A student responded to all of the 22 questions on a test and

Juaz uses the following approach:

A student responded to all of the 22 questions on a test and received a score of 63.5. If the scores were derived by adding 3.5 points for each correct answer and deducting 1 point for each incorrect answer, how many questions did the student answer incorrectly?
(A) 3
(B) 4
(C) 15
(D) 18
(E) 20

We have that 3.5*x-1*y=63.5, where x and y are the # of correct and incorrect answers.

Notice that x must be odd number in order the sum (63.5) to have 5 as the tenths digit (if x=even then 3.5*x-1*y=integer). So, y=22-x=22-odd=odd. There are only two odd choices 3 and 15. y cannot be 15 since in this case the total score would be less than 63.5, so y=3.

Answer: A.

Hope it's clear.
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This question can be answered without solving.
Total has 0.5 at the end, so no of correct answers should be odd, in turn no of incorrect answers must be odd too. A & C are only possible answers. C would drop the score too low so answer must be A.

A-3

If x is the number of questions answered correctly...
3.5x - (22-x)*1 = 63.5
x = 19
So number of wrong answers=22-19=3

Let the number of correct answers be X
The number of incorrect answers will be 22-X
For each correct answer the student got 3.5 points for a total of 3.5X
For each incorrect answer one point was taken out which is equivalent to -(22-X)
The total he got for that was 63.5

So in short you have the following equation and solution.

3.5X-(22-X) = 63.5
3.5X-22+X = 63.5
4.5X = 63.5+22
4.5X = 85.5
4.5X/4.5 = 85.5/4.5
X = 19
So incorrect answers will be 22-X = 22-19 = 3.

Hi,

what does ,,total has O,5´´ mean?

Thanks in advance

sol:

x+y=22
3.5X - y = 63.5

X=19 and y =3

But Bunuel's method is super crazy and fastest

STRATEGY: As with all GMAT Problem Solving questions, we should immediately ask ourselves, Can I use the answer choices to my advantage?
In this case, we can easily test the answer choices.
At this point, we should typically give ourselves 15 to 20 seconds to identify a faster approach, but testing the answer choices will be incredibly easy, and I'm pretty sure I'll need to test 2 answer choices at most. So, I'll start testing the answer choices immediately.

We'll start with answer choice C - 15
There are 22 questions and total.
If the student incorrectly answered 15 questions, we know that the student correctly answered 7 questions.
Total score = (7)(3.5) - (15)(1) = 25.5 - 15 = 10.5
Since we're told the students received a score of 63.5, we know that answer choice C is incorrect.

It's also clear that, in order to achieve a score of 63.5, the student must get fewer than 15 questions wrong, which means we can also eliminate answer choices D and E.

MORE STRATEGY: At this point, I need only test ONE answer choice. For example, if I test answer choice A and it works, then I know the correct answer is A. Alternatively, if I test answer choice A and it doesn't work, then I know the correct answer is B.

Let's test choice B - 4
So, if the student incorrectly answered 4 questions, we know that the student correctly answered 18 questions.
Total score = (18)(3.5) - (4)(1) = 63.5 - 4 = 58.5
Since we're told the students received a score of 63.5, we know that answer choice B is incorrect.

By the process of elimination, the correct answer must be A.
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