A teacher grades students’ tests by subtracting twice the number of in

Question

A teacher grades students’ tests by subtracting twice the number of incorrect responses from the number of correct responses. If Student A answers each of the 100 questions on her test and receives a score of 73, how many questions did Student A answer correctly?

A. 55
B. 60
C. 73
D. 82
E. 91

A. 55 
B. 60 
C. 73 
D. 82 
E. 91

CounterSniper · Answer

let the number of correct responses be x
then the number of incorrect responses =100-x
according to question
x-2(100-x)=73 (subtracting twice of incorrect from correct)
3x=273
x=91

EMPOWERgmatRichC · Answer

Hi All,

This question can be solved by TESTing THE ANSWERS.

We're given a few facts about a particular test and a student who took that test:
1) The score on the test is generated by subtracting TWICE the number of incorrect responses from the number of correct responses.
2) A student answered ALL 100 questions.
3) That student earned a score of 73.

We're asked for the number of questions that the student answered correctly.

Since the number of incorrect answers is DOUBLED before that number is subtracted, it would clearly take MORE than 73 correct answers to get a score of 73 (since 27 wrong answers would end up leading to a score of 73 - 2(27) = 19).

Let's TEST Answer D: 82 correct

With 82 correct answers, we would have a score of 82- 2(18) = 46. This is TOO SMALL (it's supposed to be a score of 73). The only way to score HIGHER than 46 is with MORE correct answers. There's only one answer left...

Final Answer:  E

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

douglasvg · Answer

Correct = C
Incorrect = I

C + I = 100
I = 100 - C
----
C - 2I = 73
C - 2.(100 - C) = 73
C -200 + 2C = 73
3C = 273
C = 91

NagrajB · Answer

Let number of correct responses be
So the number of wrong responses = 100 - x

x - 2(100 - x) = 73
x - 200 + 2x = 73
3x = 273
x = 91

chetan2u · Answer

total Q=100..
final score=73..
let incorrect responses = y..
the score cut out of the correct answers = 2y..
total score cut =y+2y= 3y, which is equal to 100-73=27..
so y=9..
correct answers =100-9=91..
E

KarishmaB · Answer

Some observation can help you answer the question easily.
A score of 73 brings to mind that it is an odd number even though you are subtracting an even number (twice the incorrect responses) out of the correct responses score. So the correct responses score must be an odd number too (Odd - Even = Odd). 
Since the overall score is 73, the number of correct responses must be more than 73 since the student answered all questions. 
Only 91 satisfies both these conditions.

Answer (E)

ScottTargetTestPrep · Answer

We can create the following equations, in which c = the number of correct responses and w = the number of incorrect responses:

c + w = 100

w = 100 - c

and

c - 2w = 73

Substituting, we have:

c - 2(100 - c) = 73

c - 200 + 2c = 73

3c = 273

c = 91

Answer: E

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.

A teacher grades students’ tests by subtracting twice the number of in

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

A teacher grades students’ tests by subtracting twice the number of in

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