really not clear about the logic- If we add 15 and 39 yr olds then we basically add 2 people. Not clear on how and why you have just subtracted the two numbers and distributed 24 and that too by 3 . We do not even know whether 15 is average in order to say that 39-15 is an excess to be distributed among n+1 people. Overall the approach is not clear at all pls explain.
Hi All,
We're told that the average age of a group of N people INCREASES BY 2 if one more person aged 39 joins the group and instead DECREASES BY 1 if one more person aged 15 joins the group. We're asked for the value of N. This question can be solved in a number of different ways, including with a bit of 'number logic' and TESTing THE ANSWERS.
To start, it's interesting the average increases or decreases by an exact INTEGER (often, we'd see a change that creates a decimal), so the numbers 39 and 15 impact the average in a specific way - and the DIFFERENCE in those values (39 and 15) is something that we have to consider. Including an extra 39 instead of an extra 15 would increase the SUM by 24... and again, would lead to an increase in average of 3. This implies that the NEW number of people (the original N people + 1) is a factor of 24. Based on the 5 answer choices, the likely answer is either 7 (which would be 8 people when the extra person is added) or 11 (which would be 12 people when the extra person is added).
Notice how 24 = (8)(3)... which would be the new number of people and the increase in the average (between when an extra 15 is included and when an extra 39 is included), so this is far more likely to be the situation that we're dealing with. Here's how to visualize that difference:
IF....
N=7 and the sum of those ages is X....
adding a 39 would give us a sum of (X+39)
adding a 15 instead would gives us a sum of (X+15)
The difference in those 2 situations is (X+39) - (X+15) = 24.
With 8 total people, the average would INCREASE by 24/8 = 3
This is exactly what happens in the situation described about, so this must be the answer.
Final Answer:
GMAT assassins aren't born, they're made,
Rich