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# The sum of the multiples of 4 less than 100 or The sum of

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The sum of the multiples of 4 less than 100 or The sum of [#permalink]  22 Oct 2017, 06:14
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Question Stats:

56% (01:12) correct 43% (01:12) wrong based on 37 sessions
 Quantity A Quantity B The sum of the multiples of 4 less than 100 The sum of the multiples of 5 less than 100

(A) The quantity in Column A is greater
(B) The quantity in Column B is greater
(C) The two quantities are equal
(D) The relationship cannot be determined from the information given

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Re: The sum of the multiples of 4 less than 100 or The sum of [#permalink]  22 Oct 2017, 08:48
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We can proceed by steps:

1) number of elements in the two sets: we have to take the first and the last multiple, then compute last - first, divide by the number whose multiples are of interest and sum 1. In our case, in column A, we have $$\frac{100-4}{4}+1 = 25$$, while for column B we get $$\frac{100-5}{5}+1 = 20$$.

2) Compute the sum. The formula for the sum of an arithmetic progression is $$sum = \frac{n}{2}(first+last)$$, where n is the number of elements in the progression and first and last are the first and the last elements. Thus, for column A, $$\frac{25}{2}(4+100) = 1300$$, while column B equates $$\frac{20}{2}(5+100) = 1050$$.

We conclude that A is greater!
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Re: The sum of the multiples of 4 less than 100 or The sum of [#permalink]  09 Jul 2018, 18:48
Bunuel wrote:
 Quantity A Quantity B The sum of the multiples of 4 less than 100 The sum of the multiples of 5 less than 100

(A) The quantity in Column A is greater
(B) The quantity in Column B is greater
(C) The two quantities are equal
(D) The relationship cannot be determined from the information given

Kudos for correct solution.

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Re: The sum of the multiples of 4 less than 100 or The sum of [#permalink]  10 Jul 2018, 08:19
Sum of multiples of 4 = 4(1+2+..+25)=4*(25+1)*25/2=50*26

Sum of multiples of 5 = 5(1+2+..+20)=5*(1+20)*20/2=50*21

-> QA > QB -> A.
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Re: The sum of the multiples of 4 less than 100 or The sum of [#permalink]  05 Aug 2018, 15:33
IlCreatore wrote:
We can proceed by steps:

1) number of elements in the two sets: we have to take the first and the last multiple, then compute last - first, divide by the number whose multiples are of interest and sum 1. In our case, in column A, we have $$\frac{100-4}{4}+1 = 25$$, while for column B we get $$\frac{100-5}{5}+1 = 20$$.

2) Compute the sum. The formula for the sum of an arithmetic progression is $$sum = \frac{n}{2}(first+last)$$, where n is the number of elements in the progression and first and last are the first and the last elements. Thus, for column A, $$\frac{25}{2}(4+100) = 1300$$, while column B equates $$\frac{20}{2}(5+100) = 1050$$.

We conclude that A is greater!

Hi, for step 1, is there a simplified formula that is easier to remember for exam?
Also, it says less that 100, so shouldnt we consider multiples less than 100? Like is 100 still included?

And thanks for the explanation btw
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Re: The sum of the multiples of 4 less than 100 or The sum of [#permalink]  09 Aug 2018, 00:53
it should be given that multiples are of what kind...positive or negative,and inclusive or exclusive....
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Re: The sum of the multiples of 4 less than 100 or The sum of [#permalink]  09 Aug 2018, 05:19
Expert's post
ragini123 wrote:
it should be given that multiples are of what kind...positive or negative,and inclusive or exclusive....

Multiples are always considered as positive unless explicitly mentioned.

Less than 100 means that 100 should not be considered for calculation in this case.
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Re: The sum of the multiples of 4 less than 100 or The sum of   [#permalink] 09 Aug 2018, 05:19
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