Answer to Question #175939 in Algebra for Norah

Question

In a quiz, there are 20 multiple choice questions. Each correct answers scores 7points, each wrong answer scores -4 points, and each blank answer scores 0 points. Omar took the quiz and scored a 100 points. How many questions did he leave blank?

A) 0

B) 1

C) 2

D) 3

E) 4

Answer 1

total questions = 20

each correct answer obtains = 7 marks

each wrong answer obtains = -4 marks

each blank question obtains = 0 marks

the total obtained marks by omar = 100

the equation for this is as : 7X-4Y = 100

where,

X = number of correct answer.

Y = number of incorrect answer.

for scoring 100 marks number of questions must be correct is 15 or more.

thus, there is only one pair of (X,Y) which satisfy the above equation i.e. (16,3).

7*16 - 4*3 = 100

LHS = RHS

therefore, the total questions attempted by omar is = 16+3 = 19

hence, the questions leave blank are = 20-19 = 1.