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I'm posting the next set of medium/hard DS questions. I'll post OA's with detailed explanations after some discussion. Please, post your solutions along with the answers. Good luck!

1. Bonnie can paint a stolen car in x hours, and Clyde can paint the same car in y hours. They start working simultaneously and independently at their respective constant rates at 9:45am. If both x and y are odd integers, is x=y? (1) x^2+y^2<12 (2) Bonnie and Clyde complete the painting of the car at 10:30am

4. How many numbers of 5 consecutive positive integers is divisible by 4? (1) The median of these numbers is odd (2) The average (arithmetic mean) of these numbers is a prime number

7. A certain fruit stand sold total of 76 oranges to 19 customers. How many of them bought only one orange? (1) None of the customers bought more than 4 oranges (2) The difference between the number of oranges bought by any two customers is even

10. The function f is defined for all positive integers a and b by the following rule: f(a,b)=(a+b)/GCF(a,b), where GCF(a,b) is the greatest common factor of a and b. If f(10,x)=11, what is the value of x? (1) x is a square of an integer (2) The sum of the distinct prime factors of x is a prime number.

1. B 2. A 3. B 4. D 5. D 6. E 7. D 8. C 9. B 10. C 11. D 12. E

10 correct answers out of 12.

khaadu wrote:

1-b 2-a 3-b 4-a 5-b 6-e 7-d 8-b 9-e 10-a 11-d 12-a

7 correct answers out of 12.

vinayaerostar wrote:

Ans: 1-B 2-A 3-A 4-E 5-D 6-E 7-C 8-A 9-C 10-A 11-D 12-D

4 correct answers out of 12.

Good job everyone! By the way it's better if you post the solutions along with the answers: others will benefit with your approaches and you'll get 1 Kudos point per correct solution.

Will post explanations in couple of days, so that to give some more time to those who want to participate.
_________________

1. Bonnie can paint a stolen car in x hours, and Clyde can paint the same car in y hours. They start working simultaneously and independently at their respective constant rates at 9:45am. If both x and y are odd integers, is x=y? (1) x^2+y^2<12 (2) Bonnie and Clyde complete the painting of the car at 10:30am

The catch is that they are working independently.

stmt 1 - no relation there are can be multiple values of x and y stmt 2 - both started at same time, finished at same time with no breaks means they have same working rate proves x = y sufficient

My funda - Area of square is largest among all the quadilateral with same perimeter. Stmt 1 - Only possible values of x and y are 1/Sqrt(2). So sufficient as xy = 1/2 Stmt 2 - Only says x and y are equal. Not sufficient Answer A

1. Bonnie can paint a stolen car in x hours, and Clyde can paint the same car in y hours. They start working simultaneously and independently at their respective constant rates at 9:45am. If both x and y are odd integers, is x=y? (1) x^2+y^2<12 (2) Bonnie and Clyde complete the painting of the car at 10:30am

The catch is that they are working independently.

stmt 1 - no relation there are can be multiple values of x and y stmt 2 - both started at same time, finished at same time with no breaks means they have same working rate proves x = y sufficient

Answer B

The logic for (2) is not correct, (though I'm not saying that (2) is insufficient). Even if two entities have different rates if they work together they both stop when the job is done.
_________________

My funda - Area of square is largest among all the quadilateral with same perimeter. Stmt 1 - Only possible values of x and y are 1/Sqrt(2). So sufficient as xy = 1/2 Stmt 2 - Only says x and y are equal. Not sufficient Answer A

You are close to correct reasoning for (1), though from it you can not say that xy=1/2 and the only possible value for x and y are 1/Sqrt(2). Consider the following example: 0^1+1^2=1.

As for (2): x^2-y^2=0 doesn't mean that x=y.
_________________

3. If a, b and c are integers, is abc an even integer? (1) b is halfway between a and c (2) a = b - c

Funda for product abc to be even, if any one of them even then product will be even.

Stmt 1 - says b = (a+c)/2 means a+c is some even number. E + E also results in even O + O also results in Even and b can be anything even or odd so not sufficient.

Stmt 2 - says a = b - c say worst condition b an c are odd . will results in a even. or lets says any one among b or c is even then a off but since one number is even the product will be even so sufficient.

3. If a, b and c are integers, is abc an even integer? (1) b is halfway between a and c (2) a = b - c

Funda for product abc to be even, if any one of them even then product will be even.

Stmt 1 - says b = (a+c)/2 means a+c is some even number. E + E also results in even O + O also results in Even and b can be anything even or odd so not sufficient.

Stmt 2 - says a = b - c say worst condition b an c are odd . will results in a even. or lets says any one among b or c is even then a off but since one number is even the product will be even so sufficient.

1. Bonnie can paint a stolen car in x hours, and Clyde can paint the same car in y hours. They start working simultaneously and independently at their respective constant rates at 9:45am. If both x and y are odd integers, is x=y? (1) x^2+y^2<12 (2) Bonnie and Clyde complete the painting of the car at 10:30am

The catch is that they are working independently.

stmt 1 - no relation there are can be multiple values of x and y stmt 2 - both started at same time, finished at same time with no breaks means they have same working rate proves x = y sufficient

Answer B

The logic for (2) is not correct, (though I'm not saying that (2) is insufficient). Even if two entities have different rates if they work together they both stop when the job is done.

-----------------------------

yes but isn't it correct to say that when they are working independently and starting at same time (as per the question) and ending at same time as per stmt 2 then they must be working at same rate - i.e. X = Y...

As stmt 2 doesn't say they are not working together.

yes but isn't it correct to say that when they are working independently and starting at same time (as per the question) and ending at same time as per stmt 2 then they must be working at same rate - i.e. X = Y...

As stmt 2 doesn't say they are not working together.

No, that's not correct. Again when: two or more entities (machines, people, ...) are working together they all stop working when the job is done, no matter what their respective rates are. I think that you are thrown away by the phrase "they start working simultaneously and independently", which simply means that they start at the same time and work together (obviously they will also end the work at the same time, when the work is done).

4. How many numbers of 5 consecutive positive integers is divisible by 4? (1) The median of these numbers is odd (2) The average (arithmetic mean) of these numbers is a prime number

out of 5 consecutive intergers there are only 2 option either there will 1 or 2 numbers which will divide by 4. There will 2 numbers if the first number fo sequence will be divible by 4. So we have to find out if first number is divisible by 4.

Stmt 1 - Median is odd means first number is odd ( odd , even , odd, even, odd) So sufficuent to tell that there will only 1 number which be divible by 4. Stmt 2 - In case of consecutive numbers median is always equal to average. Numbers are positive so first numbers cannot be 0 to make 2 as median/average. Which means average/mean is odd, Again going by logic in stmt 1 first number should be odd which is also sufficient