# Free DI and LR Practice Test - CAT

### Question 1

**In Afghanistan, registered foreigners increased by 10% every 2 years. In 2008, 40% of the foreigners were unregistered. What was the total population of Afghanistan in 2008?**

#### SOLUTION

Solution :B

The number of registered foreigners in 2012 is 1.21 times (1.1)2 the number of registered foreiners in 2008 (as the their number increases 10% every 2 years)

So, registered foreigners in 2008 = (2.7121)×100= 2.23 million

Therefore total foreigners in 2008 = (2.2360)×100= 3.7 million

So, total population of Afghanistan in 2008 = (3.73)×100= 123 million.

### Question 2

**In 2012, registered foreigners were 4% of the total population. From 2000 to 2012, the total population increased by 55% and the number of registered foreigners increased by 670%. Hence, from 2000 to 2012 the number of unregistered foreigners increased by**

#### SOLUTION

Solution :A

In 2012, total registered foreigners = 2.7 million.

Therefore total population = (2.74)×100= 67.5 million

So, total population in 2000 = 67.51.55= 43.5 million

Total registered foreigners in 2000 = 2.77.7= 0.35 million

In 2012, total registered foreigners = 4% and total foreigners = 6%

Total unregistered foreigners = 2%

Total unregistered population in 2012 = 67.5×0.02 = 1.35 million.

Total unregistered population in 2000 = 43.5×0.01-0.35 = 1.35 million.

Hence the required increase = 1.35 - 0.085 = 1.265 million.

### Question 3

**In 2010, the total population increased by 50% over that in 2004. In 2004, foreigners from India were y% of the total population and this percentage increased by 10% in 2010. In 2010, foreigners from India as a percentage of total foreigners decreased by 20 % over that in 2004. What is y?**

#### SOLUTION

Solution :D

Let x be the total population in 2004.

So total population in 2010 = 1.5x

Foreigners from India in 2004 = xy100 and in 2010 = y+10100×1.5x

Foreigners from India as a percentage of total foreigners in 2004 = (yx100)(2x100)×100=50y

And that in 2010 = ((y+10)1.5x100)(5×1.5x100)×100=20y+200

The percentage is reduced by 20% over the given period.

50y - (20y + 200) = 20

y=7.33%

### Question 4

**The number of registered foreigners from Bangladesh increases by 10% every 2 years and that of unregistered foreigners from Bangladesh decreases by 10% every 2 years. If the total population of Afghanistan remain the same for all years and the number of foreigners from Bangladesh are 2% of the total population in 2012, then how many unregistered Bangladeshi were present in 2006. [In 2006, there were no foreigners in Afghanistan from any country except Bangladesh]**

#### SOLUTION

Solution :D

Let registered foreigners and non-registered foreigners from Bangladesh in 2006 be x and y respectively.

Registered foreigners from Bangladesh in 2012 = 1.331x

Registered foreigners from Bangladesh in 2006 = x = 2.7×0.391.331= 0.79 million

Let z be the total population.

0.79 + y = 0.025z ....(In 2006)

And 1.053 + 0.729y = 0.02z... (In 2012)

Solving for y, y = 5.9 million.

### Question 5

**In 2007, the Actual FDI Inflow from Germany is what percent of the FDI approved for the US?**

#### SOLUTION

Solution :D

For the year 2007, Actual FDI Inflow from Germany =35×22,000360

FDI Approved for U.S. = 160×55,000360

Required % = 35×22000160×55000×100=7×10080=8.75%

### Question 6

**In the year 2007, for which of the following is the percentage of FDI approved that is actually realized as FDI Inflow more than 40%?**

#### SOLUTION

Solution :D

As internal effeciency for the year 2007 is 22×10055 i.e. 40%.

The required percentage will be more than 40% for all the countries that have most share in the second pie chart

compared to the first pie chart i.e. UK, France, Germany, Japan and Others.

