In a certain office, 50 percent of the employees are college

Question

In a certain office, 50 percent of the employees are college graduates and 60 percent of the employees are over 40 years old. If 30 percent of those over 40 have master's degrees, how many of the employees over 40 have master's degrees?

(1) Exactly 100 of the employees are college graduates.
(2) Of the employees 40 years old or less, 25 percent have master's degrees.

Bunuel · Accepted Answer

In a certain office, 50 percent of the employees are college graduates and 60 percent of the employees are over 40 years old. If 30 percent of those over 40 have master's degrees, how many of the employees over 40 have master's degrees?

Let x be the number of employees in that office. Given that:
0.5x = college graduates;
0.6x = employees over 40;
0.3*0.6x = employees over 40 with master's degrees.

(1) Exactly 100 of the employees are college graduates --> 0.5x=100. We can find the value of x, thus we can determine the value of 0.3*0.6x. Sufficient.

(2) Of the employees 40 years old or less, 25 percent have master's degrees. We have no information about the number of employees in any group, only percentages. Not sufficient.

Answer: A.

MathRevolution · Answer

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem.
Remember equal number of variables and independent equations ensures a solution.

In a certain office, 50 percent of the employees are college graduates and 60 percent of the employees are over 40 years old. If 30 percent of those over 40 have master's degrees, how many of the employees over 40 have master's degrees?

(1) Exactly 100 of the employees are college graduates.
(2) Of the employees 40 years old or less, 25 percent have master's degrees.

Transforming the original condition and the question, we have the 2by2 table that is common in GMAT math test.

Attachment:

GC DS Walkabout In a certain office(20150921).jpg [ 56.35 KiB | Viewed 46188 times ]

From above, we just need to know E and therefore we are dealing with 1 variable. We need 1 equation to match the number of variable and equation. Since there is 1 each in 1) and 2), there is high probability that D is the answer.

In case of 1), 50E=100 gives us E=2, 18E=36. Therefore the condition is sufficient.
In case of 2), 40E*25%=10E=x, and we can't find the value for E. Therefore the condition is not sufficient. The answer is A.

Normally for cases where we need 1 more equation, such as original conditions with 1 variable, or 2 variables and 1 equation, or 3 variables and 2 equations, we have 1 equation each in both 1) and 2). Therefore D has a high chance of being the answer, which is why we attempt to solve the question using 1) and 2) separately. Here, there is 59 % chance that D is the answer, while A or B has 38% chance. There is 3% chance that C or E is the answer for the case. Since D is most likely to be the answer according to DS definition, we solve the question assuming D would be our answer hence using 1) and 2) separately. Obviously there may be cases where the answer is A, B, C or E.

linglinrtw · Answer

In a certain office, 50 percent of the employees are college graduates and 60 percent of the employees are over 40 years old. If 30 percent of those over 40 have master's degrees, how many of the employees over 40 have master's degrees?

(1) Exactly 100 of the employees are college graduates

(2) Of the employees forty years old of less, 25 percent have master's degrees

The OA is A.

I agree with the OA if college graduates are in the same group as people with master's degrees. However, in real world, not all college graduates have master's degree. No?

NonYankee · Answer

The first statistic (50% of employees are "college graduates") is a red herring. We don't need it to answer the question asked. The final question concerns master's degrees, and we never got any info about the breakdown of degrees held among college grads. We know 60% of employees are over 40, and 30% of those over 40 have a master's degree. So the number of employees over 40 with a master's degree will be 0.3*0.6*(number of employees).

The second statement would be sufficient IF we knew the total number of master's degrees or the total number of employees. But we don't, not unless we use the first statement. The first statement alone is sufficient, whereas the second is not.

The second statement would be sufficient IF we knew the total number of master's degrees or the total number of employees. But we don't, not unless we use the first statement. The first statement alone is sufficient, whereas the second is not.

Bunuel · Answer

Merging similar topics. Please refer to the solutions above. Also, please read and follow: rules-for-posting-please-read-this-before-posting-133935.html And finally, please hide OA's under the spoiler. Thank you.

tsunagaru · Answer

Hi,

I would like to follow up on the post of linglinrtw, I initially answered the good answer however when re-reading the text, in order to be able to answer the question, we need to make an assumption on the population (it is not either college degree or master degree, it could be something else).

Basically, in many overlapping problems, it is not clearly stated black or white; 1 or 0; and never in the answer this assumption is taken into account.

However, this kind of assuption would be exactly the kind of flaws that the GMAT asks us to find in critical reasoning in the verbal part.

Am I to demanding and should take for granted the assumption in those kind of problem? What do you think? 
Thanks a lot!

EgmatQuantExpert · Answer

Your doubt is very valid. In fact, in this question, if you try to segregate the groups in a tree structure format and assume that college degree and master's degree are the only two subcategories, you'll see that your inferences would go against the information given in statement 2. (Try it for yourself. Let me know if you need my help in this.

