a, b, c, d, and e are five numbers such that a≤b≤c≤d≤e and e-c=4. A is the average (arithmetic mean) of the five numbers, and M is their median. Is A>M?

(1) e+c=34
(2) c=a+10


So I actually understand the solution provided but it seemed a little un-intuitive, was hoping someone here could discover some sort of new insight about this problem. Basically, the solution suggests plugging but I wonder if there is something nicer...

Problems with plugging-in are finding right numbers to plug and not knowing where to stop. A more methodogical algebric approach is sure shot way to solve DS. (but sometimes time consuming). Need to find the right balance between two.

Question says: a, b, c, d, and e are five numbers such that a≤b≤c≤d≤e and e-c=4

We cant assume that a,b,c,d and e are integers or positive etc. e could be 23.4 and c could be 19.4 or a, b or c could be anything negative or in decimals.
Plugging in right numbers would be very hard and very time consuming. Infact- the solution given above by suryanshg 'assumes' numbers are integers.. and is therefore incorrect.
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Lets take a look at the problem.
given is e-c =4 and a≤b≤c≤d≤e
Clearly c is the median. problem is finding out avergage, A = (sum/5)

statement 1: e+c=34
we can combine this with e-c=4 to find out e=19, and c=15, but nothing else. Not sufficient.

Statement 2: c =a+10 or a = c-10.
Now notice, b is a number between a and c and it can be written as
c-10<= b <=c
similarly d is a number between c and e or
c <= d <=c+4

If we add these two:
2c-10 <=b+d <= 2c+4

To find out the average, we need sum.
lets just take a look at sum
Sum = a+b+c+d+e or Sum = c-10 + b + c + d +c+4
=>Sum= 3c-6 + b +d

using b+d
3c-6 + 2c-10 <= Sum <= 3c-6 +2c+4
5c -16<=Sum <=5c-2

Hence maximum limit of sum is 5c-2, therefore average A (which is Sum/5) is always going to be less than c (the median). This is exactly what we want to know.
Sufficient.

Ans B it is!
Hope it helps.
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Look at the highlighted portion.

1st mistake-
c=a+10
e=c+4
=> e=a+14
considering
a = -10
c = 0
e = 14

2nd mistake-
A<M (-10, 10, 0, 0, 14), A>M (-10, 0, 0, 14, 14)
A=14/5, M=0 how is A<M ?

Probably should give u some idea.
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20 GMAT points and just thanks? where is kudos
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