For every correct answer, the student earns 7 points

Question

A student is taking a test. For every correct answer, the student earns 7 points and for every incorrect one the student loses 12 points.
How many questions did the student answered correctly?

(1) Student gathered 77 points in the test.
(2) Of all the answers that the student provided, 7 were incorrect.

chetan2u · Answer

Let the number of correct answers be x and that of incorrect be y. 
So 7x-12y=the marks scored.

(1) Student gathered 77 points in the test.
 7x-12y=77........12y=7(x-11) 
 We can say that y is multiple of 7 and x-11 a multiple of 12. 
(i) 12*7=7(23-11)....So x=23, and y=7.....
(ii) 12*14=7(35-11)....So, x=35, and y=14
Insufficient

(2) Of all the answers that the student provided, 7 were incorrect
We cannot say anything about x. 
Insufficient

Combined 
Statement II tells us that y=7,
From statement I we get  7x-12y=77.....7x-12*7=77....7x=77+84=161 
Thus, x=23.
Sufficient

C

GMATWhizTeam · Answer

Solution:

We are told that for every correct answer, the student earns 7 points and for every incorrect, the student loses 12 points. 
So let us assume that number of questions the student did correctly be  x  and number of questions student did incorrectly be  y . 
And we are asked the value of  x+y. 
 
Let us jump into the statements:

Statement 1:   Student gathered 77 points in the test. 
This statement basically means that  7x-12y=77 . 
  Now you might discard this instantly because there are 2 variables and only one equation. But it is always advised to see if it not the case of special equation.   
If we can get at least 2 distinct values of (x,y) that satisfy  7x-12y=77 , then we can discard this statement. 
And we see that (23,7) and (35,14) satisfy this equation. 
Thus statement 1 alone is not sufficient.

Statement 2:   Of all the answers that the student provided, 7 were incorrect.
Here we are given that y=7. But we have no information on x. Thus this statement alone is nit sufficient.

Combinning:  
On combining, we can see that when y=7, x has to be 23. 
And  x+y=7+23=30

Hence the right answer is  Option C .

IanStewart · Answer

We're asked to find the value of x, not of x+y.

Here, if right answers are worth 7 points, and wrong answers deduct 12 points, then any time a student answers 12 questions correctly and 7 incorrectly, she gets 0 points overall. So if a student gets 77 points, she might have 11 right answers and 0 wrong answers, or she might have 11 right answers, along with 12,000 additional right answers and 7,000 additional wrong answers, for example.

So Statement 1 is not sufficient alone, and Statement 2 clearly is not sufficient alone, but using both Statements, we know she needs 12 right answers to perfectly compensate for her 7 wrong answers, and an additional 11 right answers to get up to 77 points, for a total of 23 right answers, and the answer is C.

Posted from my mobile device

ConquerGMAT007 · Answer

Question :
A student is taking a test. For every correct answer, the student earns 7 points and for every incorrect one the student loses 12 points.
How many questions did the student answered correctly?

(1) Student gathered 77 points in the test.
(2) Of all the answers that the student provided, 7 were incorrect.
------------------------------------------------------

Ans:
Given --> Correct ans Student earns 7pts & Incorrect ans Student losses 12pts
** Its a 'How' question and not 'is' question

Let correct ans be : x
Let incorrect ans be: y

Statement 1:Student gathered 77 points in the test.
So, Correct *points - Incorrect*points = 77
=> x*7 - y*12 = 77 --(1)

Only one equation, under no circumstance one can find x
Hence Insufficient

Statement 2: Of all the answers that the student provided, 7 were incorrect.
So, Incorrect*12 => y*12 =>7*12 --(2)

Only one equation, with this input one cannot find x
Hence Insufficient

However, combining statement1 and statement2 :
Substituting (2) in (1)

x*7 - y*12 = 77
=>x*7 - 7*12 = 77
=>x*7=77+84
=>x*7 = 161
x=23

x is assumed to be correct ans. Hence, Sufficient

Option C

Thank you

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For every correct answer, the student earns 7 points

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