If 2 different representatives are to be selected at random from a group of 10 employees and if p is the probability that both representatives selected will be women, is p > 21?

(1) More than 21 of the 10 employees are women.
(2) The probability that both representatives selected will be men is less than 101.
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

Please provide me the solution for this. I tried to solve it and came up with option D but thats incorrect.

I am not sure but if P is a probability, how can it be greater 1. Is it a typo?

vaibhav.vkg, I am not sure where you got this question from? Did you type it yourself? A quick read will show that the question along with the options does not make any sense. Anyways, I think you are trying to get a solution to this question

If 2 different representatives are to be selected at random from a group of 10 employees and if p is the probability that both representatives selected will be women, is p >1/2?

(1) More than ½ of the 10 employees are women.
(2) The probability that both representatives selected will be men is less than 1/10.

my typing mistake...it is for p > 1/2 .. :$:$

So for the correct problem...
If 2 different representatives are to be selected at random from a group of 10 employees and if p is the probability that both representatives selected will be women, is p >1/2?

(1) More than ½ of the 10 employees are women.
(2) The probability that both representatives selected will be men is less than 1/10.

Solution , lets first Rephrase the question:
What is the probability of selecting 2 women from a group of 10. lets assume there are n women.
P(2w) = nC2 / 10C2 = n*(n-1) / 10*9

Question is asking is P(2W) >1/2
or n*n-1 / 90 >1/2
or n* n-1 > 45

Now what cud be 10 , when we know n<=10
n=10 10*9 = 90 > 45
n=9 9*8 = 72 > 45
n=8 8*7 = 56 > 45
n=7 7*6 = 42 STOP
So we know for the prob of selecting two women to be more than 1/2 , we need >=8 women in the group of 10 ppl.

St. 1
no. of women > 5 , doesnt tell us whether >=8 SO INSUFFICIENT

St. 2 P(2m) <1/10
Going by above method
m*m-1 <9
m= 0 , 0 < 9
m= 1 , 0 <9
m=2 2*1 <9
m=3 3*2 = 6 <9
m=4 4*3 STOP.
so we know that total men in the group are <=3 , which means women are >=7. But it still doesnt confirm whether women are >=8.
SO INSUFFICENT

Now comibing both of the statments.
we know m <=3 and w>=5
But still doesnt tell us that whether we have more than 8 women to have prob of selecting 2 w to be more than 1/2.

Answer E.

i agree with 'nitin_prakash_khanna' .. just on small pt.. for checking statement (1), wen can straight take extreme values.. ie.

when they say # women > 5

we can check for 6 and 10 directly.. we get contradictory ans right then..

not much difference though..

nice solution.

has this problem made it into GMATPREP?
someone please verify. the only place i've seen this problem is gmatfocus, a source we're not allowed to use.

thanks.