# Free DI and LR - 29 Practice Test - CAT

### Question 1

**Who was East Bengal’s opposition in the first round?**

#### SOLUTION

Solution :B

From the chart, total of number of goals scored for (all teams combined): 37 = total scores against (all teams); thus goals scored against JCT = 37-32 = 5.

JCT got 3 points after 3 rounds. Since its goal for ≠ goals against. All 3 matches have not been drawn. So, JCT has won 1 and lost 2 matches.

Salgaocar has 4 points. It couldn’t have drawn all 3 (although GF=GA). So it has won 1, drawn 1 and lost 1 (3+1+0).

EB has 1 GF and 4 GA. It has also won a match. Thus EB’s most likely history: 1-0,0-2,0-2

MB won in the third round and the match had 2 goals scored totally. So it was a 2-0 win. The other 2 matches to satisfy total GF=5 and GA=7 should be 1-3 and 2-4 losses.

Dempo has GF=11 and GA=5. Hence its history: 3-1,4-2,4-2. Thus, with this score-line, Dempo could’ve never faced EB.

None among Dempo, MB, EB, and JCT has drawn any match. Hence Salgaocar’s drawn match was against Churchill.

From given conditions, Churchill met Dempo in first round (and lost as Dempo won all matches), Churchill met MB in 2nd round (and won). Hence Churchill’s drawn match against Sal as in 3rd round.

MB won in the third round. Thus Dempo must’ve played JCT in the third round.

Thus EB must’ve met MB in the 3rd round and lost 0-2.

Dempo met Sal in the 2nd round

EB met Sal in 1st round

Thus, MB met JCT in 1st round.

JCT lost against Dempo 2-4 or 1-3 and won against MB 4-2 or 3-1

Also, JCT scored 4 goals and conceded 5, hence they lost against Dempo 1-3 and won against

MB 3-1

Dempo won against Churchill and Sal 4-2 each

MB lost against Churchill 2-4

Churchill and Sal drew their match 3-3

Sal won against EB 2-0 and EB won against JCT 1-0

### Question 2

How many goals did Mohun Bagan score in the first round.

#### SOLUTION

Solution :From the chart, total of number of goals scored for (all teams combined): 37 = total scores against (all teams); thus goals scored against JCT = 37-32 = 5.

JCT got 3 points after 3 rounds. Since its goal for ≠ goals against. All 3 matches have not been drawn. So, JCT has won 1 and lost 2 matches.

Salgaocar has 4 points. It couldn’t have drawn all 3 (although GF=GA). So it has won 1, drawn 1 and lost 1 (3+1+0).

EB has 1 GF and 4 GA. It has also won a match. Thus EB’s most likely history: 1-0,0-2,0-2

MB won in the third round and the match had 2 goals scored totally. So it was a 2-0 win. The other 2 matches to satisfy total GF=5 and GA=7 should be 1-3 and 2-4 losses.

Dempo has GF=11 and GA=5. Hence its history: 3-1,4-2,4-2. Thus, with this score-line, Dempo could’ve never faced EB.

None among Dempo, MB, EB, and JCT has drawn any match. Hence Salgaocar’s drawn match was against Churchill.

From given conditions, Churchill met Dempo in first round (and lost as Dempo won all matches), Churchill met MB in 2nd round (and won). Hence Churchill’s drawn match against Sal as in 3rd round.

MB won in the third round. Thus Dempo must’ve played JCT in the third round.

Thus EB must’ve met MB in the 3rd round and lost 0-2.

Dempo met Sal in the 2nd round

EB met Sal in 1st round

Thus, MB met JCT in 1st round.

JCT lost against Dempo 2-4 or 1-3 and won against MB 4-2 or 3-1

Also, JCT scored 4 goals and conceded 5, hence they lost against Dempo 1-3 and won against

MB 3-1

Dempo won against Churchill and Sal 4-2 each

MB lost against Churchill 2-4

Churchill and Sal drew their match 3-3

Sal won against EB 2-0 and EB won against JCT 1-0

### Question 3

How many goals were scored against Salgaocar in the third round?

#### SOLUTION

Solution :From the chart, total of number of goals scored for (all teams combined): 37 = total scores against (all teams); thus goals scored against JCT = 37-32 = 5.

JCT got 3 points after 3 rounds. Since its goal for ≠ goals against. All 3 matches have not been drawn. So, JCT has won 1 and lost 2 matches.

Salgaocar has 4 points. It couldn’t have drawn all 3 (although GF=GA). So it has won 1, drawn 1 and lost 1 (3+1+0).

EB has 1 GF and 4 GA. It has also won a match. Thus EB’s most likely history: 1-0,0-2,0-2

MB won in the third round and the match had 2 goals scored totally. So it was a 2-0 win. The other 2 matches to satisfy total GF=5 and GA=7 should be 1-3 and 2-4 losses.

Dempo has GF=11 and GA=5. Hence its history: 3-1,4-2,4-2. Thus, with this score-line, Dempo could’ve never faced EB.

None among Dempo, MB, EB, and JCT has drawn any match. Hence Salgaocar’s drawn match was against Churchill.

From given conditions, Churchill met Dempo in first round (and lost as Dempo won all matches), Churchill met MB in 2nd round (and won). Hence Churchill’s drawn match against Sal as in 3rd round.

