# Quantitative Reasoning – Practice – Number System:a tough one?

PSA_PRACTICE_QNR24. A quiz has been designed in such a way that correct answer fetches you 8 points, and a wrong one deducts 3 points. If Ravi scores 110 points in the quiz (that has total 25 questions), how many questions does Ravi answer?

Ans: Let Ravi answers ‘m’ correct , ‘n’ incorrect and does not attempt ‘p’ questions.

m+n+p=25

Also, total score =110= Score from correct answers – Score from incorrect answers

=> 110 = 8m-3n

=> 110= 8m -3(25-m-p) [From the first equation]

=>110= 8m -75+3m+3p

=>11m+3p=185

=>3p= 185-11m [Rearranging]

=>3p= (183+2) -(9m+2m)

=>3p = (183-9m) + 2(1-m)

This is in the form of X= Y+Z where, X=multiple of 3, Y=multiple of 3

Thus, Z must also be a multiple of 3.

Thus, possible values of m= 1,4,7,10,13,16 etc.. [AP with common difference= coefficient of ‘p’]

When m=1, p=(185-11)/3= 174/3= 58.

Therefore values of p= 58,47,36,25,14,3 etc.. [AP with common difference= coefficient of ‘m’]

Possible sets of (m,p)= (1,58), (4,47), (7,36), (10,25), (13,14)(16,3)

Out of the above, first five are rejected as total questions are only 25;

Only (16,3) is a valid combination that satisfies 110 score. [3 unattempted, 16 correct, 6 wrong= 16*8-6*3=110].