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For the team of salespeople in organization X, the amount of incentive

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For the team of salespeople in organization X, the amount of incentive [#permalink]

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New post 30 Sep 2017, 08:02
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For the team of salespeople in organization X, the amount of incentive provided (I) was found to be directly proportional to the sales in dollars (S) and the sales were found to be directly proportional to the Job satisfaction index (J). If the sales in the month of March of a certain year were $30000, find the value of the job satisfaction index in March?
(1) J = 0.5 whenever S = $10000
(2) I = 100 whenever S = $5000

The official answer is A, but shouldn't the answer be D? GMAT Ninjas, please help!

Last edited by baldelementary on 30 Sep 2017, 08:32, edited 1 time in total.

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Re: For the team of salespeople in organization X, the amount of incentive [#permalink]

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New post 30 Sep 2017, 08:17
baldelementary wrote:
For the team of salespeople in organization X, the amount of incentive provided (I) was found to be directly proportional to the sales in dollars (S) and the sales were found to be directly proportional to the Job satisfaction index (J). If the sales in the month of March of a certain year were $30000, find the value of the job satisfaction index in March?
(1) J = 0.5 whenever S = $10000
(2) I = 100 whenever S = $5000

Shouldn't the answer be D? GMAT Ninjas, please help!


Given \(I=aS\) (where \(a\) is some constant) and \(S=bJ\) (where \(b\) is some constant)
We need to find \(J\) when \(S=30000\)

Statement 1: \(S=10000\) then \(J=0.5\) and since \(S\) is directly proportional to \(J\), the value of \(J\) when \(S=30000\) will be

\(J=\frac{0.5}{10000}*30000=1.5\) Hence Sufficient.

This can also be derived as \(S=bJ\), so \(10000 =b*0.5\) or \(b=\frac{10000}{0.5}\)
so \(S=30000=bJ=>\) \(J=\frac{0.5}{10000}*30000=1.5\)

Statement 2: \(I=aS => 100=a*5000\), so we can calculate the value of \(a\). But to calculate the value of \(J\) we need to know the value of constant \(b\) which we cannot get from this statement. Hence Insufficient

Option A

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Re: For the team of salespeople in organization X, the amount of incentive [#permalink]

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New post 30 Sep 2017, 08:33
Bunuel Please help! As I understand when X is proportional to Y and Y is proportional to Z then X is proportional to Z. In which case the answer should be D.

Thanks for helping out!

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Re: For the team of salespeople in organization X, the amount of incentive [#permalink]

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New post 30 Sep 2017, 08:38
For the team of salespeople in organization X, the amount of incentive provided (I) was found to be directly proportional to the sales in dollars (S) and the sales were found to be directly proportional to the Job satisfaction index (J). If the sales in the month of March of a certain year were $30000, find the value of the job satisfaction index in March?

Given I and S are directly proportional and S and J are directly proportional
Here we have to find J when S = 30000



(1) J = 0.5 whenever S = $10000
=> When S = 10000 => J = 0.5
=> So When S = 1 => J = 0.5/10000
=> So when S = 30000 => J= 0.5/10000 * 30000 = 1.5
J=1.5
Answer. Sufficient

(2) I = 100 whenever S = $5000
=> When S = 5000 => I =100

So here we can calculate value of I for S =30000. But as we don't know relation between S and J or I and J, we cannot find value of J here ( We just know S and J are directly proportional that's it)
So Insufficient

Answer: A

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Re: For the team of salespeople in organization X, the amount of incentive [#permalink]

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New post 30 Sep 2017, 08:42
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hussammasood wrote:
Bunuel Please help! As I understand when X is proportional to Y and Y is proportional to Z then X is proportional to Z. In which case the answer should be D.

Thanks for helping out!


Hi hussammasood

You are correct in assuming that x will be directly proportional to z but when you frame an equation, you need to have a constant to replace proportionality with equality.
In this case constants will be different, hence the value will be different.

For eg. x=ay and y=bz
so x=abz (substitute the value of y). Hence here the constant is "ab" and you need to know the value of this constant.
That is why the answer will not be D as you cannot calculate the value of the constant

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Re: For the team of salespeople in organization X, the amount of incentive [#permalink]

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New post 30 Sep 2017, 08:46
Hey niks18

Thank you for clearing it up. I've been confused for the past hour. Really appreciate it.

Cheers

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Re: For the team of salespeople in organization X, the amount of incentive   [#permalink] 30 Sep 2017, 08:46
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