Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack
GMAT Club

 It is currently 25 Mar 2017, 06:53

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# New DS set!!!

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 37581
Followers: 7394

Kudos [?]: 99440 [19] , given: 11022

### Show Tags

10 Apr 2013, 08:10
19
KUDOS
Expert's post
83
This post was
BOOKMARKED
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: new-ds-set-150653-60.html#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: new-ds-set-150653-60.html#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: new-ds-set-150653-60.html#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: new-ds-set-150653-60.html#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: new-ds-set-150653-60.html#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: new-ds-set-150653-80.html#p1211908

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

(1) The median temperature in City A in March was less than the median temperature in city B
(2) The ratio of the average temperatures in A and B in March was 3 to 4, respectively

Solution: new-ds-set-150653-80.html#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: new-ds-set-150653-80.html#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: new-ds-set-150653-80.html#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: new-ds-set-150653-80.html#p1211912

Kudos points for each correct solution!!!
_________________
Intern
Joined: 10 Apr 2012
Posts: 23
Concentration: Finance, Economics
GMAT 1: 760 Q50 V44
GMAT 2: Q V
GMAT 3: Q V
Followers: 0

Kudos [?]: 35 [2] , given: 0

### Show Tags

11 Apr 2013, 16:37
2
KUDOS
See Img for my solutions.These are very good question...
Attachments

Note_20130401_142801_05.jpg [ 55.91 KiB | Viewed 13186 times ]

Note_20130401_142801_04.jpg [ 68.96 KiB | Viewed 13198 times ]

Intern
Joined: 10 Apr 2012
Posts: 23
Concentration: Finance, Economics
GMAT 1: 760 Q50 V44
GMAT 2: Q V
GMAT 3: Q V
Followers: 0

Kudos [?]: 35 [1] , given: 0

### Show Tags

11 Apr 2013, 16:39
1
KUDOS
See Img for my solutions.These are very good questions.
Attachments

Note_20130401_142801_07.jpg [ 71.59 KiB | Viewed 13083 times ]

Note_20130401_142801_06.jpg [ 76.15 KiB | Viewed 13087 times ]

Intern
Joined: 10 Apr 2012
Posts: 23
Concentration: Finance, Economics
GMAT 1: 760 Q50 V44
GMAT 2: Q V
GMAT 3: Q V
Followers: 0

Kudos [?]: 35 [1] , given: 0

### Show Tags

11 Apr 2013, 16:41
1
KUDOS
See Img for my solutions.These are very good questions.
Attachments

Note_20130401_142801_09.jpg [ 65.12 KiB | Viewed 13078 times ]

Note_20130401_142801_08.jpg [ 82.77 KiB | Viewed 13081 times ]

Senior Manager
Joined: 16 Dec 2011
Posts: 452
Followers: 11

Kudos [?]: 210 [1] , given: 70

### Show Tags

11 Apr 2013, 21:44
1
KUDOS
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

1) Set of 3 integers can be (-1,0,1,), (0,1,2), (1,2,3), (2,3,4), ……, (200,201,202),………………..
Not sufficient.

2) Set of 3 integers can be (0,1,2), (-1,0,1,), (-2,-1,0), (-3,-2,-1), ……, (-102,-101,-100),………………..
Not sufficient.

Together: Only possible sets are (-1,0,1,) and (0,1,2)for which at least one of the integers is positive and sum of the integers is less than 6. For both of these sets, product of elements is 0.
Sufficient.

Senior Manager
Joined: 16 Dec 2011
Posts: 452
Followers: 11

Kudos [?]: 210 [1] , given: 70

### Show Tags

11 Apr 2013, 21:45
1
KUDOS
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

1) Information on y is only given. No information on x. Not sufficient.
2) x/y = q + 9/y. For y > 9, remainder will be 9 when x is divided by y. But remainder will be different for other y’s, Not sufficient.

Together: y>9 --> remainder will be 9 when x is divided by y. Sufficient.

Senior Manager
Joined: 16 Dec 2011
Posts: 452
Followers: 11

Kudos [?]: 210 [2] , given: 70

### Show Tags

11 Apr 2013, 21:47
2
KUDOS
1
This post was
BOOKMARKED
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

1) There is no information on angles and which two sides are equal. Not sufficient.

2) It says that angle at B is right angle and AC is hypotenuse. If any right-angled triangle is inscribed in a circle, the hypotenuse of the triangle must be diameter of circle and the median extending to the hypotenuse of the triangle must be radius of the circle -->Median is equal to half of the hypotenuse --> AC = 24. Sufficient.

