Question

Subject matter experts at an edutech organization are asked their specialties. Among them 40% choose maths, 16% choose physics, 34% choose chemistry and remaining x% choose biology. Once the experts pick their first speciality, they are then each asked to choose a second speciality from the previous four options in case their original speciality is already filled. they may not pick their original speciality again. 20% of those who choose maths choose physics as their second choice, and the organization boasts 200 subject matter experts , then what is the total number of residents who named physics as their first or second choice in terms of x?
 $
  \left( {\text{A}} \right)8x - 128 \\
  \left( {\text{B}} \right)8x - 144 \\
  \left( {\text{C}} \right){x^2} + 24x - 188 \\
  \left( {\text{D}} \right){x^2} - 24x + 188 \\
  $

Answer 1

Hint: Since the number of candidates are given in % , try to convert them and find the number of actual students. From this you will also get the no. of students choosing biology. Then find the no. of students having maths as first preference choosing their second preferences as physics. Compare this value to the options given by substituting the value of x

Complete step-by-step answer:
After reading the entire question we come to know that the organization has 200 subject matter experts.
Now we will find out from the given information firstly about how many candidates choose their respective subject as first option
Mathematics = 40% of total candidates = 40% of 200 = $ \dfrac{{40}}{{100}} \times 200 = 80 $
Physics = 16% of total candidates = 16% of 200 = $ \dfrac{{16}}{{100}} \times 200 = 32 $
Chemistry = 34% of total candidates = 34% of 200 = $ \dfrac{{34}}{{100}} \times 200 = 68 $
Biology = x%= (100-40-16-34)% = 10% of total candidates =10% of 200 = $ \dfrac{{10}}{{100}} \times 200 = 20 $
Now we will find the number of candidates who choose their first option as mathematics and second option as physics.
20% of total maths candidates = 20% of 80 = $ \dfrac{{20}}{{100}} \times 80 = 16 $
Hence the total physics students will be 32+16=48
Since we have found the value of our x as 10 we will try to substitute this value in all of the above options and crosscheck which one of the options gives us the answer 48 which we have already found
Starting with option (A)
 $
  8x - 128 \\
   = 8\left( {10} \right) - 128 \\
   = 80 - 128 \\
   = - 48 \;
  $
which does not match our answer
option B
\[
  8x - 144 \\
   = 8\left( {10} \right) - 144 \\
   = 80 - 144 \\
   = - 64 \;
 \]
which also does not match.
Option C
 $
  {x^2} + 24x - 188 \\
   = 100 + 240 - 188 \\
   = 152 \;
  $
Which also doesn’t match
Last option D
 $
  {x^2} - 24x + 188 \\
   = 100 - 240 + 188 \\
   = 48 \;
  $
which matches our answer and hence option D is the right answer.
So, the correct answer is “Option D”.

Note: You need to solve this sums step by step and convert the percentages into actual values. Also if the answer was not expected in the terms of x, we could have kept the value which we have obtained directly with the calculations. There would be no need for the further process as done above.