Free DI and LR Practice Test - CAT 

As B - C is unusable, S - B - C - T is not possible.
The other possible ways are : S - A - T,  S - B - A - T , S - D - T, and S - D - C - T 
From these if we apply all the options:
Both option (b) and (c) are true, as in both the cases total time is same for each of the four routes.

No traffic flows from D - T. Now apply each of the options. New time will be as follows.

As it is given that traffic flow at junction A is same as that at junction C.
$\therefore$ Number of routes involving A that can be used must be same as that involving C.
Further, only the routes with minimum time can be used.
That happened in only (a), as no of the routes that can be used, the number of routes involving A is two (S-A-T and S-B-A-T) and that involving C is also two (S-B-C-T and S-D-C-T)

To ensure that all the routes from S to T get the same number of participants, Going by the answer options 
As the time must be same for all the routes, it must be option (d).

From the given options

It is very likely that option (d) is selected. But if all the five routes has the same time taken, then there will be an equal number of participant in all the five routes i.e. 20% in each route.
But then the percentage of participant in
S-A = 20%
S-B = 40% (As there are two routes involving S-B)
S-D = 40% (For the same reason as above)

But here the given condition that number of participant in S-A is equal to that in S-B, which in turn is equal to S-D is not satisfied.
As S-A = S-B = S-D.
Of the routes, that can be used the number of routes involving S-A must be the same as S-B, which in turn is same as that as S-D. It happened in only option (a).

There must be one other route other than those involving B with the least cost as most only 70% participants can only use this route.
We must take S-D-C-T as the other route.
S-B-C-T, if task time at B = 3, total time= 10.
S-D-C-T, if task time at D and C is 0, total time is 10.
$\therefore$ 10 hours is the least time.

The given information can be tabulated below.
$\begin{array}{cccc}\text{PERSON}& \text{SPORT}& \text{NATIVE}& \text{PLAYS}\\ B& & \text{Chennai}& \text{Mumbai}\\ C& \text{Swims}& \text{X Pune}& \\ & \text{Football}& \text{X Pune}& \text{Pune}\\ & \text{Hockey}& \text{Hyderabad}& \\ D& \text{X Chess}& \text{X Bangalore}& \text{Bangalore}\end{array}$

From the above table we can deduce that

1 ) D is a native of Pune

2) B plays Chess and D pays Cricket

3) C plays in Hyderabad

4) Since E is a native of Bangalore, the only row available for this is row 3 and thus, we can also deduce that E plays Football in Pune

5) therefore, C is a native of Mumbai. The table can now be completely filled

$\begin{array}{cccc}\text{PERSON}& \text{SPORT}& \text{NATIVE}& \text{PLAYS}\\ B& \text{Chess}& \text{Chennai}& \text{Mumbai}\\ C& \text{Swims}& \text{Mumbai}& \text{Hyderabad}\\ E& \text{Football}& \text{Bangalore}& \text{Pune}\\ A& \text{Hockey}& \text{Hyderabad}& \text{Chennai}\\ D& \text{Cricket}& \text{Pune}& \text{Bangalore}\end{array}$

A plays HOCKEY. Option (a)

The given information can be tabulated below.
$\begin{array}{cccc}\text{PERSON}& \text{SPORT}& \text{NATIVE}& \text{PLAYS}\\ B& & \text{Chennai}& \text{Mumbai}\\ C& \text{Swims}& \text{X Pune}& \\ & \text{Football}& \text{X Pune}& \text{Pune}\\ & \text{Hockey}& \text{Hyderabad}& \\ D& \text{X Chess}& \text{X Bangalore}& \text{Bangalore}\end{array}$

From the above table we can deduce that

1 ) D is a native of Pune

2) B plays Chess and D pays Cricket

3) C plays in Hyderabad

4) Since E is a native of Bangalore, the only row available for this is row 3 and thus, we can also deduce that E plays Football in Pune

5) therefore, C is a native of Mumbai. The table can now be completely filled

$\begin{array}{cccc}\text{PERSON}& \text{SPORT}& \text{NATIVE}& \text{PLAYS}\\ B& \text{Chess}& \text{Chennai}& \text{Mumbai}\\ C& \text{Swims}& \text{Mumbai}& \text{Hyderabad}\\ E& \text{Football}& \text{Bangalore}& \text{Pune}\\ A& \text{Hockey}& \text{Hyderabad}& \text{Chennai}\\ D& \text{Cricket}& \text{Pune}& \text{Bangalore}\end{array}$

Swimming is played in Mumbai.

