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Re: When positive integer A is divided by positive integer B
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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
Re: When positive integer A is divided by positive integer B
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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!!
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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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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