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When positive integer A is divided by positive integer B

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

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New post Updated on: 03 Jul 2014, 08:19
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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

Originally posted by prasadrg on 22 Dec 2009, 19:25.
Last edited by Bunuel on 03 Jul 2014, 08:19, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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Re: When positive integer A is divided by positive integer B  [#permalink]

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New post 22 Dec 2009, 20:14
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prasadrg wrote:
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.


we know that A,B are +ve integers and when A is divided by B we get 4.35. This 4 is the quotient obtained when A is divided by B. We get 0.35 because A is not prefectly divisible by B and this 0.35 is the remainder which we need to find out in terms of whole numbers

0.35 = 35/100 (shifting the decimal 2 places to make it a whole number)
this 35/100 is the remainder for A/B. On simplifying we get 7 as the remainder if B =20

Now we know quotient is 4 so if B = 20 A will be 4*20 + 7 = 87 (A/B gives 4.35)
If B = 100 then A will be 4*100 + 35 = 435 (A/B gives 4.35)
If B = 60 then A will be 4*60 + 21 = 261 (A/B gives 4.35)

so we can see that remainder in this case will be a multiple of 7. of the given option 14 satisfies this.
hope this helps
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Re: When positive integer A is divided by positive integer B  [#permalink]

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New post 22 Dec 2009, 19:46
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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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New post 22 Dec 2009, 19:55
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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]

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New post 22 Dec 2009, 20:30
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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New post 03 Jul 2014, 08:22
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Re: When positive integer A is divided by positive integer B  [#permalink]

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New post 17 Sep 2017, 15:40
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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


Notice that 0.35 = 35/100

So, we can write: A/B = 4 35/100 = 435/100
So, one possible case is that A = 435 and B = 100
When we divide 435 by 100, the remainder is 35
Unfortunately 35 is NOT one of the answer choices.


Now let's examine some fractions that are EQUIVALENT to 435/100
For example, 435/100 = 87/20 (= 4.35)
In other words, A = 87 and B = 20
In this case, when we divide A by B, the remainder is 7
Unfortunately 7 is NOT one of the answer choices.

Find another fraction EQUIVALENT to 435/100
How about 174/40 (= 4.35)
In other words, A = 174 and B = 40
In this case, when we divide A by B, the remainder is 14
Aha, 14 IS one of the answer choices!!

Answer:

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

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New post 22 Sep 2017, 11:44
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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]

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New post 09 May 2018, 04:55
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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]

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New post 09 May 2018, 06:13
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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New post 01 Jun 2019, 22:02
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] 01 Jun 2019, 22:02
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