CAT 2017 DILR Slot 2 Paper With Answers & Explanation
Question Numbers: (1 to 4): Funky Pizzaria was
required to supply pizzas to three different parties. The
total number of pizzas it had to deliver was 800, 70% of
which were to be delivered to Party 3 and the rest equally
divided between Party 1 and Party 2.
Pizzas could be of Thin Crust (T) or Deep Dish (D) variety
and come in either Normal Cheese (NC) or Extra
Cheese (EC) versions. Hence, There are four types of
pizzas: T-NC, T-EC, D-NC and D-EC. Partial information
about proportions of T and NC pizzas ordered by the
three parties is given below:
Q. 1 How many Thin Crust pizzas were to be delivered
to Party 3?
From table, 162 thin crust pizzas were to be
delivered to party 3.
Question Numbers: (1 to 4): Funky Pizzaria was
required to supply pizzas to three different parties. The
total number of pizzas it had to deliver was 800, 70% of
which were to be delivered to Party 3 and the rest equally
divided between Party 1 and Party 2.
Pizzas could be of Thin Crust (T) or Deep Dish (D) variety
and come in either Normal Cheese (NC) or Extra
Cheese (EC) versions. Hence, There are four types of
pizzas: T-NC, T-EC, D-NC and D-EC. Partial information
about proportions of T and NC pizzas ordered by the
three parties is given below:
Q. 2 How many Normal Cheese pizzas were required to
be delivered to Party 1?
From table, 16 normal cheese pizzas were
required to be delivered to party.
Question Numbers: (1 to 4): Funky Pizzaria was
required to supply pizzas to three different parties. The
total number of pizzas it had to deliver was 800, 70% of
which were to be delivered to Party 3 and the rest equally
divided between Party 1 and Party 2.
Pizzas could be of Thin Crust (T) or Deep Dish (D) variety
and come in either Normal Cheese (NC) or Extra
Cheese (EC) versions. Hence, There are four types of
pizzas: T-NC, T-EC, D-NC and D-EC. Partial information
about proportions of T and NC pizzas ordered by the
three parties is given below:
Q. 3 For Party 2, if 50% of the Normal Cheese pizzas
were of Thin Crust variety, what was the difference
between the numbers of T-EC and D-EC pizzas to
be delivered to Party 2?
Question Numbers: (1 to 4): Funky Pizzaria was
required to supply pizzas to three different parties. The
total number of pizzas it had to deliver was 800, 70% of
which were to be delivered to Party 3 and the rest equally
divided between Party 1 and Party 2.
Pizzas could be of Thin Crust (T) or Deep Dish (D) variety
and come in either Normal Cheese (NC) or Extra
Cheese (EC) versions. Hence, There are four types of
pizzas: T-NC, T-EC, D-NC and D-EC. Partial information
about proportions of T and NC pizzas ordered by the
three parties is given below:
Q. 4 Suppose that a T-NC pizza cost as much as a DNC
pizza, but 3/5th of the price of a D-EC pizza. A DEC
pizza costs Rs.50 more than a T-EC pizza, and
the latter costs Rs.500.
If 25% of the Normal Cheese pizzas delivered to
Party 1 were of Deep Dish variety, what was the
total bill for Party 1?
Question Numbers : (5 to 8) : There were seven
elective courses - E1 to E7 - running in a specific term
in a college. Each of the 300 students enrolled had
chosen just one elective from among these seven.
However, before the start of the term, E7 was withdrawn
as the instructor concerned had left the college. The
students who had opted for E7 were allowed to join any
of the remaining electives, Also, the students who had
chosen other electives were given one chance to change
their choice. The table below captures the movement
of the students from one elective to another during this
process. Movement from one elective to the same
elective simply means no movement. Some numbers
in the table got accidentally erased; however, it is known
that these were either 0 or 1.
Further, the following are known:
1. Before the change process there were 6 more
students in E1 than in E4, but after the reshuffle, the
number of students in E4 was 3 more than that in E1.
2. The number of students in E2 increased by 30 after
the change process.
3. Before the change process, E4 had 2 more students
than E6, while E2 had 10 more students than E3.
Q. 5 How many elective courses among E1 to E6 had a
decrease in their enrollments after the change
process?
Question Numbers : (5 to 8) : There were seven
elective courses - E1 to E7 - running in a specific term
in a college. Each of the 300 students enrolled had
chosen just one elective from among these seven.
However, before the start of the term, E7 was withdrawn
as the instructor concerned had left the college. The
students who had opted for E7 were allowed to join any
of the remaining electives, Also, the students who had
chosen other electives were given one chance to change
their choice. The table below captures the movement
of the students from one elective to another during this
process. Movement from one elective to the same
elective simply means no movement. Some numbers
in the table got accidentally erased; however, it is known
that these were either 0 or 1.
Further, the following are known:
1. Before the change process there were 6 more
students in E1 than in E4, but after the reshuffle, the
number of students in E4 was 3 more than that in E1.
2. The number of students in E2 increased by 30 after
the change process.
3. Before the change process, E4 had 2 more students
than E6, while E2 had 10 more students than E3.
Q. 6 After the change process, which of the following is
the correct sequence of number of students in the
six electives E1 to E6?
Question Numbers : (5 to 8) : There were seven
elective courses - E1 to E7 - running in a specific