Question: On a test, a student scores +4 points for each correct answer and -2 points for each incorrect answer. Jack attempt 20 questions and found that his score would have been 44 if he had got two more questions correct. How many questions did Jack get incorrect?
- 6
- 8
- 10
- 12
- 14
Answer:
Solution with Explanation:
Approach Solution (1):
Let the number of questions the student gets correct be x
Since the total questions he answers is 20, the number of questions he gets incorrect is 20 – x
Since the score the student scores is 44, if the student answered 2 more questions correctly,
The equation formed will be 4(x + 2) – 2(20 – x – 2) = 44
4(x + 2) – 2(18 – x) = 44
4x + 8 – 36 + 2x = 44
6x = 72
x = 12
Therefore, the student answers 8(20 – x) question incorrectly
Correct Option: B
Approach Solution (2):
Let Jack’s desired number of correct question = x and
Incorrect questions = 20 – x
Now
4x – 2(20 – x) = 44
Solving x = 14
So original correct question = 12
Incorrect questions = 8
Correct option: B
Approach Solution (3):
We can let c = the number of correct questions answered and w = the number of incorrect question answered.
Thus:
c + w = 20
w = 20 – c
And
4(c + 2) – 2(w – 2) = 44
4c + 8 – 2w + 4 = 44
4c – 2w = 32
2c – w = 16
Thus:
2c – (20 – c) = 16
2c – 20 + c = 16
3c = 36
c = 12
Thus, w = 20 – 12 = 8
Correct Option: B
“On a test, a student scores +4 points for each correct answer and -2 points for each incorrect answer. Jack attempt 20 questions and found that his score would have been 44 if he had got two more questions correct. How many questions did Jack get incorrect?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.
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