lheiannie07 wrote:Six numbers are randomly selected and placed within a set. If the set has a range of 16, a median of 6, a mean of 7 and a mode of 7, what is the greatest of the six numbers?
(1) The sum of the two smallest numbers is one-fifth of the sum of the two greatest numbers
(2) The middle two numbers are 5 and 7
Which of the statement is sufficient and why?
OA A
Say the smallest number is x, thus, the largest would be (x + 16). Since there are 6 (Even) terms in the set and the median = 6, the median = 6 would be average of the 3rd and the 4th number. We are given that Mode = 7, thus, there must be two 7s. One of the 7s would be the 4th number, thus, the 3rd number would be 5 since median = 6 (= average fo 5 and 7).
So far we discussed the 1st number (= x; smallest), the 3rd number (= 5), the 4th number (= 7), the 5th number (= 7; there are two 7s), and the 6th number (= x + 16; largest). We do not have any information about the 2nd number. Say the 2nd number is y.
Thus, the 6 numbers arranged in ascending order are x, y, 5, 7, 7, (x + 16).
We are given that arithmetic mean is also 7, thus, the sum of x, y, 5, 7, 7, and (x + 16) would be 7*6 = 42.
=> x + y + 5 + 7 + 7 + (x + 16) = 42
=> 2x + y = 7 ---(1)
If we get the of x, we get the value of (x + 16).
Let's take each statement one by one.
(1) The sum of the two smallest numbers is one-fifth of the sum of the two greatest numbers.
=> x + y = [7 + (x +16)]/5
=> 4x + 5y = 23 ---(2)
Solving eqns (1) and (2), we get x = 2, thus x + 16, the greatest number = 2 + 16 = 18. Sufficient.
(2) The middle two numbers are 5 and 7.
We do not have any information about the 1st, the 2nd, and the 6th number. Insufficient.
The correct answer:
A
Hope this helps!
-Jay
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