New DS set!!!

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?

The question: is P(R and R)=R/10*(R-1)/9>3/5?
Is R(R-1)>54?
Is R>7? (By number plugging) So, the question asks whether the number of red marbles is more than 7 (8, 9, or 10).

(1) The probability that both marbles selected will be blue is less than 1/10. This implies that B/10*(B-1)/9<1/10. So, we have that B(B-1)<9, thus B<4, so the number of red marbles in the jar is 7, 8, 9, or 10. Not sufficient.

(2) At least 60% of the marbles in the jar are red. This implies that the number of red marbles is 6 or more. Not sufficient.

(1)+(2) From above we have that R>6. Not sufficient.

Answer: E.

Hi,

Could you please help me on this..

how R(R-1)>54 turns R>7?

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.

I have a doubt that in set A if i substitute x as 1 and y=3 i get (1,2,3,4,5) and for set B it is (1,2,3,3,4,5) now which will have a greater standard deviation or will it be same?
Like the elements in B are more and the deviation in both sets from mean is same so B should have bigger SD but If use the logic adding nos same as mean decreases SD then Set A will have bigger SD

9. Is x^2>2x?

Is x(x-2)>0? --> is x<0 or x>2. Basically if x is not 0, 1, or 2 we have an YES answer to the question.

(1) x is a prime number. If x=2 then the answer is NO but if x is some other prime, then the answer is YES. Not sufficient.

(2) x^2 is a multiple of 9. If x=0 then the answer is NO but if x=3, then the answer is YES. Not sufficient.

(1)+(2) Since from (1) x is a prime and from (2) x^2 is a multiple of 9, then x can only be 3. Therefore the answer to the question is YES. Sufficient.

Answer: C.

Problem with statement 2. How can 0 be a multiple of 9?

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.

Median of a right angled triangle is half of the hypotenuse only if it is an isosceles triangle. Should this not be option C??

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.

Answer: C.

What is the problem with 0,1,2? isn't it also an answer and thus even both together can't answer the question

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?

Given that the ratio of the number of employees is \(3x:4x:8x\) for some positive multiple \(x\).

The question asks whether the average age, which is equal to \(\frac{(total \ age)}{(number \ of \ employees)} < 40\). This is equivalent to asking whether \(\frac{(total \ age)}{3x+4x+8x} < 40\), or in other words: is \((total \ age) < 600x\)?

(1) The total age of all the employees in these companies is 600 years.

The question simplifies to: is \(600 < 600x\)? Or equivalently, is \(1 < x\)?

We do not know that: if \(x=1\), then the answer is NO, but if \(x > 1\), then the answer is YES. Not sufficient.

(2) The average age of employees in X, Y, and Z, is 40, 20, and 50 years, respectively.

The above implies that \((total \ age)=40*3x+20*4x+50*8x=600x\), so the answer to the question is NO. Sufficient.


Answer: B

­Thank you so much for the questions and answers!

Given that the ratio of the number of employees is \(3x:4x:8x\) for some positive multiple \(x\)., why is it wrong to assume that x has to be 1 or greater than 1?
After all, we are talking about people here and the number of employees has to be an integer number.

Thanks in advance!

Looking for a DS probability trap question which goes something like this, can anyone help?

What is the probability of event X happening?

1) Probability of event X not happening is 0.2
2) Probability of event X happening is 0.8