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Directions: Read the following information carefully and answer the questions based on it.
There are three schools – P, Q, and R, number of vacancies released by schoolsP, Q, and R for thepost of Math educator are (Z + 3), Y and M respectively. Averagenumber of candidates applied per vacancy in schoolsP, Q, and R is 20, 35, and 42 respectively. Total number of candidates applied in school P is twice that of schoolQ, while total number of candidates applied in schoolR is thrice that of schoolQ. No candidate can apply in more than one school and number of candidates applied in any of the school is not more than 250.
Q. L = Difference between number of candidates applied in schoolP and Q
K = Number of candidates applied in schoolR
Find the remainder when (L + K) isdivided by 16?
  • a)
    10
  • b)
    8
  • c)
    12
  • d)
    6
  • e)
    None of these
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
Directions: Read the following information carefully and answer the q...
Total candidates applied in schoolP = 20 x (Z + 3)
Total candidates applied in schoolQ = 35Y
Total candidates applied in schoolR = 42M
Number of candidates applied in schoolQ× 2 = total candidates applied in school P
20 x (Z + 3)/35Y = 2/1
2Z + 6 = 7Y……………... (1)
Number of candidates applied in schoolR = 3 x number of candidates applied in school Q
35Y/42M = 1/3
Y/M = 2/5
Y and M must be integer.
If Y = 2, then
2Z = 7 x 2 – 6
Z = 4
So, candidates applied in schoolP = 20 x 7 = 140
Candidates applied in schoolQ = 35 x 2 = 70
Candidates applied in schoolR = 5 x 42 = 210
If Y = 4, then Z = 11
So, number of candidates applied inschoolP = 20 x (11 + 3) = 280 (not possible)
So, Y = 2, Z = 4, and M = 5
Value of L = 140 – 70 = 70
Value of K = 210
(L + K) = 210 + 70 = 280
So, 280/16 = 17 x 16 + 8
Required remainder = 8
Hence, answer is option B
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