Tom, who has 50 math questions, will get 5 points per question

Question

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

I had no clue, how to solve this question without knowing number of questions he attempted correct/wrong.
Please advise

paidlukkha · Answer

x for correct y for wrong or skip so 5x & 2y x+y=50 y = 50-x so 5x-2(50-x)=ABCDE 5x-100+2x=ABCDE 7x=ABCDE+100 always start from the median

C 294/7=42 :D

yosita18 · Answer

rudra316 · Answer

Let x be the correctly answered questions. y be the wrongly answered/ skipped ones.

We have x + y = 50; 
Score = 5x-2y

2x+2y = 100; 5x-2y = Score;
==> 7x = 100+Score;
check for answer choices where 100+Score is divisible by 7
Choice (C) 194 fits the equation !

chetan2u · Answer

Hi,
As also correctly explained above..
Let the right be x, so wrong will be 50-x...
Marks for right ... 5*x..
Marks for wrong.. -2*(50-x)= 2x-100...
Total = 5x+2x-100 =7x-100
7x = total + 100....
Look for a choice which when added to 100 is div by 7..
294 does 
C

ronny123 · Answer

Another way to look at this problem

Tom gets 5 points for correct response. But Tom loses not just 2 points but the 5 points for the correct answer as well for the wrong response. So, total loss for each wrong answer is 7 points relatively.

The maximum points Tom could score is 50 x 5 = 250
In relative terms, each wrong answer would cost Tom 7 points
So, the marks received by Tom should be 250 - 7x 
Using the options, only 194 is the acceptable answer
C

EMPOWERgmatRichC · Answer

Hi All,

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).

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

KarishmaB · Answer

If x is the number of questions answered correctly, then 50 - x is the number of questions answered incorrectly. 
5x - 2*(50 - x) = Total score
7x = Total score + 100

So the option of this form can be the total score. Try option (A). 
7x = 192 + 100 = 292
292 is not divisible by 7. It leaves remainder 5. This means 294 will be divisible by 7. 
So 294 - 100 = 194 can be the total score.

Answer (C)

ravish844 · Answer

Hi sairam595,

I solved it this way.

Suppose, Tom answered all questions correctly, then he would have scored 50 * 5 = 250 points.
Now, let's say, if 1 of his answer was wrong, how much marks would he get. From 250, deduct 5 for the correct answer, which we have assumed earlier and 2 for the negative marking (for wrong answer). So, his score would be 250 - 5 - 2 = 243 marks (for 1 wrong answer).
Again, let's say 2 answers were wrong. As we did calculation above, he would get 243 - 5 - 2 = 236 marks (for 2 wrong answers).

Now, we see that for every wrong answer, the score is getting reduced by 7. So, now reduce 7 * 7 = 49 from 250 (for 7 wrong answers) and we will get 201 score.
Now, reduce another 7 (for 1 more wrong answer) and we will get 201 - 7 = 194, which is the correct answer choice as per option C.
Note that 194 marks / score is obtained for 8 wrong answers and 42 correct answers.

Hence Answer option (C) = 194 is the correct answer.

Regards,
Ravish.

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Tom, who has 50 math questions, will get 5 points per question

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