Answer: Option D. -> If Statements (1) and (2) TOGETHER are NOT sufficient.
:
D
A suitable rephrase of this question is "What was thesum of the homes sale prices, and how many homes were sold?”
Statement (1):Insufficient
Seems SUFFICIENT as this statement tells us the sum of the home sale prices and the number of homes sold. Thus, the average home price is $\$$51,000,000/100 =$\$$510,000.
But we are not sure how many homes were there overall (may be more than 100). So INSUFFICIENT.
Statement (2) INSUFFICIENT:
This statement tells us the average condominium price, but not all of the homes sold in Green Glen Layout last July were condominiums. From this statement, we don't know anything about the other 40% of homes sold in Green Glen Layout, so we cannot calculate the average home sale price
$Average=\frac{\text{sum of condominium sale prices + sum of non - condominium sale prices}}{\text{number of condominiums sold + number of non - condominiums sold}}$
We have some information about the ratio of number of condominiums to non condominiums sold, 60%:40%, or 6:4, or 3:2, which could be used to pick working numbers for the total number of homes sold. However, the average still cannot be calculated because we don't have any information about the non-condominium prices.

Answer: Option B. -> If BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
:
B
For an overlapping set question, we can use a double-set matrix to organize theinformation and solve. The two sets in this question are the practical test (pass/fail)and the written test (pass/fail).
$\begin{array}{cccc}& \text{PRACTICAL - PASS}& \text{PRACTICAL - FAIL}& \text{TOTALS}\\ \text{WRITTEN - PASS}& .7x& .3x& x\\ \text{WRITTEN - FAIL}& & 0& \\ \text{TOTALS}& & .3x& \end{array}$
(1) INSUFFICIENT 1) INSUFFICIENT: If we add the total number of students to the information from thequestion, we do not have enough to solve for .7x.
$\begin{array}{cccc}& \text{PRACTICAL - PASS}& \text{PRACTICAL - FAIL}& \text{TOTALS}\\ \text{WRITTEN - PASS}& .7x& .3x& x\\ \text{WRITTEN - FAIL}& & 0& \\ \text{TOTALS}& & .3x& 188\end{array}$
(2) INSUFFICIENT: If we add the fact that 20% of the Batch B who passed thepractical test failed the written test to the original matrix from the question, we cancome up with the relationship .7x = .8y. However, that is not enough to solve for .7x.
$\begin{array}{cccc}& \text{PRACTICAL - PASS}& \text{PRACTICAL - FAIL}& \text{TOTALS}\\ \text{WRITTEN - PASS}& .7x=.8y& .3x& x\\ \text{WRITTEN - FAIL}& .2y& 0& .2y\\ \text{TOTALS}& y& .3x& \end{array}$
(1) AND (2) SUFFICIENT: If we combine the two statements we get a matrix that can be used to form two relationships between x and y;
$\begin{array}{cccc}& \text{PRACTICAL - PASS}& \text{PRACTICAL - FAIL}& \text{TOTALS}\\ \text{WRITTEN - PASS}& .7x=.8y& .3x& x\\ \text{WRITTEN - FAIL}& .2y& 0& .2y\\ \text{TOTALS}& y& .3x& 188\end{array}$
This would allow us to solve for x and in turn find the value of .7x, the number Batch B students who went to Batch A.

Answer: Option A. -> (I) only
:
A

From the above diagram, we can easily conclude that only statement I is true.

Answer: Option D. -> None of these
:
D

From the above three figures, we can conclude that 6 arrangements are possible.

Answer: Option D. -> 8738
:
D
$\begin{array}{ccccccc}& 2001& 2002& 2003& 2004& 2005& \\ CityA& 9372& 11252& 6127& 12345& 9877& 48973\\ CityB& 10765& 8328& 7056& 9362& 13125& 48636\\ CityC& 12823& 11675& 13157& 14106& 16132& 67893\\ CityD& 7352& 9137& 11346& 13451& 15769& 57055\\ CityE& 8767& 10789& 12523& 14323& 16239& 62641\\ & 49079& 51181& 50209& 63587& 71142& \end{array}$
Total non-local floating population in 2005= 71142
Number of people from the NRI category= 55% of 71142 = 39128
Number of people from the American NRI category = 27.8% of 39128 = 10878
Number of people fromt eh Foreign Nationals category = 18.8% of 71142 = 13375
Number of European NRI's = 16% of 13375= 2140
Difference = 10878 - 2140 = 8738.

Answer: Option C. -> Deepak
:
C
From the given data.As Ajit and Dinesh belong to same group, their last statements cannot be simultaneously true.Hence, their 2 statements must be true.Similarly, Bijay and Amit's second statements are false.The final table
$\begin{array}{cccc}& \text{Maths}& \text{Science}& \text{English}\\ 1^{st}& \text{Amit}& \text{Dinesh}& \text{Deepak}\\ 2^{nd}& \text{Dinesh}& \text{Bijay}& \text{Amit}\\ 3^{rd}& \text{Deepak}& \text{Ajit}& \text{Dinesh}\\ 4^{th}& \text{Ajit}& \text{Deepak}& \text{Bijay}\\ 5^{th}& \text{Bijay}& \text{Amit}& \text{Ajit}\end{array}$

Answer: Option D. -> 1
:
D
If N is in group II, then
Group 1: P, R, K and M.
Group 2: S, V, H and N.

Answer: Option A. -> 45%      
:
A
Since the percentages remain the same, as in the second question of this caselet, we can take the total of2001 and 2005 to consider the percentage increase percentage increase= $\left[\frac{71142-49079}{49079}\right]$ $\times$ 100% =45%.

Answer: Option D. -> 0
:
D
At least 1 $\Rightarrow$ all - (0 children) = (less than 3 + more than 2) - (0 children) ,
P = 34
Q=46
R=50
S=39
T= 49
U= 47
This is the least in P

Answer: Option D. -> Cannot be determined
:
D
The solution cannot be determined from the given data