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.

1. What is the product of three consecutive integers?

(1) At least one of the integers is positive
(2) The sum of the integers is less than 6

Solution: http://gmatclub.com/forum/new-ds-set-15 ... l#p1211902


2. If x and y are both positive integers and x>y, what the remainder when x is divided by y?

(1) y is a two-digit prime number
(2) x=qy+9, for some positive integer q

Solution: http://gmatclub.com/forum/new-ds-set-15 ... l#p1211903


3. The length of the median BD in triangle ABC is 12 centimeters, what is the length of side AC?

(1) ABC is an isosceles triangle
(2) AC^2 = AB^2 + BC^2

Solution: http://gmatclub.com/forum/new-ds-set-15 ... l#p1211904


4. Two machines, A and B, each working at a constant rate, can complete a certain task working together in 6 days. In how many days, working alone, can machine A complete the task?

(1) The average time A and B can complete the task working alone is 12.5 days.
(2) It would take machine A 5 more days to complete the task alone than it would take for machine B to complete the task

Solution: http://gmatclub.com/forum/new-ds-set-15 ... l#p1211906


5. Set A={3-2x, 3-x, 3, 3+x, 3+2x}, where x is an integer. Is the standard deviation of set A more than the standard deviation of set B={3-2x, 3-x, 3, 3+x, 3+2x, y}

(1) The standard deviation of set A is positive
(2) y=3

Solution: http://gmatclub.com/forum/new-ds-set-15 ... l#p1211907


6. The ratio of the number of employees of three companies X, Y and Z is 3:4:8, respectively. Is the average age of all employees in these companies less than 40 years?

(1) The total age of all the employees in these companies is 600
(2) The average age of employees in X, Y, and Z, is 40, 20, and 50, respectively.

Solution: http://gmatclub.com/forum/new-ds-set-15 ... l#p1211908


7. Was the average (arithmetic mean) temperature in degrees Celsius in city A in March less than the average (arithmetic mean) temperature in degrees Celsius in city B in March?

(1) The median temperature in degrees Celsius in City A in March was less than the median temperature in degrees Celsius in city B.

(2) The ratio of the average temperatures in degrees Celsius in A and B in March was 3 to 4, respectively.

Solution: http://gmatclub.com/forum/new-ds-set-15 ... l#p1211909


8. Two marbles are drawn from a jar with 10 marbles. If all marbles are either red of blue, is the probability that both marbles selected will be red greater than 3/5?

(1) The probability that both marbles selected will be blue is less than 1/10
(2) At least 60% of the marbles in the jar are red

Solution: http://gmatclub.com/forum/new-ds-set-15 ... l#p1211910


9. If x is an integer, is x^2>2x?

(1) x is a prime number.
(2) x^2 is a multiple of 9.

Solution: http://gmatclub.com/forum/new-ds-set-15 ... l#p1211911


10. What is the value of the media of set A?

(1) No number in set A is less than the average (arithmetic mean) of set A.
(2) The average (arithmetic mean) of set A is equal to the range of set A.

Solution: http://gmatclub.com/forum/new-ds-set-15 ... l#p1211912


Kudos points for each correct solution!!!
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9. If x is an integer, is x^2>2x?
(1) x is a prime number.
(2) x^2 is a multiple of 9.


1) If x = 2, x^2 = 2x. For any other integer, x^2 > 2x. Not sufficient.
2) As x^2 is a multiple of 9, x is not 2. So, x^2 > 2x. Sufficient.

Together: As x is prime number, x cannot be 0. As x^2 is multiple of 9, x can be 3, 6, 9, 12, …..
So, x^2 > 2x as x must be > 2. Sufficient.

Answer is C.

1. What is the product of three consecutive integers?

(1) At least one of the integers is positive
Clearly Not sufficient. {0, 1, 2} product=0; {1, 2, 3} product = 6
(2) The sum of the integers is less than 6
Clearly Not sufficient. {0, 1, 2} product=0; {-1, -2, -3} product = 6

(1)+(2) From 2 we know that \(a+(a+1)+(a+2)<6\) so \(a<1\)
The three integers are \(a,a+1,a+2\), and at least one is positive (knowing that a is an integer less than 1) : 1)a>0 this cannot be: there is no integer between 0 and 1;
2)a+1>0 a>-1 with a<1 there is one solution a=0 and the product is 0 {0,1,2};3) a+2>0 a>-2 here we have 2 solutions a=-1 and the numbers are {-1,0,1}=>prod=0 or a=0 and the product is 0.
IMO C
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Q8) Whether the probably of drawing 2 red marbles from a jar of 10 marbles is > 3/5

