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Re: If the average of four distinct positive integers is 60, how many inte
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17 Jun 2023, 03:09
Takeaways:
I could easily understand that A was sufficient. (please refer to Bunuel's official explanation, that's the best, as always.)
The trick was with the second option (at least I felt that, as I took a bit longer than usual to mark the correct answer. I was almost about to mark A as the correct answer).
Note the term: "Distinct positive integers" (This is always something I happen to miss out, initially, especially when moving on from one statement to the other, in a data sufficiency question.)
Each number must be different.
Let's talk about the second statement:
we know a+b+c+d = 240
Now, we also know, the mean of the 4 numbers = 50.
That can mean:
(b+c)/2 = 50
or, (b+c) = 100
again, note the word: "distinct integers". As per the question, we should look at any other scenarios other than b = c.
Which means, b must be 49, or any number less than 49.
and c must be 51 or any number more than 51.
again, we must also note that a+d = 140.
However, we don't need to do too much of calculations.
We can simply take a to be 40, b to be 49 (max possible number for b), 51(least possible number for c), and 100 (d).
possible combinations:
40, 49, 51, 100 (average = 60, median = 50)
41, 48, 52, 99 (average = 60, median = 50)
35, 40, 60, 105 (average = 60, median = 50)
1, 2, 98, 139 (average = 60, median = 50)
and so on... Note that in each case, we can see that there are only 2 numbers that can be less than 50.
Also, remember: while calculating median, the numbers must be arranged in ascending order.
So, we have 2 numbers less than 50. (which is sufficient)
So, 1 and 2 both are sufficient, independently.
Correct answer: D
Let me know if there are any discrepancies in my explanation. (This problem looked really interesting to me, so I thought of explaining it here)