CAT 2020 [Slot 2] DILR set 5

Question 1:

Total valid votes in \(A =5,00,000\) Minimum no of valid votes required to save the security deposits \(=\frac{1}{6} \times 5,00,000=83,334\)

As per \(1^{\text {st }}\) additional information \(\Rightarrow\) the gap between \(1^{\text {st }}\) and \(2^{\text {nd }}\) runners up is 10,000 So the table for \(A \Rightarrow\) total \(\rightarrow 5,00,000\)

Winner \(\rightarrow 2,75,000\)

\(1^{\text {st }}\) runner up \(\rightarrow 55,000\)

2nd runner up \(\rightarrow 85,000\)

Total \(\rightarrow 4,55,000\)

The valid votes got by the other 7 candidates \(=5,00,000-4,55,000\)

\(=45,000\)

\(\therefore\) the \(\%\) of votes by the candidates who lost the security deposit is \(=\frac{45,000}{5,00,000} \times 100=9 \%\)

Answer: 9
Question 2:

Total valid votes in A=3,25,000

Minimum no of valid votes required to save the security deposits \(=\frac{1}{6} \times 3,25,000=54,167\)

We can see the winner himself/herself has got 48,750 no of votes which is less than \(\frac{1}{6}\) th of the total votes.

\(\therefore\) all of the candidates got less than \(\frac{1}{6}\) th of the valid votes.

\(\therefore\) security deposits will be forfeited for all of the candidates as winner is exempted from this condition. (total no of such candidates \(=12-1=11)\)

Answer: 11
Question 3:

As the additional information in condition (2)

The minimum difference in no of votes between any pair of candidates = 10,000 As there are 5 candidates in c, the possible distribution of valid is as follows.

Additional 30 votes can be distributed among them to maintain the gap at least 10,000. So the possible answer is 1,40,006

Option: 1
Question 4:

Let the no of valid votes \(=100 x\)

The table looks like the following:

Total votes \(\rightarrow 100 x\)

Winner \(\rightarrow 39,375\)

\(1^{\text {st }} \rightarrow 37,500\)

\(2^{n d} \rightarrow 30,000\)

\(3^{\text {rd }} \rightarrow 10 x\)

Total \(\rightarrow 1,06,875\)

As the winner got 51 more than \(1^{\text {st }}\) runner up (as per 3 )

Total no of votes has to be more than

\(\frac{39,375+37,500+30,000}{0.9}\)

\(=1,10,208\)

\(\therefore\) option (62,500) is ruled out.

To eliminate two more options, lets consider 1,50,000 to be the correct one [as one option is less than \(\&\) the other one is the greater than this option]

\(\therefore 100 x=1,50,000\)

Total \(\rightarrow 1,50,000\)

Winner \(\rightarrow 45,000\)

\(1^{\text {st }} \rightarrow 37,500\)

\(2^{\text {nd }} \rightarrow 30,000\)

\(3^{\text {rd }} \rightarrow 15,000\)

Total \(\rightarrow 1,06,875\)

Minimum rates to save security deposits \(=\frac{1}{6} \times 1,50,000=25,000\)

So we can see except 3 candidates all others have lost their security deposits.

Candidates who saved their security deposits \(=(100-35) \%=65 \%\left[\right.\) as per \(3^{\text {rd }}\) additional inform]

\(\therefore 65 \%\) of \(1,50,000=97,500\)

\(\rightarrow\) which is less than 1,12,500

\(\therefore\) answer will be more than 1,50,000

Option: 1
Question 5:

Margins

\(A \rightarrow 2,75,000-95,000=1,80,000\)

\(B \rightarrow\)

\(C \rightarrow 1,50,000-1,40,000=10,000\)

\(D \rightarrow 39,375-37,500=1,875\)

Clearly the margin in C is more than that of D. So clearly the sequence \(B , C , D , A\) is not possible.

Option: 3
Question 6:

The no. of votes got by the candidates who has lost their security deposits is as follows

In A \(\rightarrow 45,000\)

In B \(\rightarrow 3,25,000-48,750=2,76,250\)

In C \(\rightarrow 0\)

In D \(\rightarrow 1,75,000-46,250-37,500-30,000=61250\)

Req %=\(\frac{3,82,500}{5,00,000+3,25,000+6,00,000+1,75,000} \times 100\)

\(=\frac{3,82,500}{16,00,000} \times 100=23.91 \%\)

Option: 1