**Tables DI Questions for NMAT PDF:**

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**Instructions**

An agency entrusted to accredit colleges looks at four parameters: faculty quality (F), reputation (R), placement quality (P), and infrastructure (I). The four parameters are used to arrive at an overall score, which the agency uses to give an accreditation to the colleges. In each parameter, there are five possible letter grades given, each carrying certain points: A (50 points), B (40 points), C (30 points), D (20 points), and F (0 points). The overall score for a college is the weighted sum of the points scored in the four parameters. The weights of the parameters are 0.1, 0.2, 0.3 and 0.4 in some order, but the order is not disclosed. Accreditation is awarded based on the following scheme:

**Question 1:Â **What is the weight of the faculty quality parameter?

a)Â 0.2

b)Â 0.3

c)Â 0.4

d)Â 0.1

**Question 2:Â **How many colleges receive the accreditation of AAA?

**Question 3:Â **What is the highest overall score among the eight colleges ?

**Question 4:Â **How many colleges have overall scores between 31 and 40, both inclusive?

a)Â 0

b)Â 2

c)Â 1

d)Â 3

**Instructions**

In an election several candidates contested for a constituency. In any constituency, the winningÂ candidate was the one who polled the highest number of votes, the first runner up was the one whoÂ polled the second highest number of votes, the second runner up was the one who polled the thirdÂ highest number of votes, and so on. There were no ties (in terms of number of votes polled by theÂ candidates) in any of the constituencies in this election.Â In an electoral system, a security deposit is the sum of money that a candidate is required to pay to theÂ election commission before he or she is permitted to contest. Only the defeated candidates (i.e., oneÂ who is not the winning candidate) who fail to secure more than one sixth of the valid votes polled in theÂ constituency, lose their security deposits.

The following table provides some incomplete information about votes polled in four constituencies: A, B,Â C and D, in this election .

The following additional facts are known:

1. The first runner up polled 10,000 more votes than the second runner up in constituency A.

2. None of the candidates who contested in constituency C lost their security deposit. The difference in votes polled by anyÂ pair of candidates in this constituency was at least 10,000.

3. The winning candidate in constituency D polled 5% of valid votes more than that of the first runner up. All the candidatesÂ who lost their security deposits while contesting for this constituency, put together, polled 35% of the valid votes.

**Question 5:Â **What is the percentage of votes polled in total by all the candidates who lost their security deposits while contesting for constituency A?

**Question 6:Â **How many candidates who contested in constituency B lost their security deposit?

**Question 7:Â **What BEST can be concluded about the number of votes polled by the winning candidate in constituency C?

a)Â 1,40,010

b)Â between 1,40,005 and 1,40,010

c)Â less than 2,00,010

d)Â 1,40,006

**Question 8:Â **What was the number of valid votes polled in constituency D?

a)Â 1,25,000

b)Â 1,50,000

c)Â 1,75,000

d)Â 62,500

**Question 9:Â **The winning margin of a constituency is defined as the difference of votes polled by the winner and that of the first runner up. Which of the following CANNOT be the list of constituencies, in increasing order of winning margin?

a)Â D, B, C, A

b)Â B, D, C, A

c)Â B, C, D, A

d)Â D, C, B, A

**Question 10:Â **For all the four constituencies taken together, what was the approximate number of votes polled by all the candidates who lost their security deposit expressed as a percentage of the total valid votes from these four constituencies?

a)Â 38.25%

b)Â 23.54%

c)Â 23.91%

d)Â 32.00%

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**Answers & Solutions:**

**1)Â AnswerÂ (D)**

It is given that:Â High Q >Â Best Ed >Â CosmopolitanÂ andÂ Education Aid >Â A-one

We can say thatÂ High QÂ >Â Cosmopolitan

We can see that bothÂ High Q andÂ Cosmopolitan got sameÂ points inÂ reputation (R) and placement quality (P). High Q received more points in infrastructure (I) than Cosmopolitan whereasÂ Cosmopolitan received more points in faculty Quality (F) than High Q.

