Tom, who has 50 math questions, will get 5 points per question if he chooses a correct answer. If he chooses a wrong answer to a question or skips one, he will lose 2 points per question. Then, which of the following can be the score if he solves all the 50 questions?
A. 192
B. 193
C. 194
D. 195
E. 196
The OA is the option C.
I had no clue, how to solve this question without knowing the number of questions he attempted correct/wrong.
Please help.
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Tom, who has 50 math questions, will get 5 points
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regor60
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One way to do this is to use some algebra:VJesus12 wrote:Tom, who has 50 math questions, will get 5 points per question if he chooses a correct answer. If he chooses a wrong answer to a question or skips one, he will lose 2 points per question. Then, which of the following can be the score if he solves all the 50 questions?
A. 192
B. 193
C. 194
D. 195
E. 196
The OA is the option C.
I had no clue, how to solve this question without knowing the number of questions he attempted correct/wrong.
Please help.
Let C equal the number of questions answered correctly. Since there are 50 questions in total, that means 50-C are the number answered incorrectly.
The total score then would give 5 points credit for each correct answer, or 5xC, and subtract 2 points for each question answered incorrectly, or 2x(50-C)
So the total score is represented by 5C - 2(50-C), which can be reduced to 7C - 100.
Then test each of the possible total scores given as potential answers, for example:
7C - 100 = 194 therefore 7C=294.
And determine whether the result can be divided by 7 resulting in an integer.
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Since each question is worth 5 points, a perfect score on the 50-question test = 50*5 = 250.VJesus12 wrote:Tom, who has 50 math questions, will get 5 points per question if he chooses a correct answer. If he chooses a wrong answer to a question or skips one, he will lose 2 points per question. Then, which of the following can be the score if he solves all the 50 questions?
A. 192
B. 193
C. 194
D. 195
E. 196
For every question missed, Tom will forgo the 5 points attributed to the question and will lose another 2 points for missing the question, for a net loss of 7 points per missed question.
Thus, Tom's score = 250 - 7a, where a is the number of missed questions.
The expression in blue must be equal to one of the five answer choices.
If a=8, then Tom's score = 250 - (7*8) = 194.
The correct answer is C.
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Let r = the number of questions he answered correctly and let w = the number of questions he answered incorrectly. So we have r + w = 50. We are asked to determine which value in the given choices can be 5r - 2w.VJesus12 wrote:Tom, who has 50 math questions, will get 5 points per question if he chooses a correct answer. If he chooses a wrong answer to a question or skips one, he will lose 2 points per question. Then, which of the following can be the score if he solves all the 50 questions?
A. 192
B. 193
C. 194
D. 195
E. 196
Notice that w = 50 - r, so 5r - 2w = 5r - 2(50 - r) = 5r - 100 + 2r = 7r - 100. If r = 42, we have 7(42) - 100 = 194. So 194 can be his score.
Answer: C
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Hi VJesus12,
We're told that Tom, who has 50 math questions, will get 5 points per question if he chooses a correct answer and he will lose 2 points if he chooses a wrong answer to a question or skips one. We're asked which of the following COULD be the score if he solves all 50 questions.
In certain Quant questions, if you don't immediately see a simple algebraic solution, then it sometimes helps to 'brute force' a bit of the math until you see a pattern emerge. Given the 'scoring rules' that this question lays out, here are some possible score outcomes for Tom:
Answers ALL 50 correct = (50)(5) = 250 points
Answers 49 correct, 1 wrong = (49)(5) - 2(1) = 243
Answers 48 correct, 2 wrong = (48)(5) - 2(2) = 236
Answers 47 correct, 3 wrong = (47)(5) - 2(3) = 229
Etc.
Notice how with every additional wrong (or skipped) question, Tom's score drops 7 points. THAT pattern will get you to the correct answer (you can just continue 'subtracting 7' until you find the match). That would lead to possible scores of 222, 215, 208, 201 and 194.
Final Answer: C
GMAT assassins aren't born, they're made,
Rich
We're told that Tom, who has 50 math questions, will get 5 points per question if he chooses a correct answer and he will lose 2 points if he chooses a wrong answer to a question or skips one. We're asked which of the following COULD be the score if he solves all 50 questions.
In certain Quant questions, if you don't immediately see a simple algebraic solution, then it sometimes helps to 'brute force' a bit of the math until you see a pattern emerge. Given the 'scoring rules' that this question lays out, here are some possible score outcomes for Tom:
Answers ALL 50 correct = (50)(5) = 250 points
Answers 49 correct, 1 wrong = (49)(5) - 2(1) = 243
Answers 48 correct, 2 wrong = (48)(5) - 2(2) = 236
Answers 47 correct, 3 wrong = (47)(5) - 2(3) = 229
Etc.
Notice how with every additional wrong (or skipped) question, Tom's score drops 7 points. THAT pattern will get you to the correct answer (you can just continue 'subtracting 7' until you find the match). That would lead to possible scores of 222, 215, 208, 201 and 194.
Final Answer: C
GMAT assassins aren't born, they're made,
Rich