MB won in the third round. Thus Dempo must’ve played JCT in the third round.

Thus EB must’ve met MB in the 3rd round and lost 0-2.

Dempo met Sal in the 2nd round

EB met Sal in 1st round

Thus, MB met JCT in 1st round.

JCT lost against Dempo 2-4 or 1-3 and won against MB 4-2 or 3-1

Also, JCT scored 4 goals and conceded 5, hence they lost against Dempo 1-3 and won against

MB 3-1

Dempo won against Churchill and Sal 4-2 each

MB lost against Churchill 2-4

Churchill and Sal drew their match 3-3

Sal won against EB 2-0 and EB won against JCT 1-0

### Question 4

**East Bengal won against:**

#### SOLUTION

Solution :D

EB has 1 GF and 4 GA. It has also won a match. Thus EB’s most likely history: 1-0,0-2,0-2

MB won in the third round. Thus Dempo must’ve played JCT in the third round.

Thus EB must’ve met MB in the 3rd round and lost 0-2.

Dempo met Sal in the 2nd round

EB met Sal in 1st round

Thus, MB met JCT in 1st round.

JCT lost against Dempo 2-4 or 1-3 and won against MB 4-2 or 3-1

Also, JCT scored 4 goals and conceded 5, hence they lost against Dempo 1-3 and won against

MB 3-1

Dempo won against Churchill and Sal 4-2 each

MB lost against Churchill 2-4

Churchill and Sal drew their match 3-3

Sal won against EB 2-0 and EB won against JCT 1-0

### Question 5

In the second round match played by Churchill, how many total goals were scored?

#### SOLUTION

Solution :EB has 1 GF and 4 GA. It has also won a match. Thus EB’s most likely history: 1-0,0-2,0-2

MB won in the third round. Thus Dempo must’ve played JCT in the third round.

Thus EB must’ve met MB in the 3rd round and lost 0-2.

Dempo met Sal in the 2nd round

EB met Sal in 1st round

Thus, MB met JCT in 1st round.

JCT lost against Dempo 2-4 or 1-3 and won against MB 4-2 or 3-1

Also, JCT scored 4 goals and conceded 5, hence they lost against Dempo 1-3 and won against

MB 3-1

Dempo won against Churchill and Sal 4-2 each

MB lost against Churchill 2-4

Churchill and Sal drew their match 3-3

Sal won against EB 2-0 and EB won against JCT 1-0

### Question 6

Rocky spent 20% more on his bike in 2000 than in 1999. By how much did Rocky have to increase his expenses on bus travel in 2000 when compared to 1999?

#### SOLUTION

Solution :B

b. 100%

In 1999, Expenses on Bike : 25%; Bus: 30%; Expenses on bike increased in 2000 by 20%=>1.2*.25=.30

Thus expenses on bus in 2000=(40/20)*.30 = .60 => % increase: (.6-.3)/(.3)*100=100%

### Question 7

Rocky had same expenses in 2003 and 2002 on bike and car travel taken together. If he incurred 50% of his travel expenses of 2003 on bus travel, what was the increase in expenses on bus travel in 2003 when compared to 2002?

#### SOLUTION

Solution :B

b. 50%

Combined expenses on bike and car in 2002 = .6, remains same in 2003. Bus forms 50% of his expenses in 2003. Thus bus expenses in 2003=combined expense on bike and car in 2003 = .6; also bus expense in 2002=.4 => % increase: (.6-.4)/.4 * 100 = 50%

### Question 8

His expenses towards bike travel have been continuously increasing through the years 1998-2002. The increase has been same for all previous years. Then in which year was there maximum increase in total travel expense?

#### SOLUTION

Solution :C

c. 2000

Rocky’s expenses on his bike in 1998, 1999, 2000, 2001 and 2002 was times of his total expenses. Since the increase in expenses on bike increased continuously and by constant amount, the increase was most shadowed when other expenses were higher and the total expense increased the most. This happened when bike cost dropped to total cost despite continuous increase in actual bike expense from , in 2000

### Question 9

Which of the following statements must be true?

#### SOLUTION

Solution :D

d. If Rocky’s total expenses increased by ≥ 30% from 1998 to 2002, then his expenses on bike would’ve also

increased from 1998 to 2002 (the only confusion can rise in the years where the percentage is drpping from 25% to 20%)

take the total expense in 1999=100 and the expense in 2000 =130. Then , the expense on bike is 25 and 26 respectively. Thus, there is a definite increase

1. The percentage increase in expenses over the previous year on bus is highest in 2000, but the

percentage increase in expenses on Bike could’ve been highest in 1999, 2001 and 2002

2. The total expense is highest in 1999. But as the expense on bus as a percentage of total cost also

increases, we can’t be sure if the expense on bus has increased from 1999 to 2000

3. The total expense on bike and car has decreased, but then, the expense on bus can increase or

decrease.

4. The total expenses increased from 1998 to 2002, and expense on bike increased also kept increasing

continuously, this statement is definitely true.

### Question 10

If the expenses towards travel continuously decreased from 1998 to 2003, in which year was amount spent on bus travel the maximum?

#### SOLUTION

Solution :E

Let us take sample values

Hence, answer is cannot be determined. Option (e)