word problems - easy way to solve these?

[infinityzero]

Hoping someone can solve these and show perhaps a quick and efficient way to solve them. Thanks.

 

1. John is trying to remember a 3 digit ID number. He knows that one of the last 2 digits in the number 138 is wrong, but he's not sure which. He also knows that all the digits in the ID number are distinct. If he were to start trying all the combinations that fit these conditions, what is the probability he would get the right combination on the first try?

A. 1/81

B. 1/31

C. 1/14

D. 1/3

E. 1/2

 

 

2. In a certain club, the average age of the male members is 35 and the average age of the female members is 25. If 20 percent of the members are male, what is the average age of all the club members?

A. 26

B. 27

C. 28

D. 29

E. 30

 

3. Dr. Wong's physics miderm has 60 questions. He scores the test as follows: for each correct answer, he gives 2 points; for each wrong answer, he subtracts 2/3 of a point; for unanswered questions, he neither gives nor subtracts points. If Denise scored a 68 and did not answer 2 of the questions, how many questions did she answer correctly?

A. 34

B. 36

C. 38

D. 40

E. 42

 

 

 

 

Answers: CBD

[vasanchurchill]

1. Ans is 1/14. Consider the number 138. One of the last two digits is wrong. Either 3 or 8 could be wrong. If 3 is wrong we have 7 options to fill this place-0,2,4,5,6,7,9.

similarly if 8 is wrong we have 7 options to fill this place-0,2,4,5,6,7,9. In all we have 14 options. He can choose any one in the first take and only one of them is correct. Therefore the probability is 1/14.

 

2. Ans is 27.

 

For questions of this type,

 

use this formula: x%*average of that group+(100-x)%*average of another group

 

which gives us .2*35+.8*25=7+20=27.

 

3. Ans is 40.

 

Let x be the number of questions answered correctly

Let y be the number of questions answered wrongly.

The number of questions answered = 58=x+y-------------------(1)

 

For correct answer, it is +2 points

For wrong answer, it is -2/3 points

 

Total points = (x times 2) minus (y times 2/3) = 68.

 

=x*2 -y*2/3 = 68-------------------(2)

 

Solving for equations (1) and (2) we get,

x=40 and y=18.

[infinityzero]

Thanks. That helps!