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# If n is the product of the least and the greatest of 6 consecutive int

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Re: If n is the product of the least and the greatest of 6 consecutive int [#permalink]
Dillesh4096 wrote:
Bunuel wrote:
If n is the product of the least and the greatest of 6 consecutive integers, what is the value of n ?

(1) The greatest of the 6 consecutive integers is 20.
(2) The average (arithmetic mean) of the 6 consecutive integers is 17.5.

(1) The greatest of the 6 consecutive integers is 20.
--> Set of 6 integers = {15, 16, 17, 18, 19, 20}
--> Product, n = 15*20 = 300 --> Sufficient

(2) The average (arithmetic mean) of the 6 consecutive integers is 17.5.
--> (a + (a+1) + . . . . + (a+5))/6 = 17.5
--> 6a + 15 = 105
--> 6a = 90
--> a = 15
--> Product, n = 15*20 = 300 --> Sufficient

IMO Option D

Well done Dillesh!

The deduction from the first statement is perfect.

For the 2nd statement, however, we can simply do as follows:
In a set of terms having constant common difference (i.e. an AP - Arithmetic progression), the mean is simply the average of the first and the last terms
=> Sum of the 1st and the 6th number = 17.5 x 2 = 35
Since the difference between the 1st and the 6th numbers is 5:
# the 1st number = (35 - 5)/2 = 15
# the last number = (35 + 5)/2 = 20

=> product = 300

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Re: If n is the product of the least and the greatest of 6 consecutive int [#permalink]
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Re: If n is the product of the least and the greatest of 6 consecutive int [#permalink]
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