would probably help.

Thanks in advance.

Check this one: if-s-and-t-are-positive-integers-such-that-s-t-64-12-which-135190.html

Hope it helps.
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Hi All,

It looks like most of the posts have provided similar algebra explanations. 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.

Since X/Y = 96.12, we can rewrite the equation 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 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:

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

I'm still confused....

The main formula that we're using is
Dividend/Divisor = Quotient + Remainder/Divisor OR Dividend = Quotient*Divisor + Remainder

For the first part of the question, we can use the 2nd formula to derive x = Qy+9. I'm ok with this.

For the second part of the question, using the 2nd formula, why don't we get x = 96y+.12 (in the same vein as the first part)? I know it should be .12y, but I don't see how it goes along with the formula, the formula says Remainder, NOT remainder/Divisor. Not to mention, isn't the divisor 100? As in 12/100? Doesn't that make .12y redundant because it's 12/100*100?

The first and the second part of the questions are exactly alike, except the first part is missing the quotient that we end up finding after we do the second part.

Thanks!

Consider this: If 5 is divided by 4, you get quotient 1 and remainder 1

5 = 4*1 + 1

But when you write it in terms of decimals, 5/4 = 1.25
Is the remainder .25 here? No. Then, do you think it is correct to write 5 as 1*y + .25? This is what you have done above.

What is .25? It is the fraction of divisor that is leftover -> 25%. Since the divisor is 4, 25% of it i.e. 1 is leftover. So remainder is 1.

Similarly, when you have 96.12, we can say that 12% of the divisor is leftover.
12% of divisor = 9
Divisor = 75

This problem will be best solved using the remainder formula. Let’s first state the remainder formula:

When positive integer x is divided by positive integer y, if integer Q is the quotient and r is the remainder, then x/y = Q + r/y.

In this problem we are given that when positive integer x is divided by positive integer y, the remainder is 9. So we can say:

x/y = Q + 9/y

We also are given that x/y = 96.12. Using the remainder formula we can say:

x/y = 96.12

x/y = 96 + 0.12

x/y = 96 + 12/100

Because Q is always an integer, we see that Q must be 96, and thus the remainder 9/y must be 12/100. We can now equate 9/y to 12/100 and determine the value of y.

9/y = 12/100

12y = 9 x 100

y = 900/12 = 75

Note: Had we simplified 12/100 to 3/25 first, we would have also obtained the same answer. See below.

9/y = 3/25

3y = 9 x 25

y = 3 x 25 = 75

Answer is B.
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Here is a video explanation for the problem:

Why can I not take it as 95+1.12 or 94+2.12.......?
hope you understood my query?

We split it up into 96 and .12 to separate out the integer and the decimal part. The decimal part is the one that gives the remainder. If we split it as 95 + 1.12, it doesn't serve the purpose since the decimal part has still not been separated out.

This problem will be best solved using the remainder formula. Let’s first state the remainder formula:

When positive integer x is divided by positive integer y, if integer Q is the quotient and r is the remainder, then x/y = Q + r/y.

In this problem we are given that when positive integer x is divided by positive integer y, the remainder is 9. So we can say:

x/y = Q + 9/y

We also are given that x/y = 96.12. Using the remainder formula, we can say:

x/y = 96.12

x/y = 96 + 0.12

x/y = 96 + 12/100

Because Q is always an integer, we see that Q must be 96, and thus the remainder 9/y must be 12/100. We can now equate 9/y to 12/100 to determine the value of y.

9/y = 12/100

12y = 9 x 100

y = 900/12 = 75

Note: Had we simplified 12/100 to 3/25 first, we would have also obtained the same answer:

9/y = 3/25

3y = 9 x 25

y = 3 x 25 = 75

Answer: B
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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 to get: 3y = (25)(9)
Solve to get y = 75

Cheers,
Brent

To answer this question, I used the formula from the Magoosh blog i.e.: https://magoosh.com/gmat/2012/gmat-quan ... emainders/

I found this blog very useful. Thanks Magoosh !

Here is the formula:

Decimal part of the quotient = Remainder / Divisor

Given that x/y . Therefore x is dividend and y is divisor. Also given remainder is 9.

Therefore here are the numbers to plug into the formula:

Decimal part of the quotient = 0.12 (take the decimal bit i.e. the numbers after the decimal point of 96.12)
Remainder = 9
Divisor = y

We are looking for y.

9/y = 0.12

9/0.12 = y

y = 75

Answer: B

Tips: I understand that some would say that understanding the formula is better than memorising it. Fair point. But I personally feel that for GMAT Remainder type questions, it's OK to memorise this one! It has been helpful for me so far.

Solution:

Given, positive integer x is divided by positive integer y, the remainder is 9

x/y = 96.12

= 96 +12/100

=96 + 3/25

=>The remainder is 3 when divisor is 25. But we are given that when x is divided by y, the remainder is 9

=> Multiply 3 to Numerator and denominator of 3/25 to have 9 as numerator that represents the remainder

=>In that case the denominator is 75 and hence we have y = 75 (option b)

Devmitra Sen
GMAT SME
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