This is GMAT Prep Question :GRAPHICAL INTERPRETATION

[pranaygoyal02]

Refer to the pictograph of a survey of students at Central Community College. Each Symbol represents 10 students in a sample of 300

Use the drop-down menus to complete each statement according to the information presented in the diagram.

If one student is selected at random from the 300 surveyed, the chance that the student will be under 30 or a high school graduate or both is



If one student is selected at random from the 300 surveyed, the chance that the student will be both under 30 and a high school graduate is



Hi Instructors

Could you please help me out how to solve this particular question on sets.

[tim]

Before we help with this question, we need you to show some effort of your own. What did you try on this question? Where did you get stuck?

[pranaygoyal02]

Hi Tim

Here is where I have landed up :
The students under 30 are the ones which are outside the first circle and students who are high school graduate are the ones which are outside the second circle. Now a student who is 30 years of age or high school graduate or both should be a sum of all the students who are outside both these circle.The students outside the circle is 100. so the ratio can be 100/300.

I know the sets theorem which states :

AUB=A +B- (A intersection B)

How to use this here ??
And I am so confused about the "and" clause used here in the next question.And my answer is still 100 for "and" clause.

Where am I going wrong?:(

[RonPurewal]

Hi Tim

Here is where I have landed up :
The students under 30 are the ones which are outside the first circle and students who are high school graduate are the ones which are outside the second circle. Now a student who is 30 years of age or high school graduate or both should be a sum of all the students who are outside both these circle.The students outside the circle is 100. so the ratio can be 100/300.

nope. you're confusing "and" with "or".

think about something like "people with red OR blond hair" --> this is all the people with red hair, plus all the people with blond hair.

so here, you have anybody who is under 30 OR a high school graduate (or both)... so you have to count everyone who has at least one of these attributes.
that's everyone in the entire diagram except the football-shaped middle region, so we're looking at 250 out of 300 = 5/6.

I know the sets theorem which states :

AUB=A +B- (A intersection B)

How to use this here ??

you don't, really.
your "a" and "b" are extremely awkward here, because the desired conditions correspond to areas OUTSIDE the circles. so, for instance, if "a" is "under", then the "a" region is everything OUTSIDE the "30 or older" circle; that's the awkward combination of the top row (the stuff outside both circles) and the right-hand region.
it gets even uglier once you try to combine "a" with "b", which is just as ugly as "a".

in fact, there is very little doubt in my head that this problem is deliberately designed as a counterstrike against people who over-rely on the formula you've cited.

And I am so confused about the "and" clause used here in the next question.And my answer is still 100 for "and" clause.

Where am I going wrong?:(

"Under 30 and a h.s. graduate" is just the top part, so that should indeed be 100 students out of 300.

[pranaygoyal02]

Thanks Ron!It indeed helped me out.

[tim]

:)

[BernardK777]

Ron,

You said this in a previous post regarding how to attack the first part of the question: "so here, you have anybody who is under 30 OR a high school graduate (or both)... so you have to count everyone who has at least one of these attributes."

I'm still a bit confused as how to count this. For those less than 30, the answer explanation says those people are represented by the symbols outside of the left circle. Does this also include the symbols that are not in the Ven Diagram at all?

Here's how I thought about it:

Probability <30 = 40/300
Probability H.S.G. = 110/300
Pr(both) = 100/300

Add them up --> 250 / 300 = 5/6

Is this correct?

Thanks for the help?

[tim]

Are "symbols that are not in the Ven [sic] Diagram at all" outside the left circle? :) Technically the Venn Diagram encompasses everything that is in the picture, not just what's inside one or more circles.

You have actually added these correctly; just keep in mind that you have added three distinct regions, and P(<30) is not actually 40/100; instead P(<30 AND not H.S.G) is 40/100 - but this is what you wanted to use anyway. Do you see why?

[RonPurewal]

On a separate note--

The condition is "under 30 or a high school graduate or both".

That's a very ugly condition with a lot of words. It also makes you count lots of things.

On the other hand, you might want to think about the fact that non-graduates over 30 are the only people who don't satisfy the condition.
(If that's too hard to figure out from the words, you can also just look at the picture, and note that "under 30 or a high school graduate or both" encompasses everybody except one region of the diagram.)

If you have the number of people who don't satisfy the condition, then finding the number of people who do is not much further work.

[BernardK777]

Ron and Tim,

Thank you for the responses.

Tim,

If I understand your comment correctly that the Venn Diagram encompasses everything that is in the picture, not just what's inside one or more circles, then shouldn't my calculations have been the following:

Pr(<30) = 140 / 300
Pr(H.S.G.) = 210 / 300
P(both) = 100 / 300

Then to avoid double counting, you would subtract out P(both)

Pr(<30) + Pr (H.S.G.) - P(both) = 250 / 300 = 5 / 6

[tim]

Yes, that is the more conventional way to do this one (and it is generalizable more easily to larger numbers of sets).

[StephanieP33]

Hi
Could someone please post the answer to the second question?
Thanks

[Sage Pearce-Higgins]

To answer the second question, consider how many people are 'both under 30 and a high school graduate'. These people are represented by the symbols outside both circles, i.e. 100 students.

The probability of choosing one of these students will be 100/300, which is 1 in 3.