Hence, we can say thatÂ Infrastructure’s weight should be greater than Faculty quality. i.e.Â Â I > F

Similarly, We can see that bothÂ Best Ed andÂ Cosmopolitan got sameÂ points inÂ faculty Quality (F) and placement quality (P). Best Ed received more points in reputation (R) than Cosmopolitan whereasÂ Cosmopolitan received more points in infrastructure (I) than Best Ed.

Hence, we can say thatÂ reputation’s weight should be greater than infrastructure. i.e.Â Â R > I

Similarly, We can see that bothÂ Education AidÂ andÂ A-one got sameÂ points inÂ faculty Quality (F)Â and reputation (R).Â Education AidÂ received more points inÂ infrastructure (I)Â than A-one whereasÂ A-one received more points inÂ placement quality (P)Â thanÂ Education Aid.

Hence, we can say thatÂ reputation’s weight should be greater thanÂ infrastructure. i.e.Â Â I > P

So basically there are two possible cases: R > I > P > F orÂ Â R > I > F > P

Case 1:Â Â Order of weights assigned = R > I > P > F

R = 0.4, I = 0.3. P = 0.2, F = 0.1

In this case overall score received byÂ Best Ed = 0.1*40+0.4*30+0.2*20+0.3*20 = 26

In this case overall score received by High Q = 0.1*30+0.4*20+0.2*20+0.3*40 = 27

We can see thatÂ High Q’s overall score is higher thanÂ Best Ed. Hence, this is a possible case.

Case 2:Â Â Order of weights assigned =Â R > I > F > P

R = 0.4, I = 0.3. P = 0.1, F = 0.2

In this case overall score received byÂ Best Ed = 0.2*40+0.4*30+0.1*20+0.3*20 = 28

In this case overall score received by High Q = 0.2*30+0.4*20+0.1*20+0.3*40 = 28

We can see thatÂ High Q’s overall score is not greater than the overall score received Best Ed. Hence, this case is not possible.

Now that we know the weight of each parameter, we can calculate the overall score and accreditation received by each college.

We can see thatÂ weight of the faculty quality parameter = 0.1. Hence,option D is the correct answer.

**2)Â Answer:Â 3**

It is given that:Â High Q >Â Best Ed >Â CosmopolitanÂ andÂ Education Aid >Â A-one

We can say thatÂ High QÂ >Â Cosmopolitan

We can see that bothÂ High Q andÂ Cosmopolitan got sameÂ points inÂ reputation (R) and placement quality (P). High Q received more points in infrastructure (I) than Cosmopolitan whereasÂ Cosmopolitan received more points in faculty Quality (F) than High Q.

Hence, we can say thatÂ Infrastructure’s weight should be greater than Faculty quality. i.e.Â Â I > F

Similarly, We can see that bothÂ Best Ed andÂ Cosmopolitan got sameÂ points inÂ faculty Quality (F) and placement quality (P). Best Ed received more points in reputation (R) than Cosmopolitan whereasÂ Cosmopolitan received more points in infrastructure (I) than Best Ed.

Hence, we can say thatÂ reputation’s weight should be greater than infrastructure. i.e.Â Â R > I

Similarly, We can see that bothÂ Education AidÂ andÂ A-one got sameÂ points inÂ faculty Quality (F)Â and reputation (R).Â Education AidÂ received more points inÂ infrastructure (I)Â than A-one whereasÂ A-one received more points inÂ placement quality (P)Â thanÂ Education Aid.

Hence, we can say thatÂ reputation’s weight should be greater thanÂ infrastructure. i.e.Â Â I > P

So basically there are two possible cases: R > I > P > F orÂ Â R > I > F > P

Case 1:Â Â Order of weights assigned =Â R > I > P > F

R = 0.4, I = 0.3. P = 0.2, F = 0.1

In this case overall score received byÂ Best Ed = 0.1*40+0.4*30+0.2*20+0.3*20 = 26

In this case overall score received by High Q = 0.1*30+0.4*20+0.2*20+0.3*40 = 27

We can see thatÂ High Q’s overall score is higher thanÂ Best Ed. Hence, this is a possible case.