Senior Manager
Joined: 16 Dec 2011
Posts: 452
Followers: 11

Kudos [?]: 210 [2] , given: 70

### Show Tags

11 Apr 2013, 21:48
2
KUDOS
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

Assuming A and B takes x and y days respectively to finish the work alone.
In 6 days, work done by A = 6/x, work done by B = 6/y, total work done by A and B together = 6/x + 6/y
6/x + 6/y = 1 --> 6x + 6y = xy …. (eq1)

1) (x+y)/2 = 12.5 --> x+y = 25
Substituting this in eq1, 6*25 = x(25-x) --> x^2 -25x + 150 = 0 --> (x-10)(x-15) = 0 --> x = 10 or 15
Not sufficient.

2) y = x-5
Substituting this in eq1, 6x + 6x – 30 = x(x-5) --> x^2 -17x + 30 = 0 --> (x-2)(x-15) = 0 --> x = 2 or 15
If x = 2, y become -3 which is impossible. --> x = 15.
Sufficient.

Senior Manager
Joined: 16 Dec 2011
Posts: 452
Followers: 11

Kudos [?]: 210 [1] , given: 70

### Show Tags

11 Apr 2013, 21:50
1
KUDOS
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

1) Standard deviation can be positive or zero (in case of x=0). Here the information only says that x is not zero and all elements have different values. But, without knowing y, we cannot conclude. Not sufficient.
2) This says mean of both the sets is 3, no. of elements are 5 and 6 for A and B respectively. If x is not equal to 0, elements in set A will be more spread than those in set B. If x = 0, Standard deviation of both the sets will be zero. Not sufficient.

Together: x is not equal to 0 --> elements in set A will be more spread than those in set B --> standard deviation of set A is more than that of set B. Sufficient.

Senior Manager
Joined: 16 Dec 2011
Posts: 452
Followers: 11

Kudos [?]: 210 [1] , given: 70

### Show Tags

11 Apr 2013, 21:51
1
KUDOS
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.

Assuming number of employees in X, Y, Z are 3n, 4n, 8n respectively. So, total number of employees = 15x

1) We know the total age, but we do not know total number of employees or number of employees of any single company. Not sufficient.
2) Average age = (3x*40 + 4x*20+8x*50)/15x = (120+80+400)/15 = 600/15 = 40. Sufficient.

Senior Manager
Joined: 16 Dec 2011
Posts: 452
Followers: 11

Kudos [?]: 210 [0], given: 70

### Show Tags

11 Apr 2013, 21:51
7. Was the average (arithmetic mean) temperature in city A in March less than the average (arithmetic mean) temperature in city B in March?
(1) The median temperature in City A in March was less than the median temperature in city B
(2) The ratio of the average temperatures in A and B in March was 3 to 4, respectively

1) This says nothing about temperatures of other days. Not sufficient.
2) This says that the average temperature in city A in March was less than the average temperature in city B in March. Sufficient.

Senior Manager
Joined: 16 Dec 2011
Posts: 452
Followers: 11

Kudos [?]: 210 [1] , given: 70

### Show Tags

11 Apr 2013, 21:52
1
KUDOS
1
This post was
BOOKMARKED
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

1) If there are 4 blue marbles, probability of drawing 2 blue marbles = 4/10 * 3/9 = 2/15 > 1/10
If there are 3 blue marbles, probability of drawing 2 blue marbles = 3/10 * 2/9 = 1/15 < 1/10
So, there are maximum 3 blue marbles and at least 7 red marbles in the jar.
If there are 7 red marbles, probability of drawing 2 red marbles = 7/10 * 6/9 = 7/15 < 3/5
If there are 8 red marbles, probability of drawing 2 red marbles = 8/10 * 7/9 = 28/45 > 3/5
Not sufficient.

2) As seen from calculations against option 1, with 6 or 7 red marbles, probability of drawing 2 red marbles will be less than 3/5, and 8 or more red marbles, probability of drawing 2 red marbles will be more than 3/5.
Not sufficient.

Together: There is no added information found from option 1 and 2 together. Number of red marbles can be 7 or 8 or 9 10 which may result in probability of drawing 2 red marbles to be less than or more than 3/5.
Not sufficient.

Senior Manager
Joined: 16 Dec 2011
Posts: 452
Followers: 11

Kudos [?]: 210 [2] , given: 70

### Show Tags

11 Apr 2013, 21:52
2
KUDOS
1
This post was
BOOKMARKED
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.

Senior Manager
Joined: 16 Dec 2011
Posts: 452
Followers: 11

Kudos [?]: 210 [1] , given: 70

### Show Tags

11 Apr 2013, 21:55
1
KUDOS
1
This post was
BOOKMARKED
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.

1) This means all elements in the set have the same value and that is same to mean and median as well. But, we do not know the number. Not sufficient.
2) There are many sets for which average and range will be the same. Examples are: [10,10,30,30] where median is 20, or [2,2,3,3,5] where median is 3. Not sufficient.

