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# The sum of five consecutive even integers is 20. What is the product

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Math Expert
Joined: 02 Sep 2009
Posts: 54375
The sum of five consecutive even integers is 20. What is the product  [#permalink]

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16 Aug 2017, 00:23
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The sum of five consecutive even integers is 20. What is the product of the median of the sequence and the smallest integer in the sequence ?

(A) 12

(B) 10

(C) 6

(D) 4

(E) 0

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Posts: 4
Re: The sum of five consecutive even integers is 20. What is the product  [#permalink]

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16 Aug 2017, 01:02
We know :
Sum of a sequence = $$\frac{n}{2}$$($$a_1$$ + $$a_n$$) = $$\frac{5}{2}$$($$a_1$$ + $$a_5$$)= 20

i.e. $$a_1$$ + $$a_5$$ = $$\frac{(20 * 2)}{(5)}$$ = 8 -------- Statement 1

Median of the Sequence of 5 consecutive even integers = $$a_3$$ = $$\frac{1}{2}$$($$a_1$$ + $$a_5$$) ------ Statement 2

Using Statement 1 & 2 :

Median = $$a_3$$ = $$\frac{8}{2}$$ = 4

if $$a_3$$ = 4, $$a_1$$ = $$a_3$$- 4 = 0

Median * Smallest Integer = $$a_3$$ * $$a_1$$ = $$4 * 0$$ = $$0$$ ---Option (E)
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Re: The sum of five consecutive even integers is 20. What is the product  [#permalink]

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16 Aug 2017, 01:11
let 2x, 2x+2, 2x+4, 2x+6, 2x+8 be the 5 consecutive even integers. 10x+20=20, median would be 4 and smallest number 0. Thus sum should be 4.
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Re: The sum of five consecutive even integers is 20. What is the product  [#permalink]

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16 Aug 2017, 03:16
The numbers are 0,2,4,6,8.
Median is 4.
Smallest integer is 0.
So product is 4*0=0.

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The sum of five consecutive even integers is 20. What is the product  [#permalink]

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16 Aug 2017, 05:56
Bunuel wrote:
The sum of five consecutive even integers is 20. What is the product of the median of the sequence and the smallest integer in the sequence ?

(A) 12

(B) 10

(C) 6

(D) 4

(E) 0

x + (x+2) + (x+4) + (x+6) + (x+8) = 20

5x + 20 = 20
5x = 0

x = 0 = smallest term
Median is x + 4 = 4
Product: 4*0 = 0

Bunuel - I've asked the question below a couple of times. So far no response.

If at all, when $$must$$ we assign "2x" for consecutive even integers, and (2x + 1) for consecutive odd integers, as opposed to using just "x" for both?

I've seen different approaches.

Some mathematicians always use "x" to denote the first term, whether the sequence is consecutive evens, or consecutive odds.

Others always use 2x for consecutive even integers, and (2x + 1) for consecutive odd integers. I understand that these latter two formulations guarantee even and odd integers, respectively.

That said, I have only seen one problem where using simply "x" made a difference in the accuracy of the answer, and it seemed strange.

So does the difference in variable assignment matter? Obviously, the simple "x" (instead of 2x) for consecutive even integers worked here.
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The sum of five consecutive even integers is 20. What is the product   [#permalink] 16 Aug 2017, 05:56
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