### Question 7

**What is the approximate compounded average annual growth rate of the Actual Inflow of FDI over the period 2003 to 2007?**

#### SOLUTION

Solution :B

Actual Inflow of FDI

In 2003 = Rs. 2,000 crs.

In 2007 = Rs. 22,000 crs.

CAGR = (220002000)14−1=4√11−1≈1.82−1=0.82=82%

You can also use the reverse approach. Choose a middle answer option. If 82% is the answer

then 1.84+1 i.e.(182×182)+1=(32×32)+1≊(220002000)=110.

### Question 8

**If the ratio of marks obtained by Ankit in the internals of all three subjects (Economics, Finance and Accounts) in that order is 9:3: 4, then what was the ratio of marks scored by Sachin in the externals of those three subjects in the same order?**

#### SOLUTION

Solution :D

Let the total marks scored by the six students in Economics, Finance and Accounts be x, y and z respectively.

∴The ratio of marks scored by Ankit in the Internals of these papers would be:

(30% of 10% of x) : (10% of 5% of y) : (10% of 10% of z) which would be the same as (0.03x):

(0.005y) : (0.01z) = (3x) : (0.5y) : (z)

But, (3x) : (0.5y) : (z) is equal to 9 : 3 : 4.

∴ 3x = 9, 0.5y = 3 and z = 4

∴ The ratio x : y : z would be equal to 3 : 6 : 4.

The marks scored by Sachin are 30%, 25%, and 25%, the ratio of marks would be 90 : 150 : 100,

i.e. 9 : 15 : 10.

Now, the marks scored by Sachin in Internals are 20%, 10% and 10%.

∴ Marks scored by him in Externals will be 80%, 90% and 90%.

∴ The required ratio would be (80% of 9) : (90% of 15) : (90% of 10), i.e. (7.2) : (13.5) : (9)

This ratio would be equal to 72 : 135 : 90 or 24 : 45 : 30

### Question 9

**If, in the case of Ramesh, the marks scored by him in Externals in Finance is less than that scored by him in Economics and Accounts, then what is the ratio of total marks scored by all students in Finance put together to the total marks scored by all six students in all the subjects put together?**

52 : 24

17 : 25

43 : 51

Cannot be determined

#### SOLUTION

Solution :D

As we have only comparative ratios and not the exact ratios, we cannot find the required value.

### Question 10

**If the total marks scored by Ramesh in Economics and Accounts are the same, then for how many students from these six is the total marks scored in Economics more than twice the total marks scored by them in Accounts?**

0

2

4

3

#### SOLUTION

Solution :B

Sol. StudentEconomics (300)Accounts (200)PercentagemarksPercentageMarksSachin30902550Ashish10302040Tanwi15451020Ankit10301020Ramesh20603060Suresh1545510

In case of Ramesh, the marks scored by him in Economics, Finance and Accounts are 20%,20% and 30 respectively out of the total marks scored by all the students put together.

∴ 20% of the total marks of all the students in Economics =30% of the total marks of all the students in Accounts

∴ The ratio of the total marks scored by all six students put together in Economics to that of Accounts will be 3 : 2.

For simplicity, assume that the total number of marks obtained by all of them in Economics be 300 and in Accounts be 200.

Now the results can be tabulated by taking the marks in the required ratio as shown above.

∴ There are only 2 students satisfying the criteria.

### Question 11

**If Suresh had scored 20 marks in Accounts and 45 marks in Finance, then the marks scored by all six students in internals of these 2 subjects would be (All marks, at all stages of evaluation, have to be integers. So, round off any decimal to the next higher number)**

63

62

59

61

#### SOLUTION

Solution :A

Suresh scoring 20 marks in Accounts implies that the total marks scored by all six students put together would be 400 as his marks constituted 5% of the total marks.

Similarly, the total marks scored by all six students put together in Finance would be 150 as his marks constituted 30% of the total marks.

