DS, Num Properties (in Prob Solving)

[bretania]

Guys, I need your input here again. My initial answer here is A. But the OA says it's D. So I thought, yeah, it makes sense: D should be the answer. However, I re-solved it again and this time around I think it's A! Arghh.

Please check and let me know what your thoughts are:

21.
Steve took 5 history exams during a semester. Each score was one of the integers 1 through 100 inclusive. What was Steve's median score for the these 5 exams?

(1) Steve's scores on the first 4 exams were 76, 87, 73, and 96, respectively, and Steve's average (arithmetic mean) score on the last 3 exams was 89.

(2) Steve's score on the first 3 exams were 76, 87, and 73, respectively, and Steve's average (arithmetic mean) on all 5 exams was 86.

[clock60]

Originally Posted by bretania

Guys, I need your input here again. My initial answer here is A. But the OA says it's D. So I thought, yeah, it makes sense: D should be the answer. However, I re-solved it again and this time around I think it's A! Arghh.

Please check and let me know what your thoughts are:

21.
Steve took 5 history exams during a semester. Each score was one of the integers 1 through 100 inclusive. What was Steve's median score for the these 5 exams?

(1) Steve's scores on the first 4 exams were 76, 87, 73, and 96, respectively, and Steve's average (arithmetic mean) score on the last 3 exams was 89.

(2) Steve's score on the first 3 exams were 76, 87, and 73, respectively, and Steve's average (arithmetic mean) on all 5 exams was 86.

so it is quite clear with first statement let us review 2
average for 5 exams is 86 so
(76+87+73+x+y)/5=86
236+x+y=430
x+y=194
where x and y are the last two exams
in increasing order it will be 73 76 87 and x and y
so now 87 will be median score if x or y are not less than 87
but neither x nor y can not be less than 87 because if x is 86 than y=194-86=108 that can not be true according the condition of the prob
that any exam is not more that 100
the least meaning of the x is 94 and so y=100 of course we can vary them
but resulting series will be 73 76 87 x y so median is 87
(2)sufficient
hope this help

[bretania]

Thanks! I got it. My arithmetic was wrong in my solution. Arghh. Thanks for pointing it out clock60!

[Dr_GMAT]

Great explanation