Q5) Is the standard deviation of set A {3-2x, 3-x, 3, 3+x, 3+2x} > the standard deviation of set B={3-2x, 3-x, 3, 3+x, 3+2x, y}

From Stmt 1, y is not known and only SD > 0 - Not Sufficient
If y <= 3 SD of set A > SD of set B and for other values SD of set A < SD of set B

From Stmt 2, y = 3 - Sufficient
When y = 3 and for any integer value for x SD is always >= 0 and SD of set A > SD of set B

Answer is B
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See Img for my solutions.These are very good questions.

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.

Answer is C.

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.

Answer is B.

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.

Answer is B.

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.

Answer is E.

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

Answer is C.

Note: I believe the question should be read as “What is the value of the median of set A?”

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.

The correct answer is C.

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.

The correct answer C
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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.

Answer: B.
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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.

Answer: C.
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Resources:
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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