The results can be tabulated as shown above.

∴ the total marks scored by all six students in the internals of Finance are 13 and that in Accounts is 50.

∴ the required total is 63.

### Question 12

**If the marks scored by Sachin in the internals of Economics are same as that scored by Ashish in the internals of Accounts, then what is the ratio of the total marks scored by all six students in Economics put together to that scored in Accounts put together?**

#### SOLUTION

Solution :A

Let the total marks scored by an Six students put together in Economics be 'x' and that in Accounts be 'y'

Then the total marks scored by sachin in Economics = 30% of x

∴ Marks scored by Sachin in the internals of Economics = 20% of 30% of x = 0.06x

Similarly, the total marks scored by Ashish in Accounts = 20% of y

∴ Marks scored by Ashish in the internals of Accounts = 5% of 20% of y = 0.01y

From the condition given in the question, both these marks are equal.

∴ 0.06x = 0.01y

∴ x : y = 1 : 6

### Question 13

**What is the minimum number of air routes that Mr. Bajaj will have to take in order to complete his journey in the given time?**

4

5

6

7

#### SOLUTION

Solution :C

Air routes are best taken between those cities where the alternative modes of transport are too time-consuming. The total time Mr. Bajaj can take is 8 days or 192 hours.

Thus, we can try the following sequence:

New York City to London by air

London to Paris by road

Paris to Vienna by road

Vienna to Istanbul by road

Istanbul to Dubai by air

Dubai to Mumbai by ship

Mumbai to Kolkata by rail

Kolkata to Hong Kong by air

Hong Kong to Tokyo by air

Tokyo to San Francisco by air

San Francisco to New York City by air.

Calculating the total time and money for this sequence, we find that he takes 190.5 hours and $7465. Now, if we try to replace any more air routes by an alternative mode of transport, we see that he overshoots his time limit. Thus, the minimum number of air routes that Bajaj will have to take is 6.

### Question 14

**What is the minimum total travel fare in which Bajaj can complete his journey within the given time?**

#### SOLUTION

Solution :B

We have already seen in the explanation for previous question, a sequence of routes which

takes 190.5 hours and $7465. To get a cheaper sequence, we will have to replace an expensive

route with a cheaper route, without over shooting the time limit. Possible routes are by ship

from Hong kong to Tokyo, or by rail from San Francisco to New York City. Butt to fit either of

these routes in the sequence, we will have to replace some other non-air routes by air routes.

The best non-air routes to replace are those where the corresponding air routes take much less

time and do not cost as much as air routes between other cities, i.e. Dubai to Mumbai and

Mumbai to Kolkata.

Therefore, if Balaji travels by air from New York City to London, by road from london to Paris to

Vienna to Istanbul, by air from Istanbul to Dubai to Mumbai to Kolkata to Hong Kong to Tokyo

to San Francisco, and by rail from San Francisco to New York City, then he will take 171 hours

and $7225.

The other possible sequence (by ship instead of air from Hong Kong to Tokyo and by air instead

of rail from San Francisco to New York City) tales 177.5 hours and $7265. Therefore, the

minimum total travel fare possible is $7225.

### Question 15

**What is the minimum total time in which Bajaj can complete his journey within the given budget?**

#### SOLUTION

Solution :B

We have already seen in the explanation for previous question, a sequence of routes which

takes 171 hours and costs $7225. To get a sequence which takes lesser time, we must look for

alternative modes of transport which are faster but not much more expensive. We cannot

replace any of the non-air routes by air routes, as that would overshoot the budget. Thus, the

only possibility is changing the mode of transport from London to istanbul from road to rail.

However, if Balaji travels by rail on all three routes, that would cost $305 more. So he travels by

rail on only two routes (Paris to Vienna to Istanbul) and by road from London to Paris. For all

other routes, he travels by air, except San Francisco to New York City where he travels by rail.

This sequence would take 151 hours and cost $7490.