The given information can be tabulated below.

$\begin{array}{cccc}\text{PERSON}& \text{SPORT}& \text{NATIVE}& \text{PLAYS}\\ B& & \text{Chennai}& \text{Mumbai}\\ C& \text{Swims}& \text{X Pune}& \\ & \text{Football}& \text{X Pune}& \text{Pune}\\ & \text{Hockey}& \text{Hyderabad}& \\ D& \text{X Chess}& \text{X Bangalore}& \text{Bangalore}\end{array}$

From the above table we can deduce that

1 ) D is a native of Pune

2) B plays Chess and D pays Cricket

3) C plays in Hyderabad

4) Since E is a native of Bangalore, the only row available for this is row 3 and thus, we can also deduce that E plays Football in Pune

5) therefore, C is a native of Mumbai. The table can now be completely filled

$\begin{array}{cccc}\text{PERSON}& \text{SPORT}& \text{NATIVE}& \text{PLAYS}\\ B& \text{Chess}& \text{Chennai}& \text{Mumbai}\\ C& \text{Swims}& \text{Mumbai}& \text{Hyderabad}\\ E& \text{Football}& \text{Bangalore}& \text{Pune}\\ A& \text{Hockey}& \text{Hyderabad}& \text{Chennai}\\ D& \text{Cricket}& \text{Pune}& \text{Bangalore}\end{array}$

D is a native of Pune. Option (c)

A enters before B. 15 students before B including the 5 between and A. Therefore total 9+A+5+B+4=20

For Database H, total number of entries =1,00,000

We will represent the number of people (in percentage terms) whose data is available by lines as shown in the figure.

As the maximum of 5 out of 6 is asked, we will first consider the 5 details with maximum number of people.

Starting with Name, draw a line to corresponding to 100% people

Now, when we represent students whose address is available,70 % of them, we should ensure that these 70%people are also a part of the 100% whose name details are available. This way, we are maximizing the number of people for whom both the name & address is available

If you want to visualize this using the circles we are used to

Similarly, for the remaining 3 details, we try to have the maximum area of overlap.

For the next 3 details, the figure would be:

Thus the number of people for whom all five of Name Address Email Mobile and Age data is available Is 30%

However, there are 10% people with Fax No. also who have not been considered. We will place those people strategically, them so that the overlapped region for 5 lines, becomes maximum as follows.

Now count the regions where 5 lines are overlapping. It is 40% of the total

Answer is 40% of 100000= 40000. Option (c)

The second question asks for exactly the opposite of the first question. We need minimum overlap of the three regions (name, fax and telephone number)

1) Database E= Total Entries= Using line technique, we will try drawing lines in such a way that the overlap is minimized as follows

$\begin{array}{ccc}\text{Name}& \text{Fax Number}& \text{Telephone Number}\\ 100& 50& 80\end{array}$

Thus, the region of minimum overlap of 3 lines is 30% of 15000 = 4500. Option (c)

To visualize this using venn diagrams, see below

Line technique is an alternative and better representation of sets where there is no upper limit to the details which need to be compared.

Strategy- Change the scale to minimize calculation

From both Import and Export figures, strike out the last 4 digits = 1750 & 1400 approximately

The answer options are far apart, therefore we can easily approximate.

