24 Very Imp++....Questions........

Great job Manish!

Q1. The answer is 39(E). Clearly if we are to look at a minimal set of 6 primes, the set would be {2,3,5,7,11,13}. Since the set is even number-ed, the median = average of 3rd and 4th element.

Now In any case the 3rd and 4th element cannot be 2. So the Median will always an integer (odd+odd/2 = integer). So we can eliminate 9.5 and 12.5 from the choices. Like I have mentioned before, the minimal set being {2,3,5,7,11,13}, the median will always be greater than 6. Hence 2,3 are eliminated. Hence, 39!

Q2. The answer would be (B). Statement 1, provides the exact value of the average daily high temp i.e. 72 degrees, but doesn't talk abt the median. But Statement 2, clearly states that 60% of the daily high temps are below the average. Hence, the median, which will lie on the mid of the ordered set of daily high temps will be clearly less that the average! Hence, just B is sufficient!

Q3. The answer would be [C]. Statement 1 gives the information that, 25% of total projects (Let the total be x) have 4 or more employes. Clearly not sufficient.
But can be concluded that 3/4x projects have 0,1,2,3 employes assigned.
Statement 2, states that 35% of x have {0,1,2}employes assigned. Now individually the statement in insufficient. But, when added with Statement 1 can be used to find the ratio of projects with 3 employes assigned i.e 40% of x.

To visualize the median, Please imagine a number line, with 35/100x number of projects have {0,1,2} Range : 0 - 35/100x
for {3} Range : 35/100x - 75/100x. Since the half value lies between the above range, the median will be 3. Hence, both the statements are needed. [C]
for {4....} Range: 75/100x- x.

Q4 Answer would be [C] again! Statement 1 and 2 are individually not sufficient, but when combined tell us that the complete set is of 49 books i.e. odd. Hence the median will not be an average, but a single number. Plotting them in this manner just gives you a better view:

25 24
<-------------> <---------------->
1.2......400 475, 476.......

Hence, the median would be 400. Both the statements together are sufficient. Hence [C]

Q5. The Answer is [C]. Statement 1, just states that k<n, Hence, there can be many sets like {6,k,n,12,17} or {6,k,12,n,17} and so on. Nothing has been said on the order yet and this can not yield the value of n. Hence insufficient.

Statement 2: Since the median is 10 less than 12 and 17, only two possible unknowns arise in the list i.e. k,n. It cannot be said concretely if k =10 or n = 10.
But when combining the both, the only possible arrangements for the same would be {6,k,n,12,17} or {k,6,n,12,17} with median = 10 i.e. n = 10 **typo! corrected!!. Hence [C].

Q6. Answer is (B). Prity easy to figure it out! One look at the choices and you can. Statement 1, clearly is not sufficient as it would mearly give you the sum of the cost of the houses of Jane ans Sue.

But Statement 2 states that the average of the 3 houses = House cost of Jane. Now in case when the average = individual member of a set, it can be seen that the median will the member itself i.e. Jane is the median. Hence, (B).

En route on the other ones

Regards,
Arpan

P.S Editing the post as I solve more!