### Question 16

**If Mr. Bajaj decides to travel from Istanbul to Dubai by road, then what is the minimum total time in which he can complete the entire journey within the given budget?**

#### SOLUTION

Solution :C

If Bajaj travels from Istanbul to Dubai by road and on all other routes by air, then he will take 146.5 hours and 8705.Therefore,wehavetosearchforalternativemodesoftransporttoreducethetotalfareby1205.

The best options are taking the road or rail from London to Istanbul, as the air fares on those routes are very high. Trying a few combinations of road and rail, we see that the only one that fits the total budget is by road from London to Paris, by rail from Paris to Vienna, by road from Vienna to Istanbul to Dubai, and by air for all other routes. This combination takes exactly $7500 and 190.5 hours.

### Question 17

How much money did Ajay receive this month?

#### SOLUTION

Solution :Let Vijay's age be x years

Shyam's age = 6 years (given)

Ajay's age = Shyam's age + Vijay's age = (x + 6) years

∴ Ajay's share = x+6x+6+(x+6)×amount=12×1080= Rs 540

When Ajay takes Rs 540, the balance amount left would be Rs 540

∴Vijay's share = x2(x+6)×540. His actual share = x2(x+6)×1080

The difference between these two amounts is Rs 180 (which he received in the evening from his father)

∴ x2(x+6)×1080−x2(x+6)×540=180

x = 12 years

∴ Vijay's actual share = 122×18×1080= Rs. 360

Out of this,

He received Rs 180 later. Hence, he should have taken Rs 180 initially. Balance amount left when shyam came home was = 1080 - (540 + 180)

= Rs. 360

Out of this, the amount Shyam took

=62(x+6)×360

=62×18×360= Rs 60

Balance amount received by Shyam later

### Question 18

What was the amount that Shyam took initially?

#### SOLUTION

Solution :Let Vijay's age be x years

Shyam's age = 6 years (given)

Ajay's age = Shyam's age + Vijay's age = (x + 6) years

∴ Ajay's share = x+6x+6+(x+6)×amount=12×1080= Rs 540

When Ajay takes Rs 540, the balance amount left would be Rs 540

∴Vijay's share = x2(x+6)×540. His actual share = x2(x+6)×1080

The difference between these two amounts is Rs 180 (which he received in the evening from his father)

∴ x2(x+6)×1080−x2(x+6)×540=180

x = 12 years

∴ Vijay's actual share = 122×18×1080= Rs. 360

Out of this,

He received Rs 180 later. Hence, he should have taken Rs 180 initially. Balance amount left when shyam came home was = 1080 - (540 + 180)

= Rs. 360

Out of this, the amount Shyam took

=62(x+6)×360

=62×18×360= Rs 60

### Question 19

How old is Vijay's elder brother?

#### SOLUTION

Solution :Let Vijay's age be x years

Shyam's age = 6 years (given)

Ajay's age = Shyam's age + Vijay's age = (x + 6) years

∴ Ajay's share = x+6x+6+(x+6)×amount=12×1080= Rs 540

When Ajay takes Rs 540, the balance amount left would be Rs 540

∴Vijay's share = x2(x+6)×540. His actual share = x2(x+6)×1080

The difference between these two amounts is Rs 180 (which he received in the evening from his father)

∴ x2(x+6)×1080−x2(x+6)×540=180

x = 12 years

∴ Vijay's actual share = 122×18×1080= Rs. 360

Out of this, the amount Shyam took

=62(x+6)×360

=62×18×360= Rs 60

Balance amount received by Shyam later

Ajay's age = 12+6 =18

### Question 20

The sum of ages of all three sons of Ram is?