Together: This is possible only when all elements have the same value as 0 --> average = range = 0 --> median = 0

Note: I believe the question should be read as “What is the value of the median of set A?”
Manager
Status: Pushing Hard
Affiliations: GNGO2, SSCRB
Joined: 30 Sep 2012
Posts: 89
Location: India
Concentration: Finance, Entrepreneurship
GPA: 3.33
WE: Analyst (Health Care)
Followers: 1

Kudos [?]: 83 [1] , given: 11

### Show Tags

11 Apr 2013, 23:07
1
KUDOS
Bunuel wrote:
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

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

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

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

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

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.

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

(1) The median temperature in City A in March was less than the median temperature in city B
(2) The ratio of the average temperatures in A and B in March was 3 to 4, respectively

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

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

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

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.

Kudos points for each correct solution!!!

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

-------------------------------------
Bunuel wrote:
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

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

We have to find out the product of n*(n+1)*(n+2).....
stmt. 1 -- At least one of the integers is positive --- Not sufficient
stmt. 2 -- The sum of the integers is less than 6, that means n+n+1+n+2<6, so 3n+3<6. therefore, n<1, so with the help of stmt 2 we will get different values... not sufficient.

now 1+2 ----- At least one of the integers is positive & n<1 ...... we will get the desired answer.
hence, C.

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

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

for this I think the answer is C....

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

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.

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

As given in the Question, we have the ratio of the number of employees of three companies X, Y and Z is 3:4:8 & the Question asks us that Is 3x+4y+8z/15 <40 or Is 3x+4y+8z < 600 ....

Remember that this is a Yes/No question ....

stmt. 1 ---- it clearly tells us that 3x+4y+8z =600 ... therefore it says that 3x+4y+8z = 600 but not < 600.

stmt. 2 ---- after calculating, it also clearly says that 3x+4y+8z=600 but not < 600.

Hence, D... Both stmts are sufficient.

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

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

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

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

stmt 2 clearly says average temperature in city A in March less than the average temperature in city B in March.

Hence, as I can understand, B is sufficient.
----------------------------------------------------------------

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

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

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

For me B is suffient ....

-------------------------------------------
Kudos points for each correct solution!!!

_________________

If you don’t make mistakes, you’re not working hard. And Now that’s a Huge mistake.

Tutor
Joined: 20 Apr 2012
Posts: 101
Location: Ukraine
GMAT 1: 690 Q51 V31
GMAT 2: 730 Q51 V38
WE: Education (Education)
Followers: 26

Kudos [?]: 276 [3] , given: 36

### Show Tags

12 Apr 2013, 03:48
3
KUDOS
1
This post was
BOOKMARKED
1. (1) Insufficient. It could be {0,1,2} and the product is 0, or it could be {1,2,3} and their product is 6.
(2) Insufficient. It could be {0,1,2} and the product is 0, or it could be {-3,-2,-1} and the product is -6

(1)+(2) Sufficient. Suppose the least number is n, so the second is (n+1) and the third is (n+2). Their sum must be less than 6: n+(n+1)+(n+2)<6 or 3n+3<6 or n<1. By first statement at least one of the integers must be positive, it means that the largest is positive: n+2>0 or n>-2. So n=-1 or n=0. Therefore, there are two possible sets {-1, 0, 1} or {0, 1, 2}. The product anyway is 0.

2. (1) Insufficient. For x=11 and y=10 the remainder when x is divided by y is 1, for x=12 and y=2 the remainder when x is divied by y is 2.
(2) Insufficient. The main point here is the remainder must be less than the divisor. We don't know is y>9 or y<=9. For y=1 the remainder when x is divided by y is 0, for y=2, x=2q+9 the remainder is 1 when x is divided by 2.

(1)+(2) Sufficient. If y is a two-digit number the when qy is divided by y there is remainder 0, and when 9 is divided by y the remainder is 9, since 9<y. So, x when divided by y gives the remainder 9.

_________________

I'm happy, if I make math for you slightly clearer
And yes, I like kudos:)

Math Expert
Joined: 02 Sep 2009
Posts: 37581
Followers: 7394

Kudos [?]: 99440 [3] , given: 11022

### Show Tags

14 Apr 2013, 08:59
3
KUDOS
Expert's post
4
This post was
BOOKMARKED
SOLUTION:

1. What is the product of three consecutive integers?

(1) At least one of the integers is positive.

We can have three cases:
(i) All three integers are positive. In this case the product will obviously be positive.
(ii) Two of the integers are positive: {0, 1, 2}. In this case the product will be zero.
(iii) Only one of the integers is positive: {-1, 0, 1}. In this case the product will be zero.

