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In country Z, 10% of the people do not have a university dip
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Updated on: 27 Jun 2013, 02:04
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Difficulty:
75% (hard)
Question Stats:
60% (02:19) correct 40% (02:07) wrong based on 598 sessions
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In country Z, 10% of the people do not have a university diploma but have the job of their choice, and 25% of the people who do not have the job of their choice have a university diploma. If 40% of the people have the job of their choice, what percent of the people have a university diploma?
In country Z, 10% of the people do not have a university diploma but have the job of their choice, and 25% of the people who do not have the job of their choice have a university diploma. If 40% of the people have the job of their choice, what percent of the people have a university diploma? 35% 45% 55% 65% 75%
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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Can someone help me to understand why do we do 25 % of 60 instead of just adding 30 +25??
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
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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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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.
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60% (02:19) correct 