#### SOLUTION

Solution :Let Vijay's age be x years

Shyam's age = 6 years (given)

Ajay's age = Shyam's age + Vijay's age = (x + 6) years

∴ Ajay's share = x+6x+6+(x+6)×amount=12×1080= Rs 540

When Ajay takes Rs 540, the balance amount left would be Rs 540

∴Vijay's share = x2(x+6)×540. His actual share = x2(x+6)×1080

The difference between these two amounts is Rs 180 (which he received in the evening from his father)

∴ x2(x+6)×1080−x2(x+6)×540=180

x = 12 years

∴ Vijay's actual share = 122×18×1080= Rs. 360

Out of this, the amount Shyam took

=62(x+6)×360

=62×18×360= Rs 60

Balance amount received by Shyam later

Ajay's age = 12+6 =18

Age of three brothers = 18+12+6 = 36

### Question 21

Who operates under the name 'U'?

Shoaib

Tauqir

Usman

Vusi

#### SOLUTION

Solution :C

From (I), if Tauqir is U, then Vusi is V. However we cannot conclude that if Vusi is V, then Tauqir is U.

Let us assume that Tauqir is U. Then, Vusi is V.

from (III), as Vusi is not W, Wasim is V. But both Vusi and Wasim cannot be V.

So, our assumption (that Tauqir is U) itself is not valid.

∴ Tauqir is not U.

If Tauqir is V, then Shoaib is T [from IV]. In such a case, Usman is V [from II]. Once again it is not acceptable, as Tauqir and Usman both cannot be V.

∴ the assumption made (that Tauqir is V) is invalid.

∴Tauqir is not V.

If Tauqir is S, then Shoaib is T [from IV]. In this case, Usman is V [from II]. As Usman is not W, Tauqir is not S [from V]. This contradicts the assumption that Tauqir is S. So, this is also invalid.

∴Tauqir is not S.

As Tauqir is neither V nor S, it is clear from (IV) that Shoaib is not T.

If Vusi is V, then Vusi is not W and thus Wasim is V [From (III)] . This is not possible, as both Vusi and Wasim cannot be V.

∴Vusi is not V.

Tauqir can only be either T or W. Now if Tauqir is T, Vusi is U and Wasim is not V [from VI].

But if Vusi is U, then Vusi is not W and thus Wasim must be V, according to (III).

∴Tauqir is not T.

Let us summarize the findings till now.

Shoaib: Not T

Tauqir: Not U, Not S, Not V and Not T

Vusi: Not V

So, the only possibility is that Tauqir is W.

From (VI), Vusi is U and Wasim is not V, if and only if Tauqir is T. Now, as Tauqir is not T, it follows that Vusi is not U. It also follows that Wasim is V.

If Shoaib is U, then Usman is W [from VII]. But we know that Tauqir is W, so Usman is not W.

∴ It follows that Shoaib is not U.

∴Shoaib is not U, Shoaib is not T, Shoaib is not W (as Tauqir is W) and Shoaib is not V (as Wasim is V).

∴Shoaib is S.

Also, Vusi is neither S nor V or W. Also, Vusi is not U.

∴Vusi is T. Thus, Usman has to be U.

So Shoaib, Tauqir, Usman, Vusi and Wasim operate under the names of S, W, U, T and V respectively.

### Question 22

Who operates under the name 'T'?

Tauqir

Usman

Vusi

Wasim

#### SOLUTION

Solution :C

From (I), if Tauqir is U, then Vusi is V. However we cannot conclude that if Vusi is V, then Tauqir is U.

Let us assume that Tauqir is U. Then, Vusi is V.

from (III), as Vusi is not W, Wasim is V. But both Vusi and Wasim cannot be V.

So, our assumption (that Tauqir is U) itself is not valid.

∴ Tauqir is not U.

If Tauqir is V, then Shoaib is T [from IV]. In such a case, Usman is V [from II]. Once again it is not acceptable, as Tauqir and Usman both cannot be V.

∴ the assumption made (that Tauqir is V) is invalid.

∴Tauqir is not V.

