In a school that had a total of 600 students enrolled in the junior

In DS questions always try to have an idea of the Maximum or Minimum (range of) values that are possible -

In a school that had a total of 600 students enrolled in the junior and senior classes, the students contributed to a certain fund. If all of the juniors but only half of the seniors contributed, was the total amount contributed more than $740 ?

(1) Each junior contributed $1 and each senior contributed gave $3.
(2) There were more juniors than seniors enrolled in the school.


(1) Each junior contributed $1 and each senior contributed gave $3.

For Max contribution -
We should assume most students to be seniors and least students to be juniors.
So we have 598 seniors and 2 juniors.
Senior contribution (598/2) * 3 = some value above 740 for sure. So dont even bother calculating more.

For Minimum contribution-
Lets assume 2 seniors and 598 juniors.
Obviously some value less than 700.
So we can have values less than 740 or more than 740.. SO INSUFFICIENT



(2) There were more juniors than seniors enrolled in the school.
Clearly INSUFFICIENT.


Combining BOTH (A) and (B) -
Again similar to what we did above.

For Max contribution -
Seniors 298 and juniors 302
So total = (298/2 * 3) + 302 = 740+ for sure. (749)

For Minimum contribution-
Juniors = 598
Seniors = 2
Dont even waste time calculating because we know its less than 740 obviously.
So we can have values less than 740 or more than 740.. SO INSUFFICIENT

Hence, OPTION E.
I have taken Senior students number as even number because it says half of them contributed. So we cannot take 1 student. How can we cut the poor senior in half

See how simple it gets when u focus on the range.
Hope it helps.

Total students,T=J+S=600
If all of the juniors but only half of the seniors contributed. Implies that all juniors contributed excluding half of the seniors.
No of contributors: Junior=J, Senior=\(\frac{S}{2}\)
Non-contributors: J=0, Senior=\(\frac{S}{2}\)

Question stem:- Was the total amount contributed more than $740 ?
Or, Was J*(unit contribution fees of Juniors)+\(\frac{S}{2}\)*(unit contribution fees of Seniors)>740 ?

St1:- Each junior contributed $1 and each senior who contributed gave $3.

We have total contribution=J*1+\(\frac{S}{2}\)*3=600-S+\(\frac{S}{2}\)*3----------(1)
Since we don't have info on number of seniors or juniors , we can't determine the total contribution.
Insufficient.

St2:- There were more juniors than seniors enrolled in the school.
No information on per head contribution of Juniors and seniors.
Insufficient.

Combining, from(2) , we have J>S
we have range of S: 1<S<300 (Least #seniors=2 and highest #seniors=299)
When S=2, we have from(1),
Total contribution=600-2+\(\frac{2}{2}\)*3=598+3=601<740
When S=299, we have,
Total contribution=600-299+\(\frac{299}{2}\)*3=301+448.5=749.5>740

Insufficient.

Ans. (E)
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Bunuel

Hello Bunuel

Shouldn't the number of seniors max should be 298???

because 299 cannot be divided into half.....

Please let me know if my thinking is wrong.....

thank you

Hi hrishibasri,

You are absolutely correct in your reasoning. However, it doesn't alter the final answer.
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PKN

thank you for the clarification

Quick solution:
Both 1) and 2) are clearly insufficient - neither gives us data on both the amounts of each group, and how much they contributed.
Combined: let's take it to extremes:
max junior extreme: 598 juniors, 2 seniors = 598*1+2*1/2 *3=598+3=601<740
min junior extreme: 302 juniors, 298 seniors = 302*1+298*1/2*3=302+149*3=302+447=749>740
two contradicting answers - insufficient!

I used a different approach. Took 1'54s for this.

Let x be the number of junior
600-x will be the number of senior. Half the number of senior will be 300-x/2
a is the amount of contribution per junior
b is the amount of contribution per senior

The question: is a*x + b*(300-x/2) > 740 ???

(1) a = 1; b=3

x + 3*(300-x/2) > 740?
900 - x/2 >740?

x < 320?

Since no information is given for x, INSUFF

(2) x> 600/2 or x>300. No info on a and b. INSUFF

(1) and (2). We need to compare x to 320 to get the definite answer. How ever we have x>300. So there is 19 values of x (301-319) which will yield YES and 180 values of x that will yield NO. INSUFF

E.

In this question we should quickly be able to tell that neither statement is sufficient alone. The question is are the statements combined sufficient?

Test extreme scenarios:

599 juniors & 1 senior: total amount contributed is $602

301 juniors and 299 seniors: total amount contributed is more than $740

May or may not be more than $740. Answer is E.
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(1) No information about the number of junior and senior are given. For example:

All are senior, then the contribution is \(600*\frac{1}{2}=300*3=900\) which is greater than \($740\) The answer is \(Yes. \)

All are junior, then the contribution is \(600*1= $600\), which is less than \($740, \), The answer is \(No. \)

Insufficient.

(2) No information about the contributed amount is given. Insufficient.

Considering both:
Let, the juniors=302, Contribution \(= 302*1=$302\)
The seniors=298, Contribution \(=298*1/2=149*3=$447\)

Total contribution \(=302+447=749\), which is greater than $740, the answer is Yes

Let, the juniors=598, Contribution \(= 598*1=$598\)
The seniors=2, Contribution \(=2*1/2=1*3=$3\)

Total contribution \(=598+3=601\), which is less than \($740\), the answer is No.
Insufficient.

The answer is \( E. \)
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When we combine both statements, how did we get 302/298 split for "max"? I get the concept, but I had to shoot around in the dark a little bit before I could even get numbers in that range.
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Can't both be correct? In some situations, they may be the correct answers if only one team of students is considered. I encountered similar problems when I took an online class with my tutor in 2020. I found it very difficult, but thanks to help from agency, I was able to figure out what the correct answer was. I am sure that you will also be interested in trying such online classes with an experienced mentor who constantly mentors you and impart important knowledge. You can also contact him.

Bunuel
How would you approach this question?

My first instinct was to test extreme scenarios, so I'd solve the same way as several people did above. Each statement is clearly insufficient. When taken together:

Scenario 1 - get max possible contribution:
Juniors = 302 and seniors = 298 --> contribution = 302*1 + 298*3/2 > 740.

Scenario 2 - get min possible contribution:
Juniors = 600 and seniors = 0 --> contribution = 600*1 + 0*3/2 < 740.

Answer: E.
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