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Sets tough Problem Try it......

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Director
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Sets tough Problem Try it...... [#permalink] New post 03 Jan 2012, 04:48
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XYZ Tech is an IT company with 100 employees who all are software developers.The ratio of developers working on Java to developers working on PHP is 5:3.The ratio of developers working on PHP to developers working on Java and PHP is 6:4.The ratio of developers working on PHP to developers not working on Java and PHP is 3:1.

Find.
1. How many developers work only on Java?
2. How many developers work only on PHP?
3. How many developers work only on both Java and PHP?
4. How many developers neither work on Java nor PHP?

Answers for the 4 questions are
1.50
2.10
3.20
4.10
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Re: Sets tough Problem Try it...... [#permalink] New post 03 Jan 2012, 10:13
Still working on figuring out the right answer but the answers posted cannot be correct. They total number of employees in the answers you gave add up to 90 and the total number of employees is 100 will work on the answer and get back to you on that.
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Re: Sets tough Problem Try it...... [#permalink] New post 04 Jan 2012, 00:24
Expert's post
kotela wrote:
XYZ Tech is an IT company with 100 employees who all are software developers.The ratio of developers working on Java to developers working on PHP is 5:3.The ratio of developers working on PHP to developers working on Java and PHP is 6:4.The ratio of developers working on PHP to developers not working on Java and PHP is 3:1.

Find.
1. How many developers work only on Java?
2. How many developers work only on PHP?
3. How many developers work only on both Java and PHP?
4. How many developers neither work on Java nor PHP?

Answers for the 4 questions are
1.50
2.10
3.20
4.10


There is a problem with the numbers given (as pointed out in the post above). The solution would look something like this:

Ratio of developers working on Java:developers working on PHP = 5:3
Ratio of developers working on PHP:developers working on both = 6:4 = 3:2
Ratio of developers working on PHP:developers not working on Java and PHP = 3:1

Ratio of developers working on Java:developers working on PHP:developers working on both:developers working on neither Java nor PHP = 5:3:2:1

Say, developers working on Java is 5n. Then developers working on PHP is 3n, developers working on both is 2n and developers working on neither is n.

100 - n = 5n + 3n - 2n
100 = 7n
n cannot be a non-integral value since it represents the number of people. This is the problem with the numbers here. Either total number of people cannot be 100 or some of the ratios are incorrect.
Once we get n, it is straightforward to find everything needed.
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Re: Sets tough Problem Try it...... [#permalink] New post 04 Jan 2012, 11:57
I won't provide a complete numerical solution, but will give equations to work with.

First, let number of only Java = x, number of only PHP = y, number of Java + PHP = z

First ratio: J:P = 5:3 -> (x+z)/(y+z) = 5/3
Second ratio: P:(J+P) = 6:4 -> (y+z)/z = 6/4
Third ratio: P: !(J+P) = 3:1 -> (y+z)/[100-(x+y+z)] = 3/1

May be try solving the above equations. However, Karishma's explanation sounds easier. I tried to solve it in Venn diagram form.
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Director
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Re: Sets tough Problem Try it...... [#permalink] New post 04 Jan 2012, 17:11
VeritasPrepKarishma wrote:
kotela wrote:
XYZ Tech is an IT company with 100 employees who all are software developers.The ratio of developers working on Java to developers working on PHP is 5:3.The ratio of developers working on PHP to developers working on Java and PHP is 6:4.The ratio of developers working on PHP to developers not working on Java and PHP is 3:1.

Find.
1. How many developers work only on Java?
2. How many developers work only on PHP?
3. How many developers work only on both Java and PHP?
4. How many developers neither work on Java nor PHP?

Answers for the 4 questions are
1.50
2.10
3.20
4.10


There is a problem with the numbers given (as pointed out in the post above). The solution would look something like this:

Ratio of developers working on Java:developers working on PHP = 5:3
Ratio of developers working on PHP:developers working on both = 6:4 = 3:2
Ratio of developers working on PHP:developers not working on Java and PHP = 3:1

Ratio of developers working on Java:developers working on PHP:developers working on both:developers working on neither Java nor PHP = 5:3:2:1

Say, developers working on Java is 5n. Then developers working on PHP is 3n, developers working on both is 2n and developers working on neither is n.

100 - n = 5n + 3n - 2n
100 = 7n
n cannot be a non-integral value since it represents the number of people. This is the problem with the numbers here. Either total number of people cannot be 100 or some of the ratios are incorrect.
Once we get n, it is straightforward to find everything needed.


Thanks you made it look simple.......

+1 Kudos for you
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Re: Sets tough Problem Try it...... [#permalink] New post 04 Jan 2012, 20:24
VeritasPrepKarishma wrote:
kotela wrote:
XYZ Tech is an IT company with 100 employees who all are software developers.The ratio of developers working on Java to developers working on PHP is 5:3.The ratio of developers working on PHP to developers working on Java and PHP is 6:4.The ratio of developers working on PHP to developers not working on Java and PHP is 3:1.

Find.
1. How many developers work only on Java?
2. How many developers work only on PHP?
3. How many developers work only on both Java and PHP?
4. How many developers neither work on Java nor PHP?

Answers for the 4 questions are
1.50
2.10
3.20
4.10


There is a problem with the numbers given (as pointed out in the post above). The solution would look something like this:

Ratio of developers working on Java:developers working on PHP = 5:3
Ratio of developers working on PHP:developers working on both = 6:4 = 3:2
Ratio of developers working on PHP:developers not working on Java and PHP = 3:1

Ratio of developers working on Java:developers working on PHP:developers working on both:developers working on neither Java nor PHP = 5:3:2:1

Say, developers working on Java is 5n. Then developers working on PHP is 3n, developers working on both is 2n and developers working on neither is n.

100 - n = 5n + 3n - 2n
100 = 7n
n cannot be a non-integral value since it represents the number of people. This is the problem with the numbers here. Either total number of people cannot be 100 or some of the ratios are incorrect.
Once we get n, it is straightforward to find everything needed.


I used the below approach.

let number of only Java = x, number of only PHP = z, number of Java + PHP = y

so acc to the question:

(x+y)/(y+z) = 5/3
(y+z)/y = 6/4
(z+y)/z = 3/1

on solving the above 3 equations we get
x=3z, y=2z and z

so x+y+z = 100 => 6z = 100

for the first question we have to get the value of x => 3*50/3 = 50
but for the remaining question I am getting answers in farctions.

I think the question is not correct. Correct me if I am wrong.
Re: Sets tough Problem Try it......   [#permalink] 04 Jan 2012, 20:24
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