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Re: When positive integer A is divided by positive integer B [#permalink]
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prasadrg wrote:
When a positive integer A is divided by Positive integer B the result is 4.35. Which of the following could be the reminder when A is divided by B?

    A.13
    B.14
    C.15
    D.16
    E.17



the remainder will be obtained from the decimal part when A is divided by B i.e. 0.35

0.35 = 35/100 = 7/20 so possible remainders are 7,14,21,28. Only option B-14 satisfies this

PS: for B-14 A=174 and B=40
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Re: When positive integer A is divided by positive integer B [#permalink]
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Thank you for solving. I am still not clear the concept behind dividing 35/100 to get the reminder.

How do we assume 100 here?

I know it is subtle, and I am not able to catch it. Appreciate your help.
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Re: When positive integer A is divided by positive integer B [#permalink]
Thank you very much for the detailed explanation and it makes sense.

Appreciate.
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Re: When positive integer A is divided by positive integer B [#permalink]
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prasadrg wrote:
When positive integer A is divided by positive integer B, the result is 4.35. Which of the following could be the reminder when A is divided by B?

(A) 13
(B) 14
(C) 15
(D) 16
(E) 17


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if-s-and-t-are-positive-integers-such-that-s-t-64-12-which-135190.html
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Re: When positive integer A is divided by positive integer B [#permalink]
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prasadrg wrote:
When positive integer A is divided by positive integer B, the result is 4.35. Which of the following could be the reminder when A is divided by B?

(A) 13
(B) 14
(C) 15
(D) 16
(E) 17


We can create the following equation:

A/B = 4.35

A/B = Q + 35/100

A/B = Q + 7/20

We see that the remainder is a multiple of 7; thus, the remainder could be 14.

Answer: B
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Re: When positive integer A is divided by positive integer B [#permalink]
ScottTargetTestPrep GMATPrepNow niks18 gmatbusters Bunuel

Quote:
We see that the remainder is a multiple of 7; thus, the remainder could be 14.


I did not get the highlighted part. In the question stem, we are only given that dividend and
divisor are positive integers, is it an inherent property that a remainder will always be an integer?
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Re: When positive integer A is divided by positive integer B [#permalink]
Expert Reply
adkikani

The remainder is the integer "left over" after dividing one integer by another to produce an integer quotient (integer division).

dividend = (integer quotient)*(divisor) + remainder (integer)



The Remainder is a integer always less than divisor.

In the division of 43 by 5 we have:

43 = 8 × 5 + 3,
so 3 is the remainder.

Quote:
We see that the remainder is a multiple of 7; thus, the remainder could be 14.


I did not get the highlighted part. In the question stem, we are only given that dividend and
divisor are positive integers, is it an inherent property that a remainder will always be an integer?[/quote]
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Re: When positive integer A is divided by positive integer B [#permalink]
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Given:

\(\frac{A}{B}\) = 4.35 = 4 + 0.35

A = 4B + 0.35B

Since A and B are positive integers, 4B is also a positive integer and 0.35B also will be a positive integer.

The remainder is 0.35B. We'll equate 0.35B with the given options to find the possible answer:

0.35B = \(\frac{35}{100}\)B = \(\frac{7}{20}\) B

Now,

If \(\frac{7}{20}\) B = 13, B will not be an integer.

If \(\frac{7}{20}\) B = 14, B will be an integer.

If \(\frac{7}{20}\) B = 15, B will not be an integer.

If \(\frac{7}{20}\) B = 16, B will not be an integer.

If \(\frac{7}{20}\) B = 17, B will not be an integer.

The correct answer is B
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Re: When positive integer A is divided by positive integer B [#permalink]
prasadrg wrote:
When positive integer A is divided by positive integer B, the result is 4.35. Which of the following could be the reminder when A is divided by B?

(A) 13
(B) 14
(C) 15
(D) 16
(E) 17


A/B = 4.35 = 4 + 0.35
A = 4B + 0.35B
The latter part is our remainder. => r = 0.35B
r/0.35 = B
r*100/35 = B

Now, since B is an Integer, we need to find an option that resolves [r*100/35] into an Integer. Only option C (i.e. r=14) satisfies it.

Answer = C
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Re: When positive integer A is divided by positive integer B [#permalink]
Expert Reply
A is divided by positive integer B, the result is 4.35

=> \(\frac{A }{ B}\) = 4.35

=> \(\frac{A }{ B}\) = \(\frac{435 }{ 100}\)

So, Let A be 435 and B be 100 giving result as 4.35.

Simplifying, \(\frac{435 }{ 100 }\)

=> 4+ \(\frac{35 }{ 100}\)

35/ 100 is a remainder which can be further simplified as \(\frac{7 }{ 20}\).

So, the remainder has to be multiple of 7.

Option 14 satisfies it.

Answer B
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Re: When positive integer A is divided by positive integer B [#permalink]
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When positive integer A is divided by positive integer B, the result is 4.35

\(\frac{A}{B}\) = 4.35
=> A = B*4.35 = B *(4 + 0.35)
=> A = B*4 + B*0.35
=> A when divided by B gives 4 as Quotient and 0.35B as remainder

=> B *0.35 is an integer
Remainder = B * \(\frac{35}{100}\) = B * \(\frac{7}{20}\)
= \(\frac{B}{20}\) * 7
=> Remainder is a multiple of 7
Only, option choice possible is 14

So, Answer will be B
Hope it helps!

Watch the following video to learn the Basics of Remainders

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Re: When positive integer A is divided by positive integer B [#permalink]
B.

Quick solution to this:

If \(\frac{A}{B}\) = 9.35, then 0.35 * B = remainder.

Now try it out:

(A) 13 = 0.35*B <=>\( \frac{13}{0.35}\) = B <=> B = \(\frac{13*20}{7}\) <-- not an integer!

(B) 14 = 0.35*B <=> ... <=> B = 40 <-- integer!

--> (B) is the correct answer.
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Re: When positive integer A is divided by positive integer B [#permalink]
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