If Tauqir is S, then Shoaib is T [from IV]. In this case, Usman is V [from II]. As Usman is not W, Tauqir is not S [from V]. This contradicts the assumption that Tauqir is S. So, this is also invalid.

∴Tauqir is not S.

As Tauqir is neither V nor S, it is clear from (IV) that Shoaib is not T.

If Vusi is V, then Vusi is not W and thus Wasim is V [From (III)] . This is not possible, as both Vusi and Wasim cannot be V.

∴ Vusi is not V.

Tauqir can only be either T or W. Now if Tauqir is T, Vusi is U and Wasim is not V [from VI].

But if Vusi is U, then Vusi is not W and thus Wasim must be V, according to (III).

∴ Tauqir is not T.

Let us summarize the findings till now.

Shoaib: Not T

Tauqir: Not U, Not S, Not V and Not T

Vusi: Not V

So, the only possibility is that Tauqir is W.

From (VI), Vusi is U and Wasim is not V, if and only if Tauqir is T. Now, as Tauqir is not T, it follows that Vusi is not U. It also follows that Wasim is V.

If Shoaib is U, then Usman is W [from VII]. But we know that Tauqir is W, so Usman is not W.

∴ It follows that Shoaib is not U.

∴ Shoaib is not U, Shoaib is not T, Shoaib is not W (as Tauqir is W) and Shoaib is not V (as Wasim is V).

∴ Shoaib is S.

Also, Vusi is neither S nor V or W. Also, Vusi is not U.

∴ Vusi is T. Thus, Usman has to be U.

So Shoaib, Tauqir, Usman, Vusi and Wasim operate under the names of S, W, U, T and V respectively.

### Question 23

Under what name does Tauqir operate?

S

U

V

W

#### SOLUTION

Solution :D

From (I), if Tauqir is U, then Vusi is V. However we cannot conclude that if Vusi is V, then Tauqir is U.

Let us assume that Tauqir is U. Then, Vusi is V.

from (III), as Vusi is not W, Wasim is V. But both Vusi and Wasim cannot be V.

So, our assumption (that Tauqir is U) itself is not valid.

∴ Tauqir is not U.

If Tauqir is V, then Shoaib is T [from IV]. In such a case, Usman is V [from II]. Once again it is not acceptable, as Tauqir and Usman both cannot be V.

∴ the assumption made (that Tauqir is V) is invalid.

∴ Tauqir is not V.

If Tauqir is S, then Shoaib is T [from IV]. In this case, Usman is V [from II]. As Usman is not W, Tauqir is not S [from V]. This contradicts the assumption that Tauqir is S. So, this is also invalid.

∴ Tauqir is not S.

As Tauqir is neither V nor S, it is clear from (IV) that Shoaib is not T.

If Vusi is V, then Vusi is not W and thus Wasim is V [From (III)] . This is not possible, as both Vusi and Wasim cannot be V.

∴ Vusi is not V.

Tauqir can only be either T or W. Now if Tauqir is T, Vusi is U and Wasim is not V [from VI].

But if Vusi is U, then Vusi is not W and thus Wasim must be V, according to (III).

∴ Tauqir is not T.

Let us summarize the findings till now.

Shoaib: Not T

Tauqir: Not U, Not S, Not V and Not T

Vusi: Not V

So, the only possibility is that Tauqir is W.

From (VI), Vusi is U and Wasim is not V, if and only if Tauqir is T. Now, as Tauqir is not T, it follows that Vusi is not U. It also follows that Wasim is V.

If Shoaib is U, then Usman is W [from VII]. But we know that Tauqir is W, so Usman is not W.

∴ It follows that Shoaib is not U.

∴ Shoaib is not U, Shoaib is not T, Shoaib is not W (as Tauqir is W) and Shoaib is not V (as Wasim is V).

∴ Shoaib is S.

Also, Vusi is neither S nor V or W. Also, Vusi is not U.

∴ Vusi is T. Thus, Usman has to be U.

