CAT 2019 Question Paper With Answers & Explanation
DILR
Question Numbers (35 to 38): Answer the questions on the basis of the information given below.
The Ministry of Home Affairs is analysing crimes committed by foreigners in different states and union territories (UT)
of India. All cases refer to the ones registered against foreigners in 2016.
The number of cases – classified into three categories: IPC crimes, SLL crimes and other crimes – for nine states/UTs
are shown in the figure below. These nine belong to the top ten states/UTs in terms of the total number of cases
registered. The remaining state (among top ten) is West Bengal, where all the 520 cases registered were SLL crimes.
The table below shows the ranks of the ten states/UTs
mentioned above among ALL states/UTs of India in terms
of the number of cases registered in each of the three
category of crimes. A state/UT is given rank r for a
category of crimes if there are (r-1) states/UTs having a
larger number of cases registered in that category of
crimes. For example, if two states have the same number
of cases in a category, and exactly three other states/
UTs have larger numbers of cases registered in the same
category, then both the states are given rank 4 in that
category. Missing ranks in the table are denoted by *.
Q. 1 What is the rank of Kerala in the ‘IPC crimes’
category?
Can simply observe from given graph that Kerala
has rank 5 in IPC crimes, (Delhi, Karnataka, Goa,
Maharashtra are ranked above it)
Q. 2 In the two states where the highest total number of
cases are registered, the ratio of the total number of
cases in IPC crimes to the total number in SLL
crimes is closest to
Can observe from the graph that in “other crimes”
Delhi > Tamil Nadu > Puducherry > Karnataka
So option 1 is correct, where Tamil Nadu rank = 2,
Puducherry = 3
Q. 4 What is the sum of the ranks of Delhi in the three
categories of crimes?
Question Numbers (39 to 42): Answer the questions
on the basis of the information given below.
The following table represents addition of two
six-digit numbers given in the first and the second rows,
while the sum is given in the third row. In the
representation, each of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8,
9 has been coded with one letter among A, B, C, D, E,
F, G, H, J, K, with distinct letters representing distinct
digits.
Question Numbers (43 to 46): Answer the questions
on the basis of the information given below.
A new game show on TV has 100 boxes numbered 1, 2,
. . . , 100 in a row, each containing a mystery prize. The
prizes are items of different types, a, b, c, . . . , in
decreasing order of value. The most expensive item is of
type a, a diamond ring, and there is exactly one of these.
You are told that the number of items at least doubles
as you move to the next type. For example, there would
be at least twice as many items of type b as of type a,
at least twice as many items of type c as of type b and
so on. There is no particular order in which the prizes
are placed in the boxes.
Q. 9 What is the minimum possible number of different
types of prizes?
It is given that the most expensive item is a diamond
ring of type a and there is exactly one of these.
Since the item b should be at least twice.
The minimum number of items will be obtained
when a = 1 and b = 99, which means there are
only two different types of items.
Q. 10 What is the maximum possible number of different
types of prizes?
It is given that the most expensive item is a diamond
ring of type a and there is exactly one of these.
Since the number of items of type b should be at
least twice of that of a and the number of items of
type c should be at least twice of that of b and so
on. So the maximum number of different types of
items of a, b and c will be obtained when a = 1, b
= 2, c = 4, d = 8, e = 16, f = 69. Hence the maximum
number of different types of items will be 6.
If the number of items is 7, then the minimum
number of prizes should be 1 + 2 + 4 + 8 + 16 + 32
+ 64 = 127 which is more than 100. Hence, 6 is
the answer.
Option 1: There are exactly 75 items of type e.
a = 1, b = 2, c = 4, d = 8, e = 85. Here the maximum
value of e = 85. Hence it can take the value 75.
An example of such case is a = 1, b = 2, c = 4,
d = 18, e = 75
Option 2: There are exactly 45 items of type c.
Since the value of d should be at least 90, it means
that d is not present because 45 + 90 will be more
than 100(maximum number of items). Only a, b
and c are present.
The maximum value of b = 22 and a = 1,
but 45 + 22 + 1 = 68, which is less than 100. So
this case is not possible.
Option 3: There are exactly 30 items of type b.
a = 1, b = 30 and c = 69. Hence this case is also
possible.
Option 4: There are exactly 60 items of type d.
d = 60, c = 30, b = 9 and a = 1. a + b + c + d
= 100. Hence, this case is possible.
2 is the answer.
Q. 12 You ask for the type of item in box 45. Instead of
being given a direct answer, you are told that there
are 31 items of the same type as box 45 in boxes 1
to 44 and 43 items of the same type as box 45 in
boxes 46 to 100.
What is the maximum possible number of different
types of items?
The total number of items from 1 to 100, which are of same type as in box 45 = 31 + 1 + 43 = 75
Now to maximize the number of items, a = 1, b = 2, c = 4, d = 18 and e = 75(given)
There can be maximum 5 types of items.
