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# If the average (arithmetic mean) of seven consecutive intege

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Director
Joined: 07 Jan 2018
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If the average (arithmetic mean) of seven consecutive intege [#permalink]  13 Jun 2018, 22:21
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If the average (arithmetic mean) of seven consecutive integers is k + 2, then the product of the greatest and least integer is ?

A. $$k^2$$ – 9

B. $$k^2$$ – 2k + 1

C. $$k^2$$ + 4k – 12

D. $$k^2$$ + 6k + 9

E. $$k^2$$ + 4k – 5
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Director
Joined: 20 Apr 2016
Posts: 761
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Re: If the average (arithmetic mean) of seven consecutive intege [#permalink]  27 Jun 2018, 01:39
amorphous wrote:
If the average (arithmetic mean) of seven consecutive integers is k + 2, then the product of the greatest and least integer is ?

A. $$k^2$$ – 9

B. $$k^2$$ – 2k + 1

C. $$k^2$$ + 4k – 12

D. $$k^2$$ + 6k + 9

E. $$k^2$$ + 4k – 5

Here
we know k + 2 is the Arithmetic Mean and there are 7 nos

SO the numbers are; K - 1, K , K + 2 , K + 3, K + 4, K + 5

i.e. arithmetic mean = $$\frac{{(K - 1) + (K) + (K + 2) + (K + 3) + (K + 4) + K + 5)}}{7}$$= k + 2

So the greatest number = k + 5 and the smallest number = K - 1

So the product =(k + 5) * (k - 1) = $$k^2$$ + 4k – 5
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Re: If the average (arithmetic mean) of seven consecutive intege   [#permalink] 27 Jun 2018, 01:39
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