Tough PS-3

[satishchandra]

There are four numbers in sequence. The average of first three is 6; the average of the last three is 7 and
the last number is 3 more than the first. The average of second & third numbers is:
(A) 6 (B) 6.5 (C) 5.75 (D) 7 (E) Indeterminate

[anuprajan5]

Hi,

The answer is B

The question tells me the 4 numbers are in sequence. It does not tell me the difference between the numbers in the sequence.

It tells me that the last number, which is also the 4th number is 3 more than the last. This tells me that the numbers are a consecutive series. Taking the statements about the average into account, it tells me

(x+x+1+x+2)/3 = 6

and (x+1+x+2+x+3)/3 = 7 both of which give me that x=5

Therefore the average of the 2nd and 3rd numbers is 6.5.

[satishchandra]

OA is E

[Brent@GMATPrepNow]

There are four numbers in sequence. The average of first three is 6; the average of the last three is 7 and
the last number is 3 more than the first. The average of second & third numbers is:
(A) 6 (B) 6.5 (C) 5.75 (D) 7 (E) Indeterminate

This question is tricky if we make assumptions about what a sequence is.
A sequence is an ordered list of numbers.
Note: A sequence need not have a "nice" pattern like {5, 10, 15, 20, etc}
For example, {4, -1, 11, 999999} is a sequence.

Let's say that our sequence looks like this: {w, x, y, z}

The average of first three is 6
So, (w+x+y)/3 = 6, which means w+x+y = 18

The average of the last three is 7
So, (x+y+z)/3 = 7, which means x+y+z = 21

When we take the top equation (w+x+y = 18) and subtract it from the bottom equation (x+y+z = 21), we get z-w=3. In other words, z is 3 more than w.

So, we're already able to conclude that the last number is 3 more than the first without being told that this is true. Hmmm, this suggests that the answer may be E

Consider the following sequences that meet the given conditions:
case a: the sequence is: 6, 6, 6, 9
Here, the average of the 2nd and 3rd numbers is 6

case b: the sequence is: 5, 6, 7, 8
Here, the average of the 2nd and 3rd numbers is 6.5

The correct answer is E

Cheers,
Brent