here are the answers of first 5 questions....

1. The sum of the even numbers between 1 and n is 79*80, where n is an odd number, then n=?

Sol:
First term a=2,
common difference d=2
since even numbertherefore sum to first n numbers of Arithmetic progression would be
x/2(2a+(x-1)d)
=> x/2(2*2+(x-1)*2)=x(x+1)
and this is equal to 79*80
therefore x=79 which is odd...
so number of even terms between 1 and n are 79.
means n= (1+2*79) =159


2. The price of a bushel of corn is currently $3.20, and the price of a peck of wheat is $5.80. The price of corn is increasing at a constant rate of 5x cents per day while the price of wheat is decreasing at a constant rate of cents per day. What is the approximate price when a bushel of corn costs the same amount as a peck of wheat?(A) $4.50(B) $5.10(C) $5.30(D) $5.50(E) $5.60

Soln:
320 + 5x = 580 - .41x; x = # of days after price is same;
solving for x; x is approximately 48,
thus the required price is 320 + 5 * 48 = 560
cents = $5.6

3. How many randomly assembled people do u need to have a better than 50% prob. that at least 1 of them was born in a leap year?

Soln:
Prob. of a randomly selected person to have NOT been born in a leap yr = 3/4Take 2 people,
probability that none of them was born in a leap = 3/4*3/4 = 9/16.
The probability at least one born in leap = 1- 9/16 = 7/16 < year =" 3/4*3/4*3/4" born =" 1" 64 =" 37/64"> 0.5
Thus min 3 people are needed.

4. In a basketball contest, players must make 10 free throws. Assuming a player has 90% chance of making each of his shots, how likely is it that he will make all of his first 10 shots?

Ans:
The probability of making all of his first 10 shots is given by(9/10)* (9/10)* (9/10)* (9/10)* (9/10)* (9/10)* (9/10)* (9/10)* (9/10)* (9/10) = (9/10)^10 = 0.348
=> 35%

5. A and B ran a race of 480 m. In the first heat, A gives B a head start of 48 m and beats him by 1/10th of a minute. In the second heat, A gives B a head start of 144 m and is beaten by 1/30th of a minute. What is B’s speed in m/s?(A) 12(B) 14(C) 16(D) 18(E) 20

Ans:
race 1 :- ta = tb-6 ( because A beats B by 6 sec)
race 2 :- Ta = tb+2 ( because A looses to B by 2 sec)
By the formula D= S * T
we get two equations
480/Sa = 432/Sb -6 ------------1)
480/Sa = 336/Sb +2------------2)
Equating these two equations we get
Sb = 12ta,
Sa stand for time taken by A and speed of A resp.