paata01 wrote:
A test has 50 questions. A student scores 1 mark for a correct answer, –1/3 for a wrong
answer, and –1/6 for not attempting a question. If the net score of a student is 32, the number
of questions answered wrongly by that student cannot be less than
1. 6 2. 12 3. 3 4. 9
Soln. (3) — Let the number of correct answers be ‘x’, number of wrong answers be ‘y’ and
number of questions not attempted be ‘z’.
Thus, x + y + z = 50 … (i)
And x – y – z 32
3 6
The second equation can be written as,
6x – 2y – z = 192 … (ii)
Adding the two equations we get,
7x – y = 242 or x = 242 + y
7
Since, x and y are both integers, y cannot be 1 or 2. The minimum value that y can
have is 3.
can u explain why Y can not be 1 or 2....i tried to make 242/7+Y integer but even 3 is not enough
The equation you get is 7x - y = 242
x = (242 + y)/7 (don't forget that the entire 242+y is divided by 7, not just 242)
Since x must be an integer, (242+y) must be divisible by 7. After 242, the closest multiple of 7 is 245 (if you are wondering how to get it, divide 242 by 7. You get 4 as remainder. So you need another 3 to go to the next multiple of 7). So y must be at least 3.
Think: Can y take other values? If yes, which ones?
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Karishma
Veritas Prep GMAT Instructor
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