OG-Question 65-2nd Edition

[shanice]

Please help me with the below question?

If the average(arithmetic mean) of n consecutive odd integers is 10, what is the least of the integers?

(1)The range of the n integers is 14.
(2)The greatest of the n integers is 17.

Answer is D - Each Statement alone is sufficient.

[das.ashmita]

let the first term and last term be a and Tn respectively. d= 2

avg = Sum (n) / n => Sum (n) = 10n
Sum(n) = n/2[2a+(n-1)d]
10n = n/2[2a+(n-1)2]
10=a+n-1
a=11-n....1

(1)The range of the n integers is 14.

Tn-a= 14
=> a+(n-1)2-a = 14
=> n = 8
subs value in 1 we get a.... Suff

(2)The greatest of the n integers is 17.

Tn= 17
=>a+(n-1)2 = 17.....(2)

2 equations, 2 unknowns we can find a... Suff

therefore ans is D

[Brent@GMATPrepNow]

Please help me with the below question?

If the average(arithmetic mean) of n consecutive odd integers is 10, what is the least of the integers?

(1)The range of the n integers is 14.
(2)The greatest of the n integers is 17.

Answer is D - Each Statement alone is sufficient.

When numbers in a set a equally spaced (as they are in a set of consecutive odd numbers), the mean of that set is equal to the median of the set. So, we can conclude that the median of the set of numbers is also 10.
If the median is 10, then half of the numbers in the set are greater than 10 and have are less than 10.

Statement 1: The range of the n integers is 14.
Divide the range in half to get 7.
So, the greatest number in the set is 10 + 7 (17) and the smallest number in the set is 10 - 7 (3)
Since we can determine the smallest number, statement 1 is SUFFICIENT

Statement 2: The greatest of the n integers is 17.
If the biggest number (17) is 7 more than the median (10), then the smallest number in the set must be 7 less than the mean (since all of the numbers are equally spaced).
In other words, the smallest number = 10 - 7 = 3
Since we can determine the smallest number, statement 2 is SUFFICIENT

Answer = D
Cheers,
Brent

[shanice]

Thank you guys

[tisrar02]

My way of this question would be:

From Question Stem: The Average has to be 10 no matter what. Keep that in mind, Also all the integers must be odd as well. Now the only way to get 10 from a consecutive set of odd integers is if you had an even set of numbers with 9 and 11 being in the middle.

1) The range is 14 so you just divide this by half and add it to 10 to see if the restrictions work,
10+7= 17 and 10-7=3.... 17-3= 14. It works. The Average is 10 as well so this is SUFFICIENT

2) The greatest value is 17 but the AVERAGE MUST be 10. So for however many integers you have from 11-17 (remember only odd integers) that's how many integers you will have below 9. The set is 3-17 once again. SUFFICIENT.


Best regards