From Stmt 1, the probability that both marbles selected will be blue is < 1/10 and since there are only red and blue marbles in the jar

The probability of selecting both marbles red = 1 - LT 1/10 ==> GT 9/10 - Sufficient

From Stmt 2, the number of red marbles in the jar is at least 60 % is >= 6 of 10 marbles in the jar

The probability of selecting both marbles red >= 6/10 * 5/9 >= 0.333 which can be less than 3/5 when there are 6 red marbles and more than 3/5 when there are 9 red marbles - Not Sufficient

Hence answer is A
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Q10) What is the value of the media of set A?

From Stmt 1, No number in set A < Avg, of set A

This implies all the numbers in the set are equal to the average otherwise the Avg of the set A will be more if any one number is more than the Avg. Hence the median of set A in which all the numbers are same as the Avg. is none other than the Avg. value. - Sufficient.

From Stmt 2, Avg. of set A is = Amax - Amin of Set A.

This only implies the lower and upper limit of Set A and they could be even or odd number of values in the set. This will result in various values for median within Amin and Amin. - Not Sufficient.

Answer is A
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6. The ratio of the number of employees of three companies X, Y and Z is 3:4:8, respectively. Is the average age of all employees in these companies less than 40 years?

(1) The total age of all the employees in these companies is 600
Not sufficient. ie totEmployees= 15 (3+4+8) => average age = 600/15=40 or totEmployees = 30 (2*(3+4+8))=> average age = 600/30=20. In the first case the answer is NO, in the second is YES
(2) The average age of employees in X, Y, and Z, is 40, 20, and 50, respectively.
\(\frac{(40*3+20*4+50*8)}{15}=\frac{120+80+400}{15}=\frac{600}{15}=40\) If you weight the average age with the ratios you find out that the average age is 40, which is NOT less than 40. Sufficient
IMO B
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Q6) Is Avg. age of employees of three companies X, Y and Z < 40 years?

Using the unknown multiplier approach, the number of employees in companies X, Y, and Z are 3x, 4x, and 8x respectively

From Stmt 1, the total age of all the employees in 3 companies is 600 - Not Sufficient

If x = 1, the total employees in companies X, Y and Z is 3 + 4 + 8 = 15, so the avg. age of employees is 600 / 15 = 40 years
If x = 2, the total employees in companies X, Y and Z is 6 + 8 + 16 = 30, so the avg. age of employees is 600 / 30 = 20 years

From Stmt 2, avg age of X is 40, avg age of Y is 20, and avg age of z is 50 - Sufficient

If x = 1, the total employees in companies X, Y and Z is 3 + 4 + 8 = 15, so the avg. age of employees is (40*3+20*4+50*8) / 15 = 40 years
If x = 2, the total employees in companies X, Y and Z is 6 + 8 + 16 = 30, so the avg. age of employees is (40*6+20*8+50*16) / 30 = 40 years

Answer is B
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Q7) Average (arithmetic mean) temperature in city A in March < the average (arithmetic mean) temperature in city B in March?

From Stmt 1, average temperate for City A and B cannot be determined from median - Not Sufficient

mean = median IFF the temperature in City A and City B in March follows a sequence of evenly spaced values.

From Stmt 2, Avg Temp A / Avg Temp B = 3 / 4 - Sufficient

Using unknown multiplier approach Avg Temp in A is 3x and Avg Temp in B is 4x so no matter what the value of x the Avg. temp in B > Avg. temp in A

Answer is - B
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1. What is the product of three consecutive integers?

(1) At least one of the integers is positive
(2) The sum of the integers is less than 6

My answer C

Stmt 1: Three consecutive integers can be any among (-1,0,1) or (1,2,3) or (99,100,101) etc...no sufficient.
Stmt 2: Three consecutive integers can be any among (-100,-99,-98) or (-1,0,1) or (-16,-15,-14) etc...no sufficient.

combining both statements we have only 2 sets (-1,0,1) or (0,1,2). and in ether case product is 0. hence C

3. The length of the median BD in triangle ABC is 12 centimeters, what is the length of side AC?

(1) ABC is an isosceles triangle
(2) AC^2 = AB^2 + BC^2

My answer C. Solution in the attachment