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)

_________________

Regards,

PKN

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