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answer incorrectly

by nidhis.1408 » Wed Nov 16, 2011 4:46 pm
A student has 24 questions remaining on an exam. If she has correctly answered 75% of the questions so far, and has to answer at least 75 percent of all the questions on the exam correctly, what is the maximum number of the remaining questions she can answer incorrectly?

a. 4
b. 6
c. 12
d. 18
e. it cannot be determined from the information given
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by rijul007 » Wed Nov 16, 2011 5:47 pm
no of questions already attempted = x
max no of questions that one can wrong in the remaining 24 = n

25% of x + n = 25% of (x+24)
x/4 + n = x/4 + 6
n = x/4 + 6 - x/4
n = 6

Option B[/spoiler]
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by shankar.ashwin » Wed Nov 16, 2011 9:29 pm
You could also pick numbers.

Assume she has attempted 100 questions until now and got 75 correct.

She has 24 remaining, so total = 124. 75% of 124 = 93. Therefore she has to get 18 more answers right.

So, she can get a max of 6 incorrect. B IMO

P.S Actually you dont have to calculate anything here. You have 2 things (one of which is 75% and the other some % and together they form 75% again)

So the other should also be 75% right (or) 25% wrong, (or) 1/4th of 24 (or) 6
Last edited by shankar.ashwin on Wed Nov 16, 2011 10:53 pm, edited 2 times in total.
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by anemsurya » Wed Nov 16, 2011 10:38 pm
Let x be the total number of questions answered till now.
Number of questions answered correctly = 0.75x.

Let y be the number of questions that are yet to be answered correctly so that the total number of questions answered correct will be 75%

Hence,

0.75x + y = (24+x)(0.75)
y = 18

The maximum number of questions that can go wrong are 24-18 = 6
IMO B
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by knight247 » Wed Nov 16, 2011 10:40 pm
I prefer the weighted averages method for this. U can solve it in under 30 secs

Let the Total number of questions be x.
The questions remaining are 24 so the questions already answered is x-24

The weighted average has to be 25 meaning she can have 25 incorrect answers in the entire test

75% of x-24 have been answered correctly so it follows that 25% of x-24 have been answered incorrectly. So we can have at most z% of the remaining 24 questions answered incorrectly. We can form the equation as follows

[(x-24)/x}*25 + (24/x)*z=25 (Don't be alarmed by the two variables as x gets cancelled out)
Solving for z we get
z=25% i.e. She can get atmost 25% of the remaining questions wrong.
(25/100)24=24/4= 6 Hence B
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