BTGmoderatorDC wrote:What is the average (arithmetic mean) of a list of 6 consecutive two-digit integers?
(1) The remainder when the fourth integer is divided by 5 is 3.
(2) The ratio of the largest integer to the smallest integer is 5 : 4.
OA B
Source: Princeton Review
Say the 6 consecutive two-digit integers are x, (x + 2), (x + 4), (x + 6), (x + 8), and (x + 10). Since the numbers are evenly spaced, the average of the 6 consecutive two-digit integers would be the average of the two middle-most numbers = [(x + 4) + (x + 6)]/2 = x + 5
So, we have to get the value of x + 5.
Let's take each statement one by one.
(1) The remainder when the fourth integer is divided by 5 is 3.
=> x + 4 = 5q + 3. where q is a posotive integer
Thus, x + 5 = 5q + 4. Since the value of q is not known, we cannot get the unique value of x + 5. insufficient.
(2) The ratio of the largest integer to the smallest integer is 5 : 4.
=> (x + 10)/x = 5/4 => x = 40 => x + 5 = 40 + 5 = 45. Unique value. Sufficient.
The correct answer:
B
Hope this helps!
-Jay
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