Case 2:Â Â Order of weights assigned =Â R > I > F > P

R = 0.4, I = 0.3. P = 0.1, F = 0.2

In this case overall score received byÂ Best Ed = 0.2*40+0.4*30+0.1*20+0.3*20 = 28

In this case overall score received by High Q = 0.2*30+0.4*20+0.1*20+0.3*40 = 28

We can see thatÂ High Q’s overall score is not greater than the overall score received Best Ed. Hence, this case is not possible.

Now that we know the weight of each parameter, we can calculate the overall score and accreditation received by each college.

From the table, we can see that threeÂ received the accreditation of AAA.

**3)Â Answer:Â 48**

It is given that:Â High Q >Â Best Ed >Â CosmopolitanÂ andÂ Education Aid >Â A-one

We can say thatÂ High QÂ >Â Cosmopolitan

We can see that bothÂ High Q andÂ Cosmopolitan got sameÂ points inÂ reputation (R) and placement quality (P). High Q received more points in infrastructure (I) than Cosmopolitan whereasÂ Cosmopolitan received more points in faculty Quality (F) than High Q.

Hence, we can say thatÂ Infrastructure’s weight should be greater than Faculty quality. i.e.Â Â I > F

Similarly, We can see that bothÂ Best Ed andÂ Cosmopolitan got sameÂ points inÂ faculty Quality (F) and placement quality (P). Best Ed received more points in reputation (R) than Cosmopolitan whereasÂ Cosmopolitan received more points in infrastructure (I) than Best Ed.

Hence, we can say thatÂ reputation’s weight should be greater than infrastructure. i.e.Â Â R > I

Similarly, We can see that bothÂ Education AidÂ andÂ A-one got sameÂ points inÂ faculty Quality (F)Â and reputation (R).Â Education AidÂ received more points inÂ infrastructure (I)Â than A-one whereasÂ A-one received more points inÂ placement quality (P)Â thanÂ Education Aid.

Hence, we can say thatÂ reputation’s weight should be greater thanÂ infrastructure. i.e.Â Â I > P

So basically there are two possible cases: R > I > P > F orÂ Â R > I > F > P

Case 1:Â Â Order of weights assigned =Â R > I > P > F

R = 0.4, I = 0.3. P = 0.2, F = 0.1

In this case overall score received byÂ Best Ed = 0.1*40+0.4*30+0.2*20+0.3*20 = 26

In this case overall score received by High Q = 0.1*30+0.4*20+0.2*20+0.3*40 = 27

We can see thatÂ High Q’s overall score is higher thanÂ Best Ed. Hence, this is a possible case.

Case 2:Â Â Order of weights assigned =Â R > I > F > P

R = 0.4, I = 0.3. P = 0.1, F = 0.2

In this case overall score received byÂ Best Ed = 0.2*40+0.4*30+0.1*20+0.3*20 = 28

In this case overall score received by High Q = 0.2*30+0.4*20+0.1*20+0.3*40 = 28

We can see thatÂ High Q’s overall score is not greater than the overall score received Best Ed. Hence, this case is not possible.

Now that we know the weight of each parameter, we can calculate the overall score and accreditation received by each college.

From the table we can see that Education Aid scored the highest overall score = 48.

**4)Â AnswerÂ (A)**

It is given that:Â High Q >Â Best Ed >Â CosmopolitanÂ andÂ Education Aid >Â A-one

We can say thatÂ High QÂ >Â Cosmopolitan

Hence, we can say thatÂ reputation’s weight should be greater than infrastructure. i.e.Â Â R > I

Hence, we can say thatÂ reputation’s weight should be greater thanÂ infrastructure. i.e.Â Â I > P

So basically there are two possible cases: R > I > P > F orÂ Â R > I > F > P

Case 1:Â Â Order of weights assigned =Â R > I > P > F

R = 0.4, I = 0.3. P = 0.2, F = 0.1

In this case overall score received byÂ Best Ed = 0.1*40+0.4*30+0.2*20+0.3*20 = 26

In this case overall score received by High Q = 0.1*30+0.4*20+0.2*20+0.3*40 = 27

We can see thatÂ High Q’s overall score is higher thanÂ Best Ed. Hence, this is a possible case.