) That essentially indicates that the categories listed out in the question are not exhaustive. However, the question very clearly asks about the number of employees " Above the age 40 AND having a Master's degree ". The percentages given are also exactly relevant to this. ( % of employees above 40 and % of master's degree holders among employees above 40 ) So the problem essentially boils down to finding the total number of employees in the office itself. In other words, we need not worry about other possible groups among these employees.

In questions where grouping needs to be conveyed very clearly, the GMAT makes sure that the classification is unambiguous. For instance, Red colored balls and Blue colored balls AND Big and small balls among each color. (There is no scope of confusion here because a ball cannot be both Red and Blue at the same time.

) Hope this helps.

Regards, Krishna

carrerswitch · Answer

Hi,

Could you help me understand what I am doing wrong here. 
According to Statement 2, 
25% of the 40% of the employees( since 60% are 40 years old) have masters degree and are either 40 or under 40. 
The question stem tell us that 50% of all employees are college graduates (which the question is assuming is same as masters degree)
so why can I not make an equation out of it?
(.25)(.4x) + (.3)(.6x)= (.5x)

Thanks

Bunuel · Answer

College graduates and those who have a master degree are not the same group.

carrerswitch · Answer

Merging similar topics. Please refer to the solutions above.

Also, please read and follow: rules-for-posting-please-read-this-before-posting-133935.html

And finally, please hide OA's under the spoiler. Thank you.[/quote]

Hi,

Could you help me understand what I am doing wrong here.
According to Statement 2,
25% of the 40% of the employees( since 60% are 40 years old) have masters degree and are either 40 or under 40.
The question stem tell us that 50% of all employees are college graduates (which the question is assuming is same as masters degree)
so why can I not make an equation out of it?
(.25)(.4x) + (.3)(.6x)= (.5x)

Thanks[/quote]

College graduates and those who have a master degree are not the same group.[/quote]

Thanks. I should not make such assumptions

zoezhuyan · Answer

Hi experts,

I need your help,
I picked up E, because I doubt whether there are only two group , master and college, in the certain company.
and the question does not state only two group in the company.

no matter statement #1 or #2 or both #1 and #2, each is insufficient,

please clarify.

thanks in advance
have a nice day
>_~

fskilnik · Answer

This would be a perfect place for the "grid" (double matrix, table, you-name-it) ... but there is one more characteristic involved than expected, correct?

In this (rare) case our method suggests the following:

Put in the "grid" two of the three characteristics, the ones with "more info"... the third characteristic is dealt "in parallel" ... see the grid below!

https://preview.ibb.co/fcwzRz/02_Oct18_2w.gif

Now it´s really simple...

\left( 1 \right)\,\,5T = 100\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,? = {3 \over {10}}\left( {6T} \right)\,\,\,\,{\rm{unique}}\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{SUFF}}.

(2) Insufficient: one possible VIABLE BIFURCATION (36 or 18, when T equals 20 or 10) is shown in blue and pink below:

https://preview.ibb.co/b8cneK/02_Oct18_5f.gif

This solution follows the notations and rationale taught in the GMATH method.

Regards, 
Fabio.

Hoozan · Answer

Similar Question: https://gmatclub.com/forum/in-a-certain ... 48439.html

GMATinsight · Answer

Answer: Option A

Video solution by  GMATinsight

https://www.youtube.com/watch?v=6rDyNz0c_8k

Elite097 · Answer

When we solve St 2 qhat is happening why are the equations not adding up and how do we know master s degree and graduates are different?  MartyTargetTestPrep  ? Also  GMATinsight  how did you get 32% for grads? The sum of all 4 boxes is 50% and not just those 2.  KarishmaB

KarishmaB · Answer

This is given to us in the question stem: Screenshot 2022-06-13 at 10.22.37 AM.png Since 30% of those over 40 yrs (which is 60% of Total) have masters degree, the crimson section is 30% of 60% of Total = 18% of Total We need to find the value of this 18% of Total for which we need the Total. (1) Exactly 100 of the employees are college graduates. College grads = 50% of Total = 100 This gives us Total Sufficient alone. (2) Of the employees 40 years old or less, 25 percent have master's degrees. This again gives us percent information. We need at least one actual value to get the actual number of people who are 40+ yrs with masters degree. Without any actual numbers, we cannot get this value. Not sufficient Answer (A)

Elite097 · Answer

GMATinsight  pls answer the question about the video solution posted by you. Certainly something is offabout it. How can it be 32%? Also if it is 32% of total then it s even more wrong.

KarishmaB  how did you know about distinguishing grads from masters?

GMATinsight · Answer

Hi Elite097 check video now. You pointed out the right thing and I have updated the video.

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In a certain office, 50 percent of the employees are college

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In a certain office, 50 percent of the employees are college

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