So Shoaib, Tauqir, Usman, Vusi and Wasim operate under the names of S, W, U, T and V respectively.

### Question 24

Under what name does Wasim operate?

S

T

U

V

#### SOLUTION

Solution :D

From (I), if Tauqir is U, then Vusi is V. However we cannot conclude that if Vusi is V, then Tauqir is U.

Let us assume that Tauqir is U. Then, Vusi is V.

from (III), as Vusi is not W, Wasim is V. But both Vusi and Wasim cannot be V.

So, our assumption (that Tauqir is U) itself is not valid.

∴ Tauqir is not U.

If Tauqir is V, then Shoaib is T [from IV]. In such a case, Usman is V [from II]. Once again it is not acceptable, as Tauqir and Usman both cannot be V.

∴ the assumption made (that Tauqir is V) is invalid.

∴ Tauqir is not V.

If Tauqir is S, then Shoaib is T [from IV]. In this case, Usman is V [from II]. As Usman is not W, Tauqir is not S [from V]. This contradicts the assumption that Tauqir is S. So, this is also invalid.

∴ Tauqir is not S.

As Tauqir is neither V nor S, it is clear from (IV) that Shoaib is not T.

If Vusi is V, then Vusi is not W and thus Wasim is V [From (III)] . This is not possible, as both Vusi and Wasim cannot be V.

∴ Vusi is not V.

Tauqir can only be either T or W. Now if Tauqir is T, Vusi is U and Wasim is not V [from VI].

But if Vusi is U, then Vusi is not W and thus Wasim must be V, according to (III).

∴ Tauqir is not T.

Let us summarize the findings till now.

Shoaib: Not T

Tauqir: Not U, Not S, Not V and Not T

Vusi: Not V

So, the only possibility is that Tauqir is W.

From (VI), Vusi is U and Wasim is not V, if and only if Tauqir is T. Now, as Tauqir is not T, it follows that Vusi is not U. It also follows that Wasim is V.

If Shoaib is U, then Usman is W [from VII]. But we know that Tauqir is W, so Usman is not W.

∴ It follows that Shoaib is not U.

∴ Shoaib is not U, Shoaib is not T, Shoaib is not W (as Tauqir is W) and Shoaib is not V (as Wasim is V).

∴ Shoaib is S.

Also, Vusi is neither S nor V or W. Also, Vusi is not U.

∴ Vusi is T. Thus, Usman has to be U.

So Shoaib, Tauqir, Usman, Vusi and Wasim operate under the names of S, W, U, T and V respectively.

### Question 25

**Which team was at the second position at the end of group matches?**

#### SOLUTION

Solution :C

∵ 3 matches ended in a draw, total number of bonus points scored is 14 and Everton lost against Bournemouth by 1 - 4.

∴ Bournemouth won 1 match and drew 0 matches as the total number of matches played by each team is 5.

∴ Arsenal scores 13 points only if its 1 match ended in a draw and it lost 2 matches.

∵ Southampton lost 1 matches and drew 0 matches, it won 4 matches as the total number of matches played by each team is 5.

∵ Bournemouth won its only match against Everton by 4 - 1, they scored only one bonus point as the difference between number of goals scored is 3.

Also, 3 matches ended in a draw.

∴ Total number of wins and losses will be 12 as the total number of matches played is 15.

Following table can be made on the basis of above statements:Now, total number of bonus points is 14.

∴ Southampton scored 5 bonus points.

∴ Southampton scored a total of 25 points and the difference between the total points scored by Southampton and Aston Villa is 12.

∴ Aston Villa scored 13 points and won 2 matches with 1 match ending in a draw.

∵ 3 matches ended in a draw, the total number of draws is 6.

∴ Sunderland drew 2 matches, lost 1 match and scored a total of 18 points.

Finally, the total number of wins and losses is 12.

∴ Everton won 1 match and lost 2 and scored a total of 11 points.

