Problem Soving question : Similar question in ORG as well

[freedomfromIT]

Of 40 applicants for a job, 32 had at least
5 years of prior work experience, 24 had
advanced degrees, and 16 had at least
5 years of prior work experience and
advanced degrees. How many of the
applicants had neither 5 years of prior
work experience nor advanced degrees?
A. 0
B. 2
C. 4
D. 8
E.16

How do we go about soving this question .I have seen similar question in ORG 12 revsion PS 169 0r 167 .Can any one guide on this?

[DanaJ]

There are two traits attributed (or not) to members of a group of 40 people:
- at least 5 years of experience
- advanced degree

Those that have at least 5 years of experience are made up of those that either have or do not have an advanced degree. Since we know 16 people hold an advanced degree and have 5 years of work experience, then 16 peoplee (i.e. 32 - 16) have the experience but don't have a diploma.

Those that have a diploma can be categorized in people with or without the required experience. Again, since you have 16 people with both traits, then in this case you'll have 8 candidates (24 - 16) with an advanced degree, but without work experience.

So all this brings you to:
- 16 people with both
- 16 people with experience, but no advanced degree
- 8 people with an advanced degree, but no work experience
- x people with neither

x will of course be 40 - 16 - 16 - 8 = 0.

There are of course other ways of solving this without going through the mental reasoning outlined above, but I've always had trouble getting the formulas to stick to my brain, so i always double check... When you have a group of objects with two traits, a and b, then you will get that:

total = (objects with a) + (objects with b) - (objects with both) + (objects with neither a nor b)

In this case:

40 = 32 + 24 - 16 + x =40 + x ---- x = 0.

[freedomfromIT]

Kewl!!!! Thanks fr such a prompt reply .Di u have a chnace to go thru the PS 169 in ORG 12 rev ..Both are similar.So this last shortcut helps in solving that as well?

[DanaJ]

I don't have the OG 12, so I can't say I've looked at them. But I can tell you one thing: if they're similar to the problem above, then using this formula will surely provide the correct answer.

[hetavdave]

DanaJ,
I thinking i am making some some stupid mistake somewhere but I am unable to trace out where i am going wrong. My ans was 0.

Can you please help me on this?

[DanaJ]

DanaJ,
I thinking i am making some some stupid mistake somewhere but I am unable to trace out where i am going wrong. My ans was 0.

Can you please help me on this?

Actually, it was I who was making the mistake. After analyzing your spreadsheet, I realized that I'd considered the number of people who hold a degree as 16 instead of 24 (just a mix-up - I didn't read the thing properly). The reasoning was still correct and the formula applies, but I'd get a wrong answer. Thanks for the heads up!

[shanmugam.d]

another way of tabulating (see the attached image):