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The average of all the multiples of 5 between 199 and 706

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The average of all the multiples of 5 between 199 and 706 [#permalink] New post 15 Sep 2017, 07:38
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69% (01:09) correct 30% (00:56) wrong based on 23 sessions



Quantity A
Quantity B
The average of all the multiples of 5 between
199 and 706
The average of all the multiples of 10 between
199 and 706


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Re: The average of all the multiples of 5 between 199 and 706 [#permalink] New post 21 Feb 2018, 02:18
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To take the average of evenly spaced numbers, we can determine it easily by taking the average of first and last numbers.
Q.A The average of all the multiples of 5 between 199 and 706 is = (200+705)/2=452.5
Q.B The average of all the multiples of 10 between 199 and 706 is = (200+700)/2= 450

So, A is the answer.
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Re: The average of all the multiples of 5 between 199 and 706 [#permalink] New post 24 Feb 2018, 17:57
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A

If you don't know the trick above, as for people like me, below is the conventional way to solve it. Hope my solution is correct.
Quantity A:- series -- 200, 205 .... 700, 705 (102 terms).
Sum of all terms in series = [n (a + l)]/2 = 102(200+705)/2 = 905*51
Average = 905*51 / 102 = 452.5
Quantity B:- series -- 200, 210 .... 690, 700 (51 terms).
Sum of all terms = 51(200+700)/2 = 51*450
Average = 51*450 / 51 = 450
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Re: The average of all the multiples of 5 between 199 and 706 [#permalink] New post 12 Mar 2018, 01:38
A is correct right
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Re: The average of all the multiples of 5 between 199 and 706 [#permalink] New post 13 Mar 2018, 15:59
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correct: A
Sum of a sequence of numbers is (a1 +an) *n/2 and when we divide it by n, it will be the average of the numbers (a1+an)/2
The average of all the multiples of 5 between 199 and 706: 200, 205, ..., 700, 705 average = (a1 + an-1) / 2 = (705+200)/2 = 905/2 = 452.5
The average of all the multiples of 10 between 199 and 706: 200, 210, 220, ..., 700 average =(700 + 200)/ 2 = 900/2 = 450
Re: The average of all the multiples of 5 between 199 and 706   [#permalink] 13 Mar 2018, 15:59
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