Is the median of the five numbers a,b,c,d,e and e equal to d?

E

analyse bothe the equations and there is discrepancy between 'a' and 'd'.

either of them ca be left or right between 'b' and 'c'

St1 : a<c<e no info about b & d hence NS
St2 : b<d<c no info about a & e hence NS

choice A,B,D can be eliminated
Combining St1 & 2 : NS counter example can be as following:
b<d<a<c<e ( d is not median)

Hence answer is E

From statement 1) a < c < e

it could be a + b + d + c + e, here d is the median.

it could also be a + d + b + c + e here b is the median. insufficient.

Eliminate A/D

Check statement 2) b < d < c

b + d + c + a + e here c is the median

it could be a + b + d + c + e here d is the median.

insufficient.

now try combining (1) and (2)

it could be a + b + d + c + e here d is the median.

or it could be b + d + a + c + e here a is the median.

Insufficient.

Answer choice E

I've a different opinion,
If we consider both the statements:
a<c<e
b<d<c

Therefore,
e can be considered smallest, b & d is smaller than c hence
b<d<c<e
Now we have to find if D is the median, so even if we can't derive a relationship between a and b, we can still conclude d to be median. I don't know if I'm logically wrong or not, but I guess my answer has some substance

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(1) No relation with b, d, and c are given. Insufficient.

(2) No relation with a, c, and e are given, Insufficient.

Considering both:

b<d<c<e but can't establish any relationship of a with d. a can be equal, less than or greater than d. Answers will different. Insufficint.

The answer is E.

Solution:

If we can determine d is the middle quantity of the five quantities when their values are listed in order, then d is the median of the five quantities.

Statement One Only:

a<c<e

We can’t determine whether d is the middle quantity of the five quantities. For, example, if b < a < d < c < e, then d is the median. However, if b < d < a < c < e, then d is not the median. Statement one alone is not sufficient.

Statement Two Only:

b<d<c

We can’t determine whether d is the middle quantity of the five quantities. For, example, if b < a < d < c < e, then d is the median. However, if b < d < a < c < e, then d is not the median. Statement one alone is not sufficient.

Statements One and Two Together:

Using the two statements, we still can’t determine whether d is the middle quantity of the five quantities since we can use the same two inequalities two show in one instance, d is the median, while in the other, d is not the median.

Answer: E

E.

Got too haphazard with this one. There are two possibilities.

a < b < d < c < e
b < d < a < c < e

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