Problem Solving

In the faculty of Reverse-Engineering, 226 second-year students study numeric methods, 423 second-year students study automatic control of airborne vehicles and 134 second-year students study them both. How many students are there in the faculty if the second-year students are approximately 80% of the total?

A. 515
B. 545
C. 618
D. 644
E. 666

The OA is D.

I solved this PS question of the following way,

NM = 226

AV = 423

Both = 134

Total second year students = (226 - 134) + (423 - 134) + 134 = 226 + 423 - 134 = 515

Assume total students = x

Therefore 0.8x = 515

x = 515/0.8 = 5150/8 = 643 approximately. Option D.

Is there another strategic approach to solve this question? Can any experts help, please? Thanks!

Hi AAPL,

You can try as follow,

The total number of students studying both are 423 + 426 - 134 = 515 (subtracting the 134 since they were included in both the other numbers already).

So 80% of the total is 515, so 100% is approximately 644.

Regards!

Numeric method = 226 second year students
Automatic control= 423 second year students
Both numeric and automatic = 134 second year students

Therefore, total second year student= (numeric + automatic) - both = [226+423]-134
=649-134= 515 second year students in faculty of reverse engineering. 2nd year student made 80% of the total student.
if 80% =515
then 100%=
$$\frac{\left(515\cdot100\right)}{80}=643.75=644$$
Hence, option D is correct