Case 2:Â Â Order of weights assigned =Â R > I > F > P

R = 0.4, I = 0.3. P = 0.1, F = 0.2

In this case overall score received byÂ Best Ed = 0.2*40+0.4*30+0.1*20+0.3*20 = 28

In this case overall score received by High Q = 0.2*30+0.4*20+0.1*20+0.3*40 = 28

From the table we can see that none of the mentioned college receivedÂ an overall scores between 31 and 40, both inclusive. Hence, option A is the correct answer.

**5)Â Answer:Â 9**

It’s given in the question that the first runner up polled 10,000 more votes than the second runner up in constituency A. Now the first runner up has got 95000 votes, hence the second runner up will get 85000 votes.

Now the remaining votes will be 500000-275000-95000-85000=45000

From 2,Â None of the candidates who contested in constituency C lost their security deposit. The difference in votes polled by any pair of candidates in this constituency was at least 10,000 => the person who got 5th highest votes must have got > 600030/6 =>Â $\ge$ 100006. Since it is also given that the difference of votes isÂ $\ge$ 10000, the only possible case is winner, 1st runner up, 2nd runner up, 3rd runner up, 4th runner up must have got 140006,130006,120006,110006,100006 respectively which sums upto exactly 600030.

Let the number of votes polled in D be 100x.

From 3, The winning candidate in constituency D must have got 15x+37500

The table now looks like:

Total votes in A = 500000 => the candidates who gotÂ $\le$ 83333 must have lost their security deposits => candidates till 2nd runner up didn’t lose their deposit =>all the candidates who received 500000-275000-95000-85000=**45000Â **lost their deposits.

The percentage of votes polled in total by all the candidates who lost their security deposits while contesting for constituency A = 45000*100/500000 =9%

**6)Â Answer:Â 11**

It’s given in the question that the first runner up polled 10,000

more votes than the second runner up in constituency A. Now the first

runner up has got 95000 votes, hence the second runner up will get 85000

votes.

Now the remaining votes will be 500000-275000-95000-85000=45000

From

2, None of the candidates who contested in constituency C lost their

security deposit. The difference in votes polled by any pair of

candidates in this constituency was at least 10,000 => the person who

got 5th highest votes must have got > 600030/6 => $\ge$ 100006.

Since it is also given that the difference of votes is $\ge$ 10000,

the only possible case is winner, 1st runner up, 2nd runner up, 3rd

runner up, 4th runner up must have got

140006,130006,120006,110006,100006 respectively which sums upto exactly

600030.

Let the number of votes polled in D be 100x.

From 3, The winning candidate in constituency D must have got 5x+37500

The table now looks like:

In constituency B, the mark for not losing the security deposit is 1/6(325000) or 54,167.

But winner himself/herself got < 54167 => all the other candidates lost their security deposits.

11 is the correct answer,

**7)Â AnswerÂ (D)**

It’s given in the question that the first runner up polled 10,000

more votes than the second runner up in constituency A. Now the first

runner up has got 95000 votes, hence the second runner up will get 85000

votes.

Now the remaining votes will be 500000-275000-95000-85000=45000

From

2,Â None of the candidates who contested in constituency C lost their

security deposit. The difference in votes polled by any pair of

candidates in this constituency was at least 10,000 => the person who

got 5th highest votes must have got > 600030/6 =>Â $\ge$ 100006.

Since it is also given that the difference of votes isÂ $\ge$ 10000,

the only possible case is winner, 1st runner up, 2nd runner up, 3rd

runner up, 4th runner up must have got

140006,130006,120006,110006,100006 respectively which sums upto exactly

600030.

Let the number of votes polled in D be 100x.

From 3, The winning candidate in constituency D must have gotÂ 37500+5x.

The table now looks like:

Number of votes polled to winning candidate must be 140006.

**8)Â AnswerÂ (C)**

more votes than the second runner up in constituency A. Now the first

runner up has got 95000 votes, hence the second runner up will get 85000

votes.