Following table can be made on the basis of above statements:Everton won against Aston Villa 2 - 0.

∴ Everton scored both its bonus points against Aston Villa.

∴ Everton did not defeat any other team of higher rank.

∴At the end of the group matches, Sunderland has the second highest number of points.

Hence, option C.

### Question 26

**Who won the match between Everton and Bournemouth?**

#### SOLUTION

Solution :A

Everton won against Aston Villa by 2 - 0.

∴ Everton scored both its bonus points against Aston Villa.

∴ Everton did not defeat any other team.

And Bournemouth did not play any draw.

∴ Bournemouth won the match against Everton

### Question 27

**What can be the minimum number of upsets caused by Southampton?**

1

2

3

4

#### SOLUTION

Solution :C

Southampton scored 5 bonus points.

Also, four teams rank higher than Southampton.

∴It can cause not more than 4 upsets and if it wins against Sunderland, then from a total of 4 wins, it can cause 3 upsets.

### Question 28

**What can be the maximum number of upsets in the tournament?**

3

5

7

8

#### SOLUTION

Solution :D

∵ Southampton can cause not more than 4 upsets, Sunderland caused 2 upsets, Arsenal and Bournemouth did not cause any upsets, Everton caused 1 upset and Aston Villa can cause 1 upset by defeating Arsenal.

∴There can be a maximum of 8 upsets in the tournament.

### Question 29

Which couple had been to Chandigarh?

#### SOLUTION

Solution :B

Create a table with the names of the husbands in the rows and the wives, surnames, cars and places visited in the columns. If any data is directly given for a husband, fill it in the table and fill the alternatives in that column for the other persons. For data where the husband is not explicitly mentioned, note them down for further reference.

Thus, we have Priyanka ≠ Kapoor and Priyanka = Shimla

Mr. and Mrs. Bhatia ≠ Alto

Santro = Chandigarh

Sunil ≠ Ankita Singh

Now, consider this table and the clues given above together.

Since Priyanka went to Shimla, Ajay and Geeta had to mandatorily go to Agra.

Sunil rode the Swift and the person riding Santro went to Chandigarh. Therefore, Sunil could not have gone to

Chandigarh and had to go to Shimla. This also means that Vijay and his wife went to Chandigarh.

Thus, the column for places is completed.

Since Sunil went to Shimla, Priyanka is Sunil's wife and so Ankita is Vijay's wife. Therefore, Rahul's wife can only be Vijeta. Thus, the column for females is also filled.

Since Priyanka is not Kapoor, her surname is Bhatia. Also, Vijay is married to Ankita Singh and so their surname is Singh. Therefore, Ajay's surname can only be Kapoor. This fills the column for surnames.

Since Vijay went to Chandigarh, he rode a Santro. Therefore, from the table, Rahul and Ajay can only ride Alto and Ritz respectively. Thus, the entire table can be filled as shown below:

Thus, Vijay and Ankita had been to Chandigarh.

Hence, option B.

### Question 30

Which car did the Bhatia's use?

#### SOLUTION

Solution :A

From the table in the solution of the first question of the set, we know that the Bhatias used a Swift car.

Hence, option A.

### Question 31

Which statement(s) from the above conditions is/are redundant in completing the entire distribution?

#### SOLUTION

Solution :E

The data required to complete the table is introduced only in the given seven statements and is not given in the common data (apart from data on place visited). Therefore, if any of these statements is ignored, we will not have complete data known as to who is the fourth male is or the fourth female and so on. For instance, if we ignore statement IV, we will not know that the fourth male is called Sunil, the fourth female is called Ankita and the fourth surname is Singh. Thus, none of the given statements is redundant. Consequently, filling the table will not be possible. This is applicable to all the statements given in the options.

Hence, option E.

### Question 32

What was Vijeta's surname?

#### SOLUTION

Solution :D

The table from the solution to the first question of the set shows us that Vijeta's surname was Jain.

Hence, option D.