On a test, a student scores +4 points for each correct answer and ­2 p

Question is asking about the Incorrect answer.

Apologies. Made the correction!!

We can let c = the number of correct questions answered and w = the number of incorrect questions 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.

Answer: B

Hi All,

To start, there's one minor issue with the wording of this question. The 'intent' is that there are 20 total questions, NOT that Jack could simply answer 2 additional questions beyond the 20 that are mentioned (meaning that he would answer 22 questions in the 'hypothetical' situation that is described).

We're told that on a test, a student scores +4 points for each correct answer and ­- 2 points for each incorrect answer. Jack attempted 20 questions and found that his score WOULD HAVE been 44 if he had got TWO MORE questions correct. We're asked for the actual number of questions that Jack got incorrect. This question can be solved in a couple of different ways, including by TESTing THE ANSWERS. There's also a great pattern in the design of this question that you can take advantage of to save some time.

Since you earn "+4" points for a correct answer and "-2" points for an incorrect answer, you can think in terms of 'cancelling out' points. For every 1 correct answer, it would take 2 incorrect answers to remove the point gain. Thus, if you got exactly 1/3 of the questions correct and 2/3 incorrect, then you would score 0 total points. With Jack's current score (and possible score), we're clearly dealing with a situation in which Jack got far MORE than 1/3 of the questions correct.... and a perfect score on a 20 question quiz would be only (4)(20) = 80 points, so Jack likely got most of the questions correct. Since we're asked for the number of INCORRECT answers, we should look for an answer that's relatively small. Let's TEST Answer B first....

Answer B: 8 incorrect answers
IF... Jack got 12 correct and 8 incorrect, the his score would be (4)(12) - (2)(8) = 48 - 16 = 32

Note that by getting 2 additional correct answers, he gets 2 FEWER answers wrong....

With 2 MORE correct answers, his score would be (4)(14) - (2)(6) = 56 - 12 = 44

This is an exact match for what were told, so this MUST be the answer!

Final Answer:

GMAT assassins aren't born, they're made,
Rich

Let the number of questions Jack got correct = x

Let the number of questions Jack got incorrect = y

Jack attempted 20 questions, therefore

x + y = 20 --------- (1)

Total score obtained by Jack = 4x - 2y



Had Jack got two more questions correct, he would have got two fewer questions incorrect. Hence -

4(x+2) - 2(y-2) = 44

4x + 8 - 2y + 4 = 44

4x - 2y = 32

2x - y = 16 --------- (2)

Adding equations (1) and (2) we get

3x = 36

x = 12

y = 20 - 12 = 8

Hence, Jack got 8 questions incorrect.

Option B