Refer to the pictograph of a survey of students at Central Community

Question 2 : option B

Question 1 : Am getting 7/6 which I think is wrong.

350/300 is what am getting for Q1

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D,B are right answers.

1) 140/300(Student under 30)+ 210/300(high school graduate)-100/300(both) = 5/6

2)Both = 100/300 =1/3

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how does under 30 is covered by left circle, it clearly says it is 30 age or older, that means can be either 30 or more than 30.

For first part of question:

We are asked: 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

Rem- we are asked 1)student will be under 30 OR 2) a high school graduate OR 3) BOTH

OR = Add

Now we have some values in the circles and some outside the circle,Lets write them down

30 years of age or older ( Circle on Left)= 11* 10= 110

No high school diploma ( Circle on Rt)=4*10=40

Both ( 30yrs of age or older and No high school diploma) = 5*10

Now look at the symbols above both circles. We are asked question which includes them also.
Lets bifurcate them as well

Symbols above left circle =5*10=50 Which indicated students under 30

Symbols above Rt circle=3* 10=30 Which indicates students with High school diploma

and symbol above middle are ( Both region) = 2*10= 20 which indicates students both under 30 and with high school diploma.

Now Lets ans question

Pr(<30)= 40+50+20+30 /300 = 140 / 300
( Note : students under 30 includes all except those 30 or older)

Pr(H.S.G.) = 110+50+20+30/300= 210 / 300
Includes all except students with no highschool diploma

P(both) = 50+20+ 30/300= 100 / 300

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

Pr(<30) + Pr (H.S.G.) - P(both)
=140+210-100
= 250 / 300 = 5 / 6

Ans is 5/6

Hope this helps

Yes you are getting 7/6 be adding 140 and 210.
140 foe students under 30 and 210 for high school graduates.
But these 210 High school graduates include those 100 under 30 students also.
You need to subtract that 100. After that you'll get 250/300

BrentGMATPrepNow how did you figure out that those symbols above two circles are high diploma... i mean those marked in red circle had no idea what it meant

is it some kinda new overlapping set?

in one word whattta group those symbols above stand for ? And why ? in the diagram it is not indicated these are high school group :/

First off, I should mention that having a high school diploma is the same as having graduated from high school.
Every person INSIDE the right circle did not graduate from high school.
This means every person OUTSIDE the right circle DID graduate from high school.
So all of the people shaded in blue DID graduate from high school.

Similarly, every person INSIDE the left circle are 30 or older
This means every person OUTSIDE the left circle are NOT 30 or older.
So, all of the people shaded in red are NOT 30 or older.
In other words, all of the people shaded in red are UNDER 30.

Does that help?

BrentGMATPrepNow many thanks! yes:)

btw BrentGMATPrepNow in the second image, in the circle to the right there are 4 symbols, in the overlap - 5 symbols: so if number of symbols in overlap exceeds that of in right circle, then group (4 symbols) can`t be under 30 pls explain

I'm not entirely sure what you're asking but I can tell you this with regard to the right circle.
Since there are 9 symbols inside the right circle, we know that 90 people do NOT have a high school diploma.
Among those 9 symbols inside the right circle, 5 symbols overlap with the left circle.
This tells us that, among the 90 people who do NOT have a high school diploma, 50 of them are 30 years or older.
But this means the remaining 40 people inside the right circle are under 30 years of age.

Does that help?

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Matrix
Q1: 140 + 110 = 250; Total 300
250/300 = 5/6
Q2
Both = 100; Total 300
100/300= 1/3

I think this question is a bit confused me a lot.
How can we conclude something outside of the circle to opposite things in the circle?
The outside should be labeled as well; otherwise, it can be interpreted in many ways, such as people who are under 25, hold Ph.D., etc.,

­1. 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 [5/6]

P(Under 30) + P(High school graduate) + P(Both) = 1 - P (>30 & No Diploma)

>30 & No Diploma: the overlapping area of the 2 circles => P (>30 & No Diploma) = 50/300 = 1/6

==> P(Under 30) + P(High school graduate) + P(Both) = 1 - 1/6 = 5/6


2. 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 [1/3]

Under 30 + High school graduate ==> Those are not in any circle

P (Under 30 + High school graduate) = 100/300 = 1/3