Problem Solving

1)
If 10 persons meet at a reunion and each person shakes hands exactly once with each of the others, what is the total number of handshakes?
(A) 10•9•8•7•6•5•4•3•2•1
(B) 10•10
(C) 10•9
(D) 45
(E) 36

OA: D
I thought it will be 10•9, since each person shakes hand 10 times with everyone. So 10*9.

2)
Trucking transportation rates are x dollars per metric ton per kilometer. How much does it cost, in dollars, to transport one dozen cars, which weigh two metric tons each, n kilometers by truck?

(A) x/12n
(B) x/24n
(C) xn/24
(D) 12xn
(E) 24xn

OA: E
This one I just don't get it. I thought the answer would be x/24n

3)
One-fifth of the light switches produced by a cer¬tain factory are defective. Four-fifths of the defective switches are rejected and of the nondefective switches are rejected by mistake. If all the switches not rejected are sold, what percent of the switches sold by the factory are defective?

(A) 4%
(B) 5%
(C) 6.25%
(D) 11%
(E) 16%

OA: B
Again no clue on this one

4)
What is the least possible product of 4 different integers, each of which has a value between –5 and 10, inclusive?
(A) –5040 (B) –3600
(C) –720 (D) –600
(E) –120

OA: B
No idea.

5)
If a motorist had driven 1 hour longer on a certain day and at an average rate of 5 miles per hour faster, he would have covered 70 more miles than he actually did. How many more miles would he have covered than he actually did if he had driven 2 hours longer and at an average rate of 10 miles per hour faster on that day?
(A) 100 (B) 120 (C) 140
(D) 150 (E) 160

OA: D
No idea here too.

Thank you in advance for your help.

1)

Lets say you name all ten people.

A,B, C, D, E,F,G,H,I,and J

A shakes everyones hand 1nce...thats 9 hand shakes.

B shakes everyones hand once (except A since A and B already shook hands) that gives you 8 more hand shakes.

C Shakes everyones hand once give you 7....(doesn't shake hands with A and B because they shook already)

Continue this process you get 6,5,4,3,2,1

Add them up you get 45.

I know there is a Algebraic way of doing this, but I don't know it...I see things like this its easier for me...sorry

2) Plug in numbers for your variables. Lets say it cost you 5 dollars per metric ton per kilometer. you traveled 20 kilometers, with the 1 dozen cars with 2 metric tons each(24 metric tons)....

No how much will it cost us using our variables? 24*5*20 = $2400...

Now go back to your answer choices and plug in these values for your variables, and which ever one equals 2400 is the right answer....and the right answer here is E.

3)
Okay i stopped here because I think there is something missing in the problem....
One-fifth of the light switches produced by a cer¬tain factory are defective. Four-fifths of the defective switches are rejected and of the nondefective switches are rejected by mistake. If all the switches not rejected are sold, what percent of the switches sold by the factory are defective?

What fraction of the non defective switches are rejected by mistake?

Answer to 4.

The integers are between -5 and 10 and we need to find product of the numbers such that the product is most negative. The quick temptation is to say 10 * 9 * 8 * 8 and stick a -ve sign to any of them to get the most negative number (ie A) but we dont have a -10 or -9 or -8 or -7. So the best we can do is 10 *9 *8 *-5

thanks
-Vittal

Answer to 5

On a normal day d = r * t
d - distance
r - rate (miles/hr)
t - time (hrs)

If the driver drove for 1 hour more at 5miles/hr faster, he goes 70miles longer;

d+70 = (r+5) * (t+1)

If the driver drove for 2 hours more at 10miles/hr fater, say he goes x miles longer;

d+x = (r+10) * (t+2)

expand and solve all three equations to get x = 150.

Cheers