Section-1

The following facts are known about the goals scored by these four players only. All the questions refer only to the goals scored by these four players.

1. Only one goal was scored in every even numbered match.

2. Harita scored more goals than Bimla.

3. The highest goal scorer scored goals in exactly 3 matches including Match 4 and Match 8.

4. Bimla scored a goal in Match 1 and one each in three other consecutive matches.

5. An equal number of goals were scored in Match 3 and Match 7, which was different from the number of goals scored in either Match 1 or Match 5.

6. The match in which the highest number of goals was scored was unique and it was not Match 5.

1

In Match 7, one goal was scored.

4

The correct sequence of goals scored in matches
1, 3, 5 and 7 is 4, 1, 2, 1.

2

Both the statements are true.

2

None of the statements is false.

3

None of the statements is true.

Some students are not interested in attending the gettogether. Those students who are interested in attending a 3-day event are also interested in attending a 2-day event; those who are interested in attending a 2-day event are also interested in attending a 1-day event.

The following facts are also known:

1. All the girls and 80% of the boys are interested in attending a 1-day event. 60% of the boys are interested in attending a 2-day event.

2. Some of the girls are interested in attending a 1-day event, but not a 2-day event; some of the other girls are interested in attending both.

3. 70% of the boys who are interested in attending a 2-day event are neither singers nor dancers. 60% of the girls who are interested in attending a 2-day event are neither singers nor dancers.

4. No girl is interested in attending a 3-day event. All male singers and 2 of the dancers are interested in attending a 3-day event.

5. The number of singers interested in attending a 2-day event is one more than the number of dancers interested in attending a 2-day event.

50

50 boys are there in the class.

I. The number of boys who are interested in attending a 1-day event and are neither dancers nor singers.

II. The number of female dancers who are interested in attending a 1-day event.

1

Statement I cannot be determined.

2

The fraction of the class interested in attending a
2-day event is 7/13.

4

The numbers of male dancers who are interested
in attending a 1-day event can be either 5 or 6.

3

Number of female dancers interested in attending
a 2-day event is equal to ‘0’.

Once all six interviews are over for a candidate, the candidate receives a funding that is Rs.1000 times the product of the face values of all the tokens. For example, if a candidate has tokens with face values 2, 5, and 7, then they get a funding of Rs.1000 × (2 × 5 × 7) = Rs.70,000.

Pragnyaa, Qahira, Rasheeda, Smera, and Tantra were five candidates who received funding. The funds they received, in descending order, were Rs.390,000, Rs.210,000, Rs.165,000, Rs.77,000, and Rs.66,000. The following additional facts are known:

1. Fathima awarded tokens to everyone except Qahira, while Adhara awarded tokens to no one except Pragnyaa.

2. Rashida received the highest number of tokens that anyone received, but she did not receive one from Esther.

3. Bithi awarded a token to Smera but not to Qahira, while Dhanavi awarded a token to Qahira but not to Smera.

2

Qahira received 2 tokens.

4

Pragnyaa definitely received a token from Bithi but not from Dhanavi.

3

Chhaya awarded 3 tokens – Pragnyaa, Rashida and either Smera or Tantra.

3

Total funds received by Smera was either 66000 or 165000, so tokens received were either (3, 2, 11) or
(3, 5, 11). In either case the total number of tokens was 3.

(a) Rs. 66,000

(b) Rs. 165,000

2

The funds received by Tantra could be either Rs.66,000 or Rs.1,65,000. Hence, option (2) is correct.

Given above is the schematic map of the metro lines in a city with rectangles denoting terminal stations (e.g. A), diamonds denoting junction stations (e.g. R) and small filled-up circles denoting other stations. Each train runs either in east-west or north-south direction, but not both. All trains stop for 2 minutes at each of the junction stations on the way and for 1 minute at each of the other stations. It takes 2 minutes to reach the next station for trains going in east-west direction and 3 minutes to reach the next station for trains going in north-south direction. From each terminal station, the first train starts at 6 am; the last trains leave the terminal stations at midnight. Otherwise, during the service hours, there are metro service every 15 minutes in the north-south lines and every 10 minutes in the east-west lines. A train must rest for at least 15 minutes after completing a trip at the terminal station, before it can undertake the next trip in the reverse direction. (All questions are related to this metro service only. Assume that if someone reaches a station exactly at the time a train is supposed to leave, (s)he can catch that train.)

3

Given that Hari is ready to board a train at 8:05 am
from station M.

Trains leave after every 10 minutes. So Hari can
catch the 8:10 train from M.

There are 17 stations, 2 junctions and 20 intervals,
so time taken to travel = 20 × 2 + 17 × 1 + 2 × 2
= 61 minutes

Hence, time at which Hari reaches station N
= 8:10 + 1:01 = 9:11 am.

2

There can be two routes that Priya can take.

**Case 1:** First travel by East-West line and then
North-South line.

Trains leave after every 10 minutes on the East-
West line.

The 10:20 am train from P reaches and then leaves
T at = 10:20 + 00:11 + 00:02 = 10:33 am
In the first case Priya will have to wait for 8 minutes
at the station before boarding the train.

So let us see if the waiting time is reduced in
case 2.

**Case 2:** First travel by North-South line and then
East-West line.

Trains leave after every 15 minutes on the North-
South line. The 10:15 am train from B will reach
T at = 10:15 + 00:11 = 10:26 am and leave T at
10:28 am. In this case Priya’s train leaves within
3 minutes of her reaching the station. This train
reaches R at = 10:28 + 00:15 = 10:43 am.

From R Priya has to catch the East-West train for
station S.

The 10:30 am train from M reaches R at = 10:30 +
00:11 = 10:41 am and leaves at 10:43 am.

Priya can catch this train and reach station S at
= 10:43 + 00:29 = 11:12 am.

4

The last (midnight) train from A reaches R at
12:11 am and leaves at 12:13 am. It will reach B at
= 12:13 + 00:17 + 00:11 = 12:41 am.

From S to R the travel time is 29 minutes. To catch
the 12:13 am train Haripriya will have to start from
S at = 12:13 – 00:29 = 11:44 pm or before that.

Trains start from N after every 10 minutes and the
time taken to reach S is 17 minutes.

There is a stoppage of 2 minutes at S.

The 11:30 pm train from N reaches S at 11:47 pm,
which does not serve the purpose.

The 11:20 pm train from N reaches S at 11:37 pm
and leaves at 11:39 pm.

This train will reach R by 11:39 + 00:29
= 12:08 am.

Then she can catch the last train from A going to B
at 12:13 am.

Haripriya can catch the train at S if she reaches
the station latest by 11:39 pm.

8

Total time for a train to travel from A to B and to
start back = 11 + 2 + 15 + 2 + 11 + 15
= 56 minutes.

Trains leave after every 15 minutes.

The minimum number of trains that are required to
provide the service on the AB line
(in the North-South direction) = [56/15] = [3.733]
= 4 trains

Hence, for both directions = 4 + 4 = 8 trains.

48

The minimum number of trains that are required to
provide the service in this city

= Trains in AB and CD lines + Trains in MN and
PQ lines.

Time taken for a train to travel from M to N and
start back

= 11 + 2 + 29 + 2 + 17 + 15 = 76 minutes.

Trains leave after every 10 minutes on this line.

The minimum number of trains required on the MN
line in the East-West direction

= [76/10] = [7.6] = 8 trains

Minimum number of trains required in both
directions on the MN line = 16 trains
Hence, total number of trains required

= (AB + CD) + (MN + PQ) = (8 + 8) + ( 16 + 16)
= 48.