If we consider number of items to be 6, then minimum number of items of 5th type will be 16,
1 + 2 + 4 + 8 + 16 + 75 = 106 which is more than 100.
Question Numbers (47 to 50): Answer the questions
on the basis of the information given below.
Princess, Queen, Rani and Samragni were the four
finalists in a dance competition. Ashman, Badal, Gagan
and Dyu were the four music composers who individually
assigned items to the dancers. Each dancer had to
individually perform in two dance items assigned by the
different composers. The first items performed by the
four dancers were all assigned by different music
composers. No dancer performed her second item before
the performance of the first item by any other dancers.
The dancers performed their second items in the same
sequence of their performance of their first items.
The following additional facts are known.
i) No composer who assigned item to Princess,
assigned any item to Queen.
ii) No composer who assigned item to Rani, assigned
any item to Samragni.
iii) The first performance was by Princess; this item was
assigned by Badal.
iv) The last performance was by Rani; this item was
assigned by Gagan.
v) The items assigned by Ashman were performed
consecutively. The number of performances between
items assigned by each of the remaining composers
was the same.
Question Numbers (51 to 54): Answer the questions
on the basis of the information given below.
Six players – Tanzi, Umeza, Wangdu, Xyla, Yonita and
Zeneca competed in an archery tournament. The
tournament had three compulsory rounds, Rounds
1 to 3. In each round every player shot an arrow at a
target. Hitting the centre of the target (called bull’s eye)
fetched the highest score of 5. The only other possible
scores that a player could achieve were 4, 3, 2 and 1.
Every bull’s eye score in the first three rounds gave a
player one additional chance to shoot in the bonus
rounds, Rounds 4 to 6. The possible scores in Rounds 4
to 6 were identical to the first three.
A player’s total score in the tournament was the sum of
his/her scores in all rounds played by him/her. The table
below presents partial information on points scored by
the players after completion of the tournament. In the
table, NP means that the player did not participate in
that round, while a hyphen means that the player
participated in that round and the score information is
missing.
The following facts are also known.
1. Tanzi, Umeza and Yonita had the same total score.
2. Total scores for all players, except one, were in
multiples of three.
3. The highest total score was one more than double of
the lowest total score.
4. The number of players hitting bull’s eye in Round 2
was double of that in Round 3.
5. Tanzi and Zeneca had the same score in Round 1
but different scores in Round 3.
Question Numbers (55 to 58): Answer the questions
on the basis of the information given below.
The figure below shows the street map for a certain region
with the street intersections marked from a through l. A
person standing at an intersection can see along straight
lines to other intersections that are in her line of sight
and all other people standing at these intersections. For
example, a person standing at intersection g can see all
people standing at intersections b, c, e, f, h, and k. In
particular, the person standing at intersection g can see
the person standing at intersection e irrespective of
whether there is a person standing at intersection f.
Six people U, V, W, X, Y, and Z, are standing at different
intersections. No two people are standing at the same
intersection.
The following additional facts are known.
1. X, U, and Z are standing at the three corners of a
triangle formed by three street segments.
2. X can see only U and Z.
3. Y can see only U and W.
4. U sees V standing in the next intersection behind Z.
5. W cannot see V or Z.
6. No one among the six is standing at intersection d.
Question Numbers (59 to 62): Answer the questions
on the basis of the information given below.
A supermarket has to place 12 items (coded A to L) in
shelves numbered 1 to 16. Five of these items are types
of biscuits, three are types of candies and the rest are
types of savouries. Only one item can be kept in a shelf.
Items are to be placed such that all items of same type
are clustered together with no empty shelf between items
of the same type and at least one empty shelf between
two different types of items. At most two empty shelves
can have consecutive numbers.
The following additional facts are known.
1. A and B are to be placed in consecutively numbered
shelves in increasing order.
2. I and J are to be placed in consecutively numbered
shelves both higher numbered than the shelves in
which A and B are kept.
3. D, E and F are savouries and are to be placed in
consecutively numbered shelves in increasing order
after all the biscuits and candies.
4. K is to be placed in shelf number 16.
5. L and J are items of the same type, while H is an
item of a different type.
6. C is a candy and is to be placed in a shelf preceded
by two empty shelves.
7. L is to be placed in a shelf preceded by exactly one
empty shelf.
Q. 25 In how many different ways can the items be arranged
on the shelves?
Question Numbers (63 to 66): Answer the questions on the basis of the information given below.
Five vendors are being considered for a service. The evaluation committee evaluated each vendor on six aspects –
Cost, Customer Service, Features, Quality, Reach, and Reliability. Each of these evaluations are on a scale of 0
(worst) to 100 (perfect). The evaluation scores on these aspects are shown in the radar chart. For example, Vendor 1
obtains a score of 52 on Reliability, Vendor 2 obtains a score of 45 on Features and Vendor 3 obtains a score of 90 on
Cost.
Q. 29 On which aspect is the median score of the five
vendors the least?
