What can be the remainder if the quotient is 3.24?

Question

Hi all,

This is modeled on a great question in MGMAT number property. However, before seeing the solution by MGMAT, I solved the problem with a method that came to my own mind. Later looking at the book solution, I think my own method is better than the algebraic one provided by MGMAT. Let's see if you agree. try to devise a method simpler than what MGMAT tells us.

Q: If A and B are both integers, and A is divided by B, resulting in the quotient 3.24, which of the below can be the remainder in this division?

A) 54
B) 62 
C) 80
D) 100
E) 240

str1der · Answer

Is it 80?

This is a long shot as I challenged myself to answer this within 2 mins. so here goes

we need to look at a multiple of 3.24 which is the quotient and then match is against the remainders as given in choices. The reason being 3.24 is the quotient and hence 3.24 x X would be a whole number, which gets subtracted from the dividend to give us a remainder (Which is gain a whole number)

3.24 x 1 = 3.24 -> numbers greated than 3.24 from which we can subtract and get a remainder are 4, 5 ,6 , 7 (post which cycle would repeat) - we don't get any remainder that is in the choices so we move on

3.24 x 2 = 6.48 -> same theory, no answer

3.24 x 3 = 9.72 -> same theory, no answer

3.24 x 4 = 12.96 -> no answer

3.24 * 5 = 16.2 -> Now if we have the number 17, we get a remainder of 0.80 and our condition can be met

Divide 1700/500 -> remainder will be 80 (500*3.24 = 1620)

hence, 80 is the answer

Please Note: this was my 2 minute solution, unsure if the answer is right. Keen to know

a) what is the simpler method for this, given you based it on number properties as explained in MGMAT
b) if my answer is wrong, why is it wrong (as both 1700 and 500 are integers and meet the requirement) and what would be the right answer

Thanks!

KarishmaB · Answer

When we talk about quotients and remainders, the quotient is an integer. Write down the exact question as given.

hakunamatata3 · Answer

You just have to find the remainder r such that x is an integer in the equation 24/100 = r/x.

So, you try

24/100 = 54/x --> x = 225
24/100 = 62/x --> x = 258.33
24/100 = 80/x --> x = 333.33
24/100 = 100/x --> x = 416.67
24/100 = 240/x --> x = 1000

Unless I made a calculation error, it seems like both 54 and 240 work. Is this the exact question?

varunmaheshwari · Answer

wjdgusqls: Even i'm getting the same answers.. An integer values for both 54 and 240.. Am I missing something?

saeedt · Answer

Yeah but not all the time. In this case the quotient is decimal. It's more safe to say the divisor must be integer than to say the quotient must be integer. Correct me if I'm wrong. Anyway, sorry there's no continuation to the question.

saeedt · Answer

wjdgusqls is right. I had better have not included 240. The choice I had in mind as the answer was 54. But 240 is right, too. Sorry for that.

And Yes, we know the the remainder divided by the divisor is responsible for the decimal in the quotient. So, 0.24/B=X , where x is the remainder. => B= X/0.24. We know that the divisor , B, must be an integer. We can try the choice to see which one yield an integer when acted as X.

KarishmaB · Answer

When you divide 5 by 4 and get 1.25, 1.25 is not called the quotient here.
The quotient is 1 and the remainder is 1. Quotient implies the integral part.
You can say it in two ways: 5/4
1. You can say 5/4 = 1.25
2. You can say 5/4 gives a quotient of 1 and remainder of 1.

If MGMAT has a question where they say 'resulting in the quotient 3.24', put the exact question down.

timeishere · Answer

I also got A and E by the same method.
I assume the question wants to say When A divided by B, the answer is 3.24.
So what will be the remainder when A is divided by B (Assuming all 3 are integers as per definition of divisibility).

Weird question if its the same way in book.

What is OA

yogesh1984 · Answer

for this type of problem I go like this-

since here you have mentioned .24 as the decimal part in the remainder- we can re write it as 24/100 that translates to 6/25 (this simplification you have to do as long as you ca have a common divisor of both numerator and denominator). now you can match up the numbers by looking for multiples of 6 .... so A, E both matches (as per the options provided)

Hope this helps!

reatsaint · Answer

If we have A = 324240 and B = 100000, In that case we get remainder 240. If we chosse A = 324100 and B = 100000, we would get 100. So it is possible to get all the remainders. So I think the question is incomplete.

saeedt · Answer

Sorry, but that's not the case with the word QUOTIENT. The quotient is an integer only when we wish to leave a remainder intact if one exists. For example if we divide 7 by 2, we can wish to have the remainder 1, in that case our quotient is definitely integer. But if we wish not to follow GMAT style and instead follow a calculator style, we can get a 3.5 as the quotient and no remainder. In this case there's nothing wrong with the decimal quotient and still we can call the whole result a quotient. Don't believe me, follow the below:

MGMAT Number Property, Page 129, middle of the page: "This quotient has an integer portion (3) and a decimal portion (0.4)". So, this sentence is clearly supporting my opinion.

Also, if you Wikipedia for the word quotient you see that it can point to ALL parts of the result of a division (Integer and decimal), however it MAY refer to the integer part alone. Wikipedia: "A quotient can  ALSO   mean just the integer part of the result of dividing two integers"

saeedt · Answer

timeishere, the question is not weird. I just meant to show another way of solving it no matter what the choices are. It's exactly modeled on a question from MGMAT. The only problem with this question is that two choices are correct. The OA is A and E

KarishmaB · Answer

I do see your point. Even dictionary.com gives both definitions of quotient which is absolutely against the norm I have seen in the past many years of doing Math questions. I guess I can pin it on cultural differences in the norms followed in different parts of the world. Thankfully, GMAC is sensitive to such differences.

What can be the remainder if the quotient is 3.24?

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