plz help -- several problems

[rmazzawi]

How many units long is the straight line segment that connects the points (-1,1) and (2,6) on a rectangular coordinate plane?
4
7
sqr of 34
sqr of 26
sqr of 58


In a sequence of terms in which each term is three times the previous term, what is the fourth term?

(1) The first term is 3.

(2) The second-to-last term is 3^10.


Which of the following is the second greatest?
0.08
8 × 10^-3
0.8/1000
8 ÷ 10
88 ÷ 10^2

A small company employs 3 men and 5 women. If a team of 4 employees is to be randomly selected to organize the company retreat, what is the probability that the team will have exactly 2 women?
1/14
1/7
2/7
3/7
1/2

A student committee that must consist of 5 members is to be formed from a pool of 8 candidates. How many different committees are possible?
5
8
40
56
336

[sl750]

1) distance = sqrt((6-1)^2+(2-(-1))^2) = sqrt(34)

2) a1 = 3
a2=a1*3
a3=3^2*3
a4=3^3*3 Sufficient
Statement 2 is insufficient

3) 8*10^-2
8*10^-3
8*10^-4
8*10^-1
88*10^-2

Second largest is 8*10^-1

4) Total outcomes 8C4
Favourable outcomes = 5C2*3C2

Probability of having exactly 2 women in a team of 4 is

5C2*3C2/8C4 = 3/7

5) 8C5 = 56

[Anurag@Gurome]

In a sequence of terms in which each term is three times the previous term, what is the fourth term?

(1) The first term is 3.

(2) The second-to-last term is 3^10.

Solution:
Consider first (1) alone.
If the first term is 3, second term is 3^2 = 9, third term is 3^3 = 27, and fourth term is 3^4 = 81.
So, (1) alone is sufficient to answer the question.
Next consider (2) alone.
Knowing the second-to-last term will not help since we need to know the number of terms in the sequence as well.
So, (2) alone is not sufficient.

The correct answer is (A).

[Anurag@Gurome]

A student committee that must consist of 5 members is to be formed from a pool of 8 candidates. How many different committees are possible?
5
8
40
56
336

Since 5 candidates are to be chosen from 8 candidates, so the number of ways of doing so = 8C5 = 8!/(5! * 3!) = (8 * 7 * 6)/6 = 56

The correct answer is D.

[Anurag@Gurome]

How many units long is the straight line segment that connects the points (-1,1) and (2,6) on a rectangular coordinate plane?
4
7
sqr of 34
sqr of 26
sqr of 58

The length/distance between two points (x1, y1) and (x2, y2) with given coordinates is given by:
√{(x2 - x1)² + (y2 - y1)²}
In the given question the distance between given points = √{[2 - (-1)]² + (6 - 1)²} = √(3² + 5²) = √( 9 + 25) = √34

The correct answer is C.

[Anurag@Gurome]

A small company employs 3 men and 5 women. If a team of 4 employees is to be randomly selected to organize the company retreat, what is the probability that the team will have exactly 2 women?
1/14
1/7
2/7
3/7
1/2

2 women can be chosen from 5 women in 5C2 = 10 ways
Since in all 4 employees are to be selected, and 2 have to be women, so the remaining 2 have to be men.
So, no. of ways of choosing 2 men from 3 men = 3C2 = 3 ways
Since in all 4 employees are chosen from 8 employees , so no. of ways of doing so = 8C4 = 70
Required probability = (10 * 3)/70 = 3/7

The correct answer is D.

[veronica1]

Can you explain this futher?

A student committee that must consist of 5 members is to be formed from a pool of 8 candidates. How many different committees are possible?
5
8
40
56
336

Since 5 candidates are to be chosen from 8 candidates, so the number of ways of doing so = 8C5 = 8!/(5! * 3!) = (8 * 7 * 6)/6 = 56

The correct answer is D.