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the smallest of six

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by sanju09 » Tue Oct 18, 2011 5:25 am
What is the smallest of six consecutive odd integers whose average (arithmetic mean) is x + 2?
(A) x - 5
(B) x - 3
(C) x - 1
(D) x
(E) x + 1
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by Anurag@Gurome » Tue Oct 18, 2011 5:33 am
sanju09 wrote:What is the smallest of six consecutive odd integers whose average (arithmetic mean) is x + 2?
Average of 6 consecutive odd integers will be an even integer which will be one more than the third integer.

Hence, the third integer = (x + 2) - 1 = (x + 1)
Hence, the smallest integer = Third integer - 4 = (x + 1) - 4 = (x - 3)

The correct answer is C.
Last edited by Anurag@Gurome on Tue Oct 18, 2011 6:08 am, edited 1 time in total.
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by moonraker » Tue Oct 18, 2011 6:05 am
The correct ans is x-3 not A.
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by neelgandham » Tue Oct 18, 2011 6:42 am
First Method :

Let the 6 consecutive odd numbers be of the form a-5, a-3, a-1, a+1, a+3, a+5 (Where is a = even number)

Average of the odd integers = a = x+2 (From the question)
Smallest of the odd integers = a-5 = x+2-5 = [spoiler]x-3 (Answer:B)[/spoiler]

Second Method :

Let the numbers be 1,3,5,7,9,11

Average of the odd integers = (6 = x+2) => x=4
Smallest of the odd integers = (1 = 4-3) = [spoiler]x-3 (Answer:B)[/spoiler]
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