Q: How many questions were answered correctly by a student who received 38 marks on an entrance exam where 3 marks were awarded for each correct answer and 1 mark was deducted for each wrong answer, given that the total number of questions was 70?  

Answer: C

 To solve this problem, we can use the fact that the total number of 
marks a student receives is equal to the number of correct answers multiplied by 3, minus the
 number of wrong answers. We can represent this relationship with the equation:

3x - y = 38

Where x is the number of correct answers and y is the number of wrong answers.

We are also given that the total number of questions is 70, so we can set up
 a second equation to represent this relationship:

x + y = 70

We can solve this system of equations by first solving for y in the first equation:

y = 3x - 38

Substituting this expression for y into the second equation gives:

x + (3x - 38) = 70

This simplifies to:

4x - 38 = 70

Adding 38 to both sides gives:

4x = 108

Dividing both sides by 4 gives:

x = 27

Therefore, the student answered 27 questions correctly.   

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