Zachary is helping his younger brother, Sterling, learn his

Question

Zachary is helping his younger brother, Sterling, learn his multiplication tables. For every question that Sterling answers correctly, Zachary gives him 3 pieces of candy. For every question that Sterling answers incorrectly, Zachary takes away two pieces of candy. After 12 questions, if Sterling had answered 2 more questions correctly, he would have earned 31 pieces of candy. How many of the 12 questions did Zachary answer correctly?

6

7

8

9

10

After 12 questions, if Sterling had answered 2 more questions correctly, he would have earned 31 pieces of candy It means after having 14 questions the candies would be 31 right?? or I am missing something here

A. 6
B. 7
C. 8
D. 9
E. 10

After 12 questions, if Sterling had answered 2 more questions correctly, he would have earned 31 pieces of candy  It means after having 14 questions the candies would be 31 right?? or I am missing something here

Qoofi · Accepted Answer

Hi Akshay,

The total number question to be answered is not 14.

Lets say X is the total questions he answered correct. and 12 - x is the total questions he answered wrong.

Now, the questions says that if he had answered 2 more questions correct, he would have got 31 candies. So

Correct = x + 2 and Wrong = 12 - x - 2 = 10 - x ( We need to subtract 2 from the wrong questions also while adding 2 to the correct questions )

The equations :

3 (x + 2 ) - 2 (10 - x) = 31

Solving, we get   X = 9

Total Questions answered correct = 9

Hope the above explanation helped.

Cheers
Qoofi

Temurkhon · Answer

i got two equations:
3x-2y=25
x+y=12

3x-2(12-x)=25
3x-24+2x=25
5x=49
x=9.8 or between 9 and 10. 
What is wrong with it?

Qoofi · Answer

I couldn't get how you got to Eqn (1). Bit light on that?

GMAT40 · Answer

If he would have answered 12 Q correctly. he would have had 12 x 3 = 36 candies
1 wrong 11 right .. Num of candies 11 x 3 - 1 x 2 = 31

Question says if he would have answers 2 more correctly the number of candies he would have is 31
The number of answer given correct so far 11 - 2 = 9

SVaidyaraman · Answer

1. Let x be the number of questions answered correctly and y be the number of questions answered wrongly
2. 12 questions are answered. Since x questions are answered correctly, two more questions answered correctly would mean x+2 questions answered correctly and y-2 questions answered incorrectly.
3. 3(x+2) - 2(y-2)=31 or 3x -2y=21
4. Also, x+ y = 12
5, Solving (3) and (4) we get, x= 9 or the number of questions answered correctly so far is 9.

hanyhamdani · Answer

Zachary is helping his younger brother, Sterling, learn his multiplication tables. For every question that Sterling answers correctly, Zachary gives him 3 pieces of candy. For every question that Sterling answers incorrectly, Zachary takes away two pieces of candy. After 12 questions, if Sterling had answered 2 more questions correctly, he would have earned 31 pieces of candy. How many of the 12 questions did Zachary answer correctly?

6

7

8

9

10

After 12 questions, if Sterling had answered 2 more questions correctly, he would have earned 31 pieces of candy It means after having 14 questions the candies would be 31 right?? or I am missing something here

A. 6
B. 7
C. 8
D. 9
E. 10

Solution:
 let "r" be the number of right questions and "w" be number of wrong questions.
 so, after 12 questions, he does 2 correct and scores 31 in total.

12q + 2(3)=31 : 3 is score for correct answer 
 12q=25 
getting to eqution: 
 3r-2w = 25 (3 and 2 denote, scores of right and wrong)
 3 ( ) -2 ( ) =25 : check values from answer choice. none but 9 satisfies.
 3( 9 ) - 2(1) =25
so, "D"

ayushkumar22941 · Answer

checking with options in this question took just 20 sec .i think this is best approach for this question.

SPatel1992 · Answer

I did the same way. Can someone explain what's wrong with this method, please? Thanks in advance!

Mehakgyl · Answer

Hello 
I also solved with the 2nd approach. Whats wrong with that?  bb   KarishmaB   GMATNinja

Mehakgyl · Answer

Hello  Qoofi  
The question clearly states "After 12 questions, if he Sterling had answered 2 more questions correctly". We cant subtract 2 from the original number of wrong questions right?

KarishmaB · Answer

Total questions answered = 12
Correct gives 3 and incorrect takes away 2.

If 2 questions were correct instead of incorrect, then Z would not lose 4 points and in fact, gain 6 points. This means that in that case, total number of candies would be 10 more than current number of candies. So current number of candies must be 21.

This means he answered 7 questions correctly and then he answered some more questions correctly whose score was negated by the incorrect answers. Score of 2 correct questions would be 6 which would be evenly cancelled off by negative score of 3 incorrect questions. 
7+2+3 = 12 so this means that 7+2 = 9 questions were answered correctly.

Method 2: Algebra

If 2 questions were correct instead of incorrect, then Z would not lose 4 points and in fact, gain 6 points. This means that in that case, total number of candies would be 10 more than current number of candies. So current number of candies must be 21.

x + y = 12
3x - 2y = 21

Solve to get x = 9

Answer (D)

KarishmaB · Answer

What the statement means is: After 12 questions, the score was reviewed. It was found that had he answered 2 questions correctly instead of incorrectly, then we would have gotten a score of 31. 
The question stem is a bit ambiguous as it is for a learner.

Zachary is helping his younger brother, Sterling, learn his

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