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>740Insufficient.
Ans. (E)
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Regards,
PKN
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