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

Question

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, of the 20 he attempted, correct. How many questions did Jack get incorrect?

a. 6

b. 8

c. 10

d. 12

e. 14

A. 6
B. 8
C. 10
D. 12
E. 14

Sasindran · Accepted Answer

Option B

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 question =8

Sent from my iPhone using GMAT Club Forum

pushpitkc · Answer

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) questions incorrectly (Option B)

gps5441 · Answer

Question is asking about the Incorrect answer.

pushpitkc · Answer

Apologies. Made the correction!!

JeffTargetTestPrep · Answer

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

EMPOWERgmatRichC · Answer

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:  B

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

gmatophobia · Answer

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

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

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