Now the remaining votes will be 500000-275000-95000-85000=45000

From

2, None of the candidates who contested in constituency C lost their

security deposit. The difference in votes polled by any pair of

candidates in this constituency was at least 10,000 => the person who

got 5th highest votes must have got > 600030/6 => $\ge$ 100006.

Since it is also given that the difference of votes is $\ge$ 10000,

the only possible case is winner, 1st runner up, 2nd runner up, 3rd

runner up, 4th runner up must have got

140006,130006,120006,110006,100006 respectively which sums upto exactly

600030.

From 3, Let the total votes in D be 100x => The winning candidate in constituency D must have got 37500+5x.

The table now looks like:

The candidates who didn’t lose the deposit must have got <16.67% => 3rd runner up must surely didn’t get the deposit.

Also,Â the candidates who got security deposit must have got 65% of votes.

Case I:

Let top three candidates got the security deposit => 37500+5x+37500+30000 =65x => x=1750 => 100x= **175000**

Case II:

Let top three candidates got the security deposit** => **37500+5x+37500 =65x => 60x = 1250 => x=125000 but 16.66% of 125000 =20834Â => 2nd runner up must got security deposit. So, this case is not valid.

The increasing order C will always come after D which is not happening in the third option. Hence that is the correct answer.

**9)Â AnswerÂ (C)**

more votes than the second runner up in constituency A. Now the first

runner up has got 95000 votes, hence the second runner up will get 85000

votes.

Now the remaining votes will be 500000-275000-95000-85000=45000

From

2, None of the candidates who contested in constituency C lost their

security deposit. The difference in votes polled by any pair of

candidates in this constituency was at least 10,000 => the person who

got 5th highest votes must have got > 600030/6 => $\ge$ 100006.

Since it is also given that the difference of votes is $\ge$ 10000,

the only possible case is winner, 1st runner up, 2nd runner up, 3rd

runner up, 4th runner up must have got

140006,130006,120006,110006,100006 respectively which sums upto exactly

600030.

From 3, The winning candidate in constituency D must have got 1.05*37500 = 39375.

Let the number of votes polled in D be 100x.

The table now looks like:

As calculated in the previous question, candidate D got 175000 votes. The winner got 5% more votes than first runner up, hence the winner got 0.05*175000 i.e 8750 more votes than first runner up . Thus 8750 is the winning margin for constituency D. Moreover margin in constituency is atleast 10000 . Hence in the increasing order C will always come after D which is not happening in the third option. Hence that is the correct answer.

**10)Â AnswerÂ (C)**

more votes than the second runner up in constituency A. Now the first

runner up has got 95000 votes, hence the second runner up will get 85000

votes.

Now the remaining votes will be 500000-275000-95000-85000=45000

2, None of the candidates who contested in constituency C lost their

security deposit. The difference in votes polled by any pair of

candidates in this constituency was at least 10,000 => the person who

got 5th highest votes must have got > 600030/6 => $\ge$ 100006.

Since it is also given that the difference of votes is $\ge$ 10000,

the only possible case is winner, 1st runner up, 2nd runner up, 3rd

runner up, 4th runner up must have got

140006,130006,120006,110006,100006 respectively which sums upto exactly

600030.

From 3, Let the total votes in D be 100x => The winning candidate in constituency D must have got 37500+5x.

The table now looks like:

The candidates who didn’t lose the deposit must have got <16.67% => 3rd runner up must surely didn’t get the deposit.

Also, the candidates who got security deposit must have got 65% of votes.

Case I:

Let top three candidates got the security deposit => 37500+5x+37500+30000 =65x => x=1750 => 100x= **175000**

Case II:

Let top three candidates got the security deposit** => **37500+5x+37500

=65x => 60x = 1250 => x=125000 but 16.66% of 125000 =20834 =>

2nd runner up must got security deposit. So, this case is not valid.

For all the constituencies lets look at the candidates who lost their security deposit.

A (500000-275000-95000-85000)=45000.

B (325000-48750)=276250

C (0) and D (61250)=175000-46250-30000-37500

Hence percentage will be 382500/1600000Ã— 100=23.91%

We hope this Tables DI Questions for NMAT pdf for NMAT exam will be highly useful for your Preparation.