$\begin{array}{ccc}China& Imports\left(1750\right)& Exports\left(1400\right)\\ Asia\left(40\%\right)& 1750\times 40\%=700& 1400\times 40\%=560\\ Korea(73\%,80\%)& 700\times 73\%=511& 560\times 80\%=448\end{array}$

Trade Deficit= Import- Export = 511 - 448$\approx$63. Hence answer is option (c)

Strategy- Change the scale to minimize calculation (strike out the last 2 from billion figures and last 5 from million figures)

Trade Deficit for China= 175 - 140$\approx$35 billion

Initial foreign exchange reserve = 11341

After withdrawal = 113 - 29 = 84

After adjusting trade deficit, 84 - 35 $\approx$ 49

Initial trade deficit$\approx$ 3449510

Import increases at a rate of 15% every year for 4 years. This means that it's final value will be

$17609863\times {1.05}^4=$ 21404898

Similarly Export increases at a rate of 5% every year for 4 years. This means that it's final value will be

$14160353\times {1.15}^4=$24766545

New trade deficit $\approx$ 3361647

Percentage increase is from 3449510 to 3361647 $\approx$ 290% increase. 

Italy / rank 2's opponent in Round 3 is what we need.

Ideal Scenario in round 3 Italy (2) opponent is 7 (as 2+7=9).

We could mark Rank 8(Spain) to be Italy's opponent in the quarters but we know Match No.7 in round 2 was an upset so Spain (7) will be replaced by the team which played and beat 7 in round 2.

Round 2, Team 7 would ideally play Team 10 (7+10=17 "Round 2 Magic Number”) so Team 10 beats 7 and replaces its position in round 3!

Answer is Team 10- Czech R (d)

Brazil / rank 1's opponent in Round 3 is what we need.

Ideal Scenario in round 3 Brazil (1) opponent is 8 (as 1+8=9).

We could mark Rank 8(Portugal) to be Brazil's opponent in the quarters but we know Portugal lost in round 2.

In Round 2, Portugal (8) would ideally play team 11 (8+11=17: "Round 2 Magic Number”) so Team 11 beats Portugal and plays Brazil in round 3!

Answer is Team 11- Nigeria (d)

Brazil (1) plays rank 4 in semi-finals (Round 4 - magic number is 5)

But, we know all even numbered matches of round 1 and all even ranked teams lose in round 1, hence lets trace rank 4's path to know which is the LOWEST ranked team that can replace it.

Round 1: 4 + 29 ("Magic number for round 1 is 33=4+29”) $=>$ 29 qualifies and takes 4's place

Round 2: 4 + 13 ("Magic number for round 2 is 17=4+13”)

But, now the round 2 match is not 4 v/s 13 but 29 v/s 13 $=>$ 13 is a better rank team and no upsets occur in round 2 so 13 qualifies and takes 4's place in the next round.

Round 3: 4 + 5 ("Magic number for round 3 is 9=4+15”)

But now here 4 is replaced by 13 so its 13 v/s 5. The winner of this match meets 1 in the next round(Semi-finals). We have the liberty to choose any of these two teams but the choice has to be of the LOWER team hence, choose rank 13 =Switzerland as the ANSWER (a)

$\begin{array}{ccccccc}Game& Opening& Playe{r}^{\prime }spick& & Deale{r}^{\prime }spick& & Closing\\ & balance& & & & & balance\\ & & Debit& Credit& Debit& Credit& \\ & & (-)& (+)& (-)& (+)& \\ 1& 0& 0& 8& 16& 0& -8\\ 2& -8& 0& 10& 0& 10& 12\\ 3& 12& 0& 6& 6& 0& 12\\ 4& 12& 0& 8& 16& 0& 4\end{array}$

$\begin{array}{ccccccc}Game& Opening& Playe{r}^{\prime }spick& & Deale{r}^{\prime }spick& & Closing\\ & balance& & & & & balance\\ & & Debit& Credit& Debit& Credit& \\ & & (-)& (+)& (-)& (+)& \\ 1& 0& 0& 8& 16& 0& -8\\ 2& -8& 0& 10& 0& 10& 12\\ 3& 12& 0& 6& 6& 0& 12\\ 4& 12& 0& 8& 16& 0& 4\end{array}$

Since the maximum negative that Ghosh Babu goes into is -8, he should begin with at least Rs. 8, so that he does not have to borrow any money at any point.

