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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.

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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).

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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).

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