You can use a Venn diagram to solve it too. 40% people have a job of their choice and 10% out of these 40% do not have diploma. That means 30% out of these 40% have a diploma and lie at the intersection of the two.
Now since 40% people have a job of their choice, 60% people do not have a job of their choice (i.e. they lie outside the 'choice job' circle). 25% of these 60% have a diploma.
Hence total % of people with diploma is 15% + 30% = 45%

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Set up a double matrix.
From the text we know that

ND and J = 10%
Call x the total of NJ (both with D and ND), and NJ and D=25%x and NJ and ND = 75%x
We know that J=40% so NJ=60% => x = 60%. Now complete the matrix, and then sum Diploma with J and Diploma with NJ : 30+15=45%

D and NJ is 25% of 60 => 15%of the total, not 25% of the total. So you cannot sum to 30 (which refers to the total) 25 (which does NOT refer to the total).

Hope it's clear

Setting up a matrix is how I solve this one.


Diploma No Diploma Totals
Job of Choice w/Diploma
Job of Choice w/o Diploma = 10%
Job of Choice Total = 40%
Not Job of Choice with Diploma =.25X
Not Job of Choice w/o Diploma= .75X
Total Not Job of Choice = X
Total with Diploma
Total without Diploma
Total citizen = 100
If 40% of people have their job of choice, then 60% of people do NOT have their job of choice. 25% of 60% = 15%. We can also see that 30% of the people have their job of choice and a diploma (40%-10%=30%). 30% + 15% = 45%. Therefore 45% of the people in Country Z have a diploma.
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this can be done using a matrix set as in the attached.

out of 100, 40 have desired jobs and 60 don't have.
out of 60,25% have university degree = 0.25 * 60 = 15

out of 40,10 do not have university degree but have desired job.
thus 30 have desired job as well as university degree

hence total = 30 + 15 = 45 have university degree.

Can someone help me to understand why do we do 25 % of 60 instead of just adding 30 +25??

Because the stem says that "25% of the people who do not have the job have a university diploma", not that "25% have a university diploma". 60% do NOT have the job, thus 25% of this group have a university diploma.

Hope it's clear.
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Bunuel, How would you solve this problem via equations??

solved it through double matrix

Is it wrong to assume that some proportion of people in country have neither a job nor a diploma?

Why not 10% of the 40%? Why we have directly used 10% in job and no University diploma?





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