#1

Question

In an original group, the probability of choosing a girl from that group was 1/3. When 1 more girl joins the group, the probability of choosing a girl out of the group changes from 1/3 to 3/7. How many boys were there in the group orginally?
a. 1
b. 2
c. 3
d. 4
e. 5

#2
A drawer contains only green marbles. After 5 red marbles are added to the drawer, probability of picking a red marble is 1/7. How many marbles were there in the drawer orginally?
a. 5
b. 7
c. 12
d. 30
e. 35

#3
The sum of the first 1million primes is N. Without knowing N's value, one can determine that the ones' digit of N cannot be
a. 1
b. 2
c. 3
d. 9

Please help.

Answer 1

#1
g/(b+g) = 1/3
3g = b+g
b = 2g

(g+1)/(b+g+1) = 3/7
7g + 7 = 3b+3g+3
4g - 3b = -4
4g - 6g = -4
g = 2
then b = 4 , which is choice d.

#3
1 million is an even number
all prime numbers are odd, except the first one, which is 2, thus even
so we have the sum of 999,999 odd numbers plus the even number 2
The sum of an even number of odds is even, but the sum of an odd number of odds is odd
Thus the sum of 999,999 odd numbers is odd, and adding an even plus an odd yields an odd
so the sum cannot end in 2 which would be even.

Answer 2

#2
number of green = x
number of marbles after 5 reds are added = x+5

prob of picking red = 1/7
5/(x+5) = 1/7
x+5 = 35
x = 30

there were 30 marbles