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.

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.

Answer is B.

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.

Answer is C.

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.

Answer is B.

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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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.

Answer: C.
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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.

Answer: B.
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