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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
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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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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?

The function f(x) = |x – 2| + |2.5 – x| + |3.6 – x|, where x is a real number, attains a minimum at 1. x = 2.3 2. x = 2.5 3. x = 2.7 4. None of the above Soln. (2) — Case 1: If x < 2, then y = 2 – x + 2.5 – x + 3.6 – x = 8.1 – 3x. This will be least if x is highest i.e. just less than 2. In this case y will be just more than 2.1 Case 2: If 2 x 2.5 , then y = x – 2 + 2.5 – x 3.6 – x = 4.1 – x Again, this will be least if x is the highest case y will be just more than 1.6. Case 3: If 2.5 x 3.6 , then y = x – 2 + x – 2.5 + 3.6 – x = x – 0.9 This will be least if x is least i.e. X = 2.5. Case 4: If In this case y = 1.6 X 3.6 , then y = x – 2 + x – 2.5 + x – 3.6 = 3x – 8.1 The minimum value of this will be at x = 3.6 = 27 Hence the minimum value of y is attained at x = 2.5

Here is another set on another 123 tricky questions covering allmost all topics in PS and DS.

If you have any doubt then please bring it on the forum. Lets analyse together.

Hello, 89th prob.., we are asked to find out the dollar amount received after sale of suits ,, but the solution ended after finding number of suits!! amount would be <price of each suit * number of suits> i.e. x*(200-x/2).., correct me if m wrong!!

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Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
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Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
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