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If 2 different representatives are to be selected at random [#permalink]
18 Aug 2007, 20:12

1. 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 both representatives selected will be men is less than 1/10

2. From a group of 3 boys and 3 girls, 4 children are to be randomly selected. What is the
probability that equal numbers of boys and girls will be selected?
A. 1/10
B. 4/9
C. 1/2
D. 3/5
E. 2/3

3. Which of the following fractions has a decimal equivalent that is a terminating decimal?
A. 10/189
B. 15/196
C. 16/225
D. 25/144
E. 39/128

4. If 5^x – 5^x - 3 = (124)(5^y), what is y in terms of x?
A. x
B. x - 6
C. x - 3
D. 2x + 3
E. 2x + 6

5. Lines k and m are parallel to each other. Is the slope of line k positive?
(1) Line k passes through the point (3, 2).
(2) Line m passes through the point (-3, 2).

6. In the xy-plane, the line with equation ax + by + c = 0, where abc ≠ 0, has slope 2/3
What is the value of b?
(1) a = 4
(2) c = −6

7. This year Henry will save a certain amount of his income, and he will spend the rest.
Next year Henry will have no income, but for each dollar that he saves this year, he will
have 1 + r dollars available to spend. In terms of r, what fraction of his income should
Henry save this year so that next year the amount he was available to spend will be equal
to half the amount that he spends this year?
A. 1/(R+2)
B. 1/(2R+2)
C. 1/(3R+2)
D. 1/(R+3)
E. 1/(2R+3)

8. Leo can buy a certain computer for p1 dollars in State A, where the sales tax is t1 percent,
or he can buy the same computer for p2 dollars in State B, where the sales tax is t2
percent. Is the total cost of the computer greater in State A than in State B?

(1) t1 > t2
(2) p1t1 > p2t2

9. Can a certain rectangular sheet of glass be positioned on a rectangular tabletop so that
it covers the entire tabletop and its edges are parallel to the edges of the tabletop?
(1) The tabletop is 36 inches wide by 60 inches long.
(2) The area of one side of the sheet of glass is 2400 square inches.

10. If X, Y, and Z are positive integers, is Y>X?
(1) Y^2=XZ
(2) Z-X>0

11. Of the 32 students in a certain class, 15 are in a music club and 20 are in a dance club.
If 10 of the students are not in either club, how many of the students are in only one of
the two clubs?
A. 5 B. 9 C.10 D. 17 E. 25

12. From May 1 to May 30 in the same year, the balance in a checking account increased.
What was the balance in the checking account on May 30?
(1) If, during this period of time, the increase in the balance in the checking
account had been 12 percent, then the balance in the account on May 30 would
have been $504
(2) During this period of time, the increase in the balance in the checking account
was 8 percent.

13. Does the decimal equivalent of P/Q, where P and Q are positive integers, contain only
a finite number of nonzero digits?
(1) P>Q
(2) Q=8

14. Each side of a certain parallelogram has length 6. if the area of the parallelogram is 18.
which of the following is the measure of one of its angles?
A. 30’ B. 45’ C. 60’ D. 90’ E.120’

2. From a group of 3 boys and 3 girls, 4 children are to be randomly selected. What is the probability that equal numbers of boys and girls will be selected? A. 1/10 B. 4/9 C. 1/2 D. 3/5 E. 2/3

11. Of the 32 students in a certain class, 15 are in a music club and 20 are in a dance club.
If 10 of the students are not in either club, how many of the students are in only one of
the two clubs?
A. 5 B. 9 C.10 D. 17 E. 25

i know..i was stuck scratchin my balls (cuz thats where i think from these day) cause i couldnt see 13 in the answer choices..then i couldnt see 2 or 7 in the answer choices..then it was like...oohhh i gotta add em both for the total number ...

Fistail wrote:

fresinha12 wrote:

**** it..i did horrible got 11 out of 14...yikes..all for not reading the question properly...NOTE: READ QUESION PROPERLY dont be in a rush to solve..

No.11 here is how i did it

total number=Music+dance+(those who do both)+who dont do either

32=(Music+who do both) + (Dance+who do both) +10

22=15+20

22=35+who do both

13=who do both

no. of who do only dance = 20-13 =7

no. of who do only musci=15-13=2

total number of who only do one activity =7+2=9

Yikes...I am horrible..no more breaks for me...

total = M + D - MD + Neither 32 = 15 + 20 - MD + 10 MD = 13

8. Leo can buy a certain computer for p1 dollars in State A, where the sales tax is t1 percent,
or he can buy the same computer for p2 dollars in State B, where the sales tax is t2
percent. Is the total cost of the computer greater in State A than in State B?

(1) t1 > t2
(2) p1t1 > p2t2

Combining the two statements, p1 could be greater than p2
e.g. p1=100 t1=20 and p2=80 and t2=1

However p2 could be 1000 with all other variables as above!

9. Can a certain rectangular sheet of glass be positioned on a rectangular tabletop so that
it covers the entire tabletop and its edges are parallel to the edges of the tabletop?
(1) The tabletop is 36 inches wide by 60 inches long.
(2) The area of one side of the sheet of glass is 2400 square inches.

As the area of the tt is less than 2400, the glass may or may not cover it (it could be 60x40 or 120x20)

2. From a group of 3 boys and 3 girls, 4 children are to be randomly selected. What is the
probability that equal numbers of boys and girls will be selected?
A. 1/10
B. 4/9
C. 1/2
D. 3/5
E. 2/3

1. 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 both representatives selected will be men is less than 1/10

St1:
There are at least 6 women.
If there are 6 women, P = 1/3 (< 1/2)
If there are 7 women, P = 7/15 (<1>1/2)
Insufficient.

St2:
If there are x number of men, then
1/x * 1/(x-1) < 1/10
1/(x^2-x) < 1/10
x^2-x < 10
x^2 - x - 10 < 0

x<=3. If x = 3, w = 7 and P <1> 1/2. Insufficient.

Using both st1 and st2, nothing extra is known. Insufficient.

2. From a group of 3 boys and 3 girls, 4 children are to be randomly selected. What is the probability that equal numbers of boys and girls will be selected?
A. 1/10
B. 4/9
C. 1/2
D. 3/5
E. 2/3

We need 2 boys and 2 girls. # of ways to pick 2 boys and 2 girls = 2(3C2) = 9
# of ways to pick 4 children = 6C4 = 15
P = 9/15 = 3/5