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

Question

https://gmatclub.com/blog/wp-content/uploads/2023/10/11.jpg

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.

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  GRAPH_1_PLACEHOLDER

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  GRAPH_2_PLACEHOLDER

BrentGMATPrepNow · Accepted Answer

A student asked me to comment on question #1, so .....

The circle on the left holds all of the students who are 30 or over. 
So all of the students who are UNDER 30 are OUTSIDE that circle.
So the students who are under 30 years of age are circled in red. 
 https://i.imgur.com/nay7nQ2.png

The circle on the right holds all of the students who did NOT graduate high school. 
So all of the students who are OUTSIDE that circle are students who DID graduate. 
So the students who graduated are circled in blue.
 https://i.imgur.com/OOI8ulQ.png

This means all of the students circled in green (below) represent students who are under 30, a high school graduate or both
 https://i.imgur.com/reZkGBx.png

There are 250 such people. 
So, P(selected student is under 30, a high school graduate or both) = 250/300 = 5/6 = 5 out of 6

Answer: D

Cheers,
Brent

urshi · Answer

Question 2 : option B

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

350/300 is what am getting for Q1

Posted from my mobile device

Bunuel · Answer

Drop-down 1: Only the students in the intersection of the two circles do not qualify. All others are either under 30 or high school graduates or both. Therefore, (30 - 5)/30 = 5/6. https://gmatclub.com/forum/download/file.php?id=82851 Drop-down 2: Those would be the students who are outside both circles. So, 10 out of 30, or 1 out of 3. https://gmatclub.com/forum/download/file.php?id=82852 Hope this helps. GMAT-Club-Forum-dtykmqm4.png GMAT-Club-Forum-3pu7zuqs.png

Apt0810 · Answer

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

Posted from my mobile device

Sajjad1994 · Answer

Official Explanation

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

The students who are under 30 years old are represented by the symbols outside the left circle. The students who are high school graduates are represented by the symbols outside the right circle. Thus, the students who meet the criteria in the sentence will be represented by all symbols except those in the intersection of the two circles. The intersection contains 5 symbols, which represent 50 students out of the 300 in the sample. Thus, 250 out of the 300 students, which is equivalent to 5 out of 6, are under 30 or a high school graduate.

The correct answer ts 5 out of 6.

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

A process of elimination is useful in completing this sentence. Given the criteria in the sentence, all the students represented by symbols in the over-30 circle and in the no diploma circle can be eliminated, leaving only the 10 symbols outside both circles. These 10 symbols represent 100 students of the total 300. Therefore, there is a 1 in 3 chance a student chosen at random is both under 30 and a high school graduate.

The correct answer is 1 out of 3.

Hope it helps

Kshah001 · Answer

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

dave13 · Answer

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

BrentGMATPrepNow · Answer

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?

dave13 · Answer

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

BrentGMATPrepNow · Answer

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?

avigutman · Answer

Video solution from Quant Reasoning starts at 2:41 Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1 https://www.youtube.com/watch?v=Z2jf8u78rQY

BLTN · Answer

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

Ghoskrp3 · Answer

From the Venn diagram, we can directly divide Students in 4 Categories using a table format:

Category	Students	Scenario
1	100	<30 yrs + Diploma
2	40	<30 yrs
3	50	>= 30 yrs
4	110	>= 30 yrs + Diploma

Q1. Referring to students less than 30 years of age or having diploma or both would comprise: Scenario 1, 2 & 4:
=> \( \frac{(100 + 40 + 110)}{300} \)
=> \( \frac{250}{300} \) => 5/6

Q2. Referring to only students under 30 years of age and also having diploma (high school graduation) would comprise: Scenario 1
=> \( \frac{100}{300} \)
=> 1/3

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

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