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

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In a school that had a total of 600 students enrolled in the junior an  [#permalink]

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New post 02 Aug 2018, 22:36
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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 who contributed gave $3.
(2) There were more juniors than seniors enrolled in the school.


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(DS07258)

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In a school that had a total of 600 students enrolled in the junior an  [#permalink]

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New post 03 Aug 2018, 03:07
Bunuel wrote:
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 who contributed gave $3.
(2) There were more juniors than seniors enrolled in the school.


NEW question from GMAT® Quantitative Review 2019


(DS07258)


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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In a school that had a total of 600 students enrolled in the junior an  [#permalink]

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New post 15 Oct 2018, 05:37
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
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Re: In a school that had a total of 600 students enrolled in the junior an  [#permalink]

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New post 15 Oct 2018, 06:01
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hrishibasri wrote:
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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Re: In a school that had a total of 600 students enrolled in the junior an  [#permalink]

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New post 15 Oct 2018, 06:07
PKN

thank you for the clarification :)
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Re: In a school that had a total of 600 students enrolled in the junior an  [#permalink]

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New post 20 Oct 2018, 03:16
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. :)
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Re: In a school that had a total of 600 students enrolled in the junior an &nbs [#permalink] 20 Oct 2018, 03:16
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