$\begin{array}{ccccccc}Game& Opening& Playe{r}^{\prime }spick& & Deale{r}^{\prime }spick& & Closing\\ & balance& & & & & balance\\ & & Debit& Credit& Debit& Credit& \\ & & (-)& (+)& (-)& (+)& \\ 1& 0& 0& 8& 16& 0& -8\\ 2& -8& 0& 10& 0& 10& 12\\ 3& 12& 0& 6& 6& 0& 12\\ 4& 12& 0& 8& 16& 0& 4\end{array}$

From the above table it is evident that in four games, Ghosh Babu makes a profit of Rs. 4. Hence, if the final amount left with Ghosh Babu is Rs. 100, the initial amount that he had would be Rs. 96.

Cannot be determined

If at 14:00 hrs 1 staff member and no priest entered, then no priest left (after 4 hrs) at 18:00 hrs.

1 devotee who entered at 16:00 hrs might have left at 17:00 hrs (after 1 hr) or at 18:00 hrs (after 2 hrs).

Then, 1 priest left at 18:00 hrs (after 4 hrs) or no staff member left at 18:00 hrs (after 4 hrs). Hence, the result cannot be determined.

None of these.

As no staff member entered at 14:00 hrs, no staff member could have left at 17:00 hrs (after 2 hrs). Hence (b) is not true.

As no devotee entered at 15:00 hrs, no devotee could have left at 17:00 hrs (after 2 hrs). Hence (c)is not true.

If at 15:00 hrs, 1 staff member and 1 priest entered, then 1 staff member left at 17:00 hrs (after 2 hrs).

If at 15:00 hrs, 2 staff members entered, then 2 staff members left at 17:00 hrs (after 2 hrs). Hence (a) may or may not be true.

Hence, none of these options.

0,0

If no staff member would have entered at 12:00 hrs and 13:00 hrs, no staff member would have left at 15:00 hrs (after 2 or 3 hrs). But it is not possible as 6 people left at 15:00 hrs and not more than 2 priests and 2 devotees could leave at the same time.

option c. twice

As no devotee left at 9:00 hrs, 1 visitor who entered at 8:00 hrs left at 10:00 hrs. 2 devotees entered at 9:00 hrs and left at 11:00 hrs or 1 left at 10:00 hrs and 1 at 11:00 hrs. Keeping in mind that at no other time did no staff member leave the unit, the table can be completed as follows:

Hence, (c ) is the answer.

The question is "Does n lie between -1 & 1?”

$n^x<n$

we cannot decide the answer based on this

if n = $\frac{1}{2}$ and x = 2 then $-1<n<1$

however, if n = -3 and x = 3 , n is less than -1

thus, the answer cannot be determined based on statement (1) alone

(2) INSUFFICIENT: $x^{-1}=-2$ can be rewritten as $x=-2^{-1}=\frac{-1}{2}$. However, this statement contains no information about n. hence, answer cannot be determined based on this statement alone as well.

(1) AND (2) SUFFICIENT: If we combine the two statements by plugging the value for x into the first statement, we get $n^{-1/2}<n$.

The only values for n that satisfy this inequality are those greater than 1.

The correct answer is (C).

The average number of vacation days taken this year can be calculated by dividing the total number of vacation days by the number of employees. Since we know the total number of employees, we can rephrase the question as: How many total vacation days did the employees of Company X take this year?

(1) INSUFFICIENT: Since we don't know the specific details of how many vacation days each employee took the year before, we cannot determine the actual numbers that a 50% increase or a 50% decrease represent. For example, a 50% increase for someone who took 40 vacation days last year is going to affect the overall average more than the same percentage increase for someone who took only 4 days of vacation last year.

(2) SUFFICIENT: If three employees took 10 more vacation days each, and two employees took 5 fewer vacation days each, then we can calculate how the number of vacation days taken this year differs from the number taken last year:
(10 more days/employee)(3 employees) - (5 fewer days/employee)(2 employees) = 20
Required Average = 16 + 4 = 20