In country Z, 10% of the people do not have a university dip

Question

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?

A. 35%
B. 45%
C. 55%
D. 65%
E. 75%

Show Answer

Official Answer

B

A. 35%
B. 45%
C. 55%
D. 65%
E. 75%

Zarrolou · Accepted Answer

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

KarishmaB · Answer

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% Ques2.jpg

cheetarah1980 · Answer

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.

agdimple333 · Answer

this can be done using a matrix set as in the attached.

amit2k9 · Answer

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.

skamal7 · Answer

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

Bunuel · Answer

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.

mvictor · Answer

solved it through double matrix

bumpbot · Answer

Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.

In country Z, 10% of the people do not have a university dip

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

In country Z, 10% of the people do not have a university dip

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards