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Problem Solving

Expert replies
by phoenix9801 » Wed May 30, 2012 11:43 pm
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?
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Source: — Problem Solving |

by aneesh.kg » Thu May 31, 2012 3:05 am
phoenix9801 wrote: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 Bangia
GMAT Math Coach
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by aneesh.kg » Thu May 31, 2012 3:08 am
phoenix9801 wrote: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 Bangia
GMAT Math Coach
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GMATPad:
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Join the discussion

by aneesh.kg » Thu May 31, 2012 3:10 am
phoenix9801 wrote: 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 Bangia
GMAT Math Coach
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GMATPad:
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by aneesh.kg » Thu May 31, 2012 3:12 am
phoenix9801 wrote: 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.
Aneesh Bangia
GMAT Math Coach
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GMATPad:
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