gmat set

[MikeJung]

2.
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 1/2 of the 10 employees are women.
2. the probability that representatives selectd will be men is less than 1/10

.

[skarya]

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 1/2 of the 10 employees are women.
6 women => 6C2/10C2 = 6*5/10*9=1/3 (2/6<3/6 i.e. 1/2)
9 women => 9C2/10C2 = 9*8/10*9 = 4/5 (8/10>5/10 i.e.1/2)
not sufficient
2. the probability that representatives selectd will be men is less than 1/10
P(men)<1/10
P(women)=1-P(men)=1-(<1/10) = (>9/10)
P(women)>9/10 (>5/10)
sufficient

B

[walidreza]

it's E

[MikeJung]

Official Answer is E. please explain walidreza

[walidreza]

1. let w be the no. of women. so wC2/10c2>1/2. solve for w and u will see that it's insuf.

2. let m be the no. of men. so mC2/10c2<1/10. solve for m. not suf.

So E

I dont know how to make a new post, would u pls tell me.

Are u going to write the gmat soon?

regards,

[skarya]

Thanks for Official Answer.
I realized my mistake

For statement 2:
P(men) < 1/10

Is possible for few values of m

mC2/10C2 < 1/10
=>m(m-1)/10*9 < 1/10
=>m(m-1)<9
=>m=1, 2, 3
=>w=8, 7
P(women)=8C2/10C2 = 8*7/10*9 = 56/90 (>45/90 i.e. 1/2)
P(women)=7C2/10C2 = 7*6/10*9 = 42/90 (<45/90 i.e. 1/2)
not sufficient

correct response is E

[MikeJung]

thanks both of u.

u two rock

[hjafferi]

had gone with B. but E makes sense