Problem Solving

[phoenix9801]

1-
Which of the following could be the average of three integers?

Indicate all such values.

A) 33
B) 31
C) 89/3
D) 91/4
E) 101/6
F) 20

2-
The amount of money Tim makes selling DVDs is directly proportional to the number of days he has been working. If Tim manages to make $765 after 20 days, how many days does he have to work to make $1071?

3-
Sawyer is able to solve 10x questions every 3y hours. If he works at the same rate, in how many hours will he be able to solve 57 questions?

a) 57x/10y
b) 171y/10x
c) 171x010y
d) 10x/171y
e) 10y/171x


4-
If Rafa hits 163 serves in the first two hours he practices, how many more hours will it take him to hit 978 serves at the same rate?

[aneesh.kg]

1-
Which of the following could be the average of three integers?

Indicate all such values.

A) 33
B) 31
C) 89/3
D) 91/4
E) 101/6
F) 20

Average = Sum of integers/3
Sum of integers = 3*(Average)
Since Sum of integers must be an integer, 3*Average must be an integer.

Option [spoiler](A),(B),(C),(F)[/spoiler] when multiplied by 3 render an integer values. Those are the correct options.

Alternatively:
(by plugging-in values)

(A) works for 32, 33, 34 and many others.
(B) works for 30, 31, 32 and many others.
(C) works for 1, 2, 86 and many others.
(D) does not work for set of three integers.
(F) does not work for any set of three integers.
(F) works for 19, 20, 21 and many others.

[aneesh.kg]

1-

2-
The amount of money Tim makes selling DVDs is directly proportional to the number of days he has been working. If Tim manages to make $765 after 20 days, how many days does he have to work to make $1071?

Since the amount of money earned is directly proportional to number of days worked,

Money/Days = constant

M1/D1 = M2/D2
765/20 = 1071/x
x = 28

He was to work for 28 days.

[aneesh.kg]

3-
Sawyer is able to solve 10x questions every 3y hours. If he works at the same rate, in how many hours will he be able to solve 57 questions?

a) 57x/10y
b) 171y/10x
c) 171x010y
d) 10x/171y
e) 10y/171x

Rate = Number of questions solved/Time spent

Since the rate is same in both cases,
N1/T1 = N2/T2
10x/3y = 57/T2
T2 = 171y/10x

[spoiler](B)[/spoiler] is correct.

[aneesh.kg]

4-
If Rafa hits 163 serves in the first two hours he practices, how many more hours will it take him to hit 978 serves at the same rate?

'more' is the word one has to notice here.
Since the rate is same,
S1/T1 = S2/T2
163/2 = 978/T2
T2 = 12

or [spoiler]12 - 2 = 10[/spoiler] more hours.