On a test, a student scores +4 points for each correct answer and Â- 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. How many questions did Jack get incorrect?
A. 6
B. 8
C. 10
D. 12
E. 14
OA is b
what is the mathematical approach to use here in order to get the correct answer?
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BTGmoderatorRO
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Not a bad one to back solve. Test C. Say Jack answered 10 questions incorrectly. This means he answered 10 questions correctly. Had he answer two more questions correctly, we'd have answered 12 questions correctly and 8 questions incorrectly, for a score of 12*4 + 8*(-2) = 48 - 16 = 32. But we know he should have received a 44. C is too small, so he had to have answered fewer questions incorrectly. Eliminate C, D, and E.Roland2rule wrote:On a test, a student scores +4 points for each correct answer and Â- 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. How many questions did Jack get incorrect?
A. 6
B. 8
C. 10
D. 12
E. 14
OA is b
what is the mathematical approach to use here in order to get the correct answer?
Test either A or B. (Note that there's no reason to test both. If whatever you try works, it's the answer. If it doesn't the answer is the other one.)
Let's try B. If he answered 8 questions incorrectly, he answered 12 questions correctly. Had he answered two more questions correctly, he'd have answered 14 questions correctly and 6 questions incorrectly, for a score of 14*4 + 6(-2) = 56 - 12 = 44. There's our answer. B is correct.
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Hi Roland2rule,On a test, a student scores +4 points for each correct answer and Â- 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. How many questions did Jack get incorrect?
A. 6
B. 8
C. 10
D. 12
E. 14
OA is b
what is the mathematical approach to use here in order to get the correct answer?
Let's take a look at your question and solve it algebraically.
Jack attempted 20 questions in total.
For each correct answer he got +4 points and for each incorrect answer he got -2 points.
The question states that Jack would have scored 44 points if he had got two more questions correct.
Let Jack solved x questions correctly and (20 - x) questions incorrectly.
If he got 2 more questions correct then he would have scored 44 points.
It means that if correct questions are (x + 2) and incorrect questions are [20 - (x + 2)] then Jack's score would have 44.
We can write it as:
$$4\left(x+2\right)-2\left[20-\left(x+2\right)\right]=44$$
$$4\left(x+2\right)-2\left[20-x-2\right]=44$$
$$4\left(x+2\right)-2\left(18-x\right)=44$$
$$4x+8-36+2x=44$$
$$6x-28=44$$
$$6x=44+28$$
$$6x=72$$
$$x=\frac{72}{6}$$
$$x=12$$
x represents the number of correct questions, we need to find the number of questions Jack get incorrect.
Number of incorrect questions = 20 - 12 = 8
Therefore, Option B is correct answer.
Hope it helps.
I am available if you'd like any follow up.
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BTGmoderatorRO wrote:On a test, a student scores +4 points for each correct answer and Â- 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. How many questions did Jack get incorrect?
A. 6
B. 8
C. 10
D. 12
E. 14
OA is b
what is the mathematical approach to use here in order to get the correct answer?
We can let c = the number of correct questions and w = the number of incorrect questions. 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
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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 Â- 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
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 Â- 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