Not sufficient.

(2) The sum of the integers is less than 6. Clearly insufficient, consider {-1, 0, 1} and {-3, -2, -1}.

(1)+(2) The second statement implies that we cannot have case (i) from (1), since the least sum of three positive consecutive integers is 1+2+3=6. Thus we have either case (ii) or case (iii). Therefore the product of the integers is zero. Sufficient.

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 37581
Followers: 7394

Kudos [?]: 99440 [4] , given: 11022

### Show Tags

14 Apr 2013, 09:00
4
KUDOS
Expert's post
11
This post was
BOOKMARKED
2. If x and y are both positive integers and x>y, what the remainder when x is divided by y?

If $$x$$ and $$y$$ are positive integers, there exist unique integers $$q$$ and $$r$$, called the quotient and remainder, respectively, such that $$y =divisor*quotient+remainder= xq + r$$ and $$0\leq{r}<x$$.

(1) y is a two-digit prime number. Clearly insufficient since we know nothinf about x.

(2) x=qy+9, for some positive integer q. It's tempting to say that this statement is sufficient and $$r=9$$, since given equation is very similar to $$y =divisor*quotient+remainder= xq + r$$ . But we don't know whether $$y>9$$: remainder must be less than divisor.

For example:
If $$x=10$$ and $$y=1$$ then $$10=1*1+9$$, then the remainder upon division 10 by 1 is zero.
If $$x=11$$ and $$y=2$$ then $$11=1*2+9$$, then the remainder upon division 11 by 2 is one.
Not sufficient.

(1)+(2) From (2) we have that $$x=qy+9$$ and from (1) that y is more than 9 (since it's a two-digit number), so we have direct formula of remainder, as given above. Sufficient.

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 37581
Followers: 7394

Kudos [?]: 99440 [0], given: 11022

### Show Tags

14 Apr 2013, 09:01
Expert's post
6
This post was
BOOKMARKED
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. Clearly insufficient.

(2) AC^2 = AB^2 + BC^2. This statement implies that ABC is a right triangle and AC is its hypotenuse. Important property: median from right angle is half of the hypotenuse, hence BD=12=AC/2, from which we have that AC=24. Sufficient.

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 37581
Followers: 7394

Kudos [?]: 99440 [5] , given: 11022

### Show Tags

14 Apr 2013, 09:01
5
KUDOS
Expert's post
3
This post was
BOOKMARKED
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?

Given that 1/A+1/B=1/6, where A is the time needed for machine A to complete the task working alone and B is the time needed for machine B to complete the task working alone.

(1) The average time A and B can complete the task working alone is 12.5 days. This statement implies that A+B=2*12.5=25. Now, since we don't know which machine works faster then even if we substitute B with 25-A (1/A + 1/(25-A) = 1/6) we must get two different answers for A and B: A<B and A>B. Not sufficient.

(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. A=B+5, so we have that 1/A+1/(A-5)=1/6. From this we can find that A=2 (not a valid solution since in this case B will be negative) or A=15. Sufficient.

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 37581
Followers: 7394

Kudos [?]: 99440 [4] , given: 11022

### Show Tags

14 Apr 2013, 09:02
4
KUDOS
Expert's post
13
This post was
BOOKMARKED
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. We know that the standard deviation of any set is more than or equal to zero. The standard deviation of a set is zero only when the set consists of identical elements. So, this statement implies that set A does NOT consists of identical elements or that x does not equal to zero. Still this statement is not sufficient to answer the question.

(2) y=3. The mean of set A is 3. Now, if $$x\neq{0}$$ for example if x=1, then the standard deviation of B would be smaller that the standard deviation A, since the elements of B would be less widespread than the element of set A. But if x=0, then A={3, 3, 3, 3, 3} and B={3, 3, 3, 3, 3, 3}, so both will have the standard deviation of zero. Bot sufficient.

(1)+(2) Since from (1) $$x\neq{0}$$, then adding a new element which equals to the mean will shrink the standard deviation, thus SD(A)>SD(B). Sufficient.

_________________
Re: New DS set!!!   [#permalink] 14 Apr 2013, 09:02

Go to page   Previous    1   2   3   4   5   6   7    Next  [ 134 posts ]

Similar topics Replies Last post
Similar
Topics:
4 When one new number is included in an existing set of 6 numbers 4 12 Sep 2014, 07:24
1 If set T was derived from set S when all elements of set S w 5 18 Mar 2014, 03:30
3 Set D is a new set created by combining all the terms of Set 9 18 Aug 2013, 13:36
373 New Set: Number Properties!!! 177 25 Mar 2013, 04:50
1 If set B is a subset of Set A, how many elements are in set 11 28 Nov 2012, 22:15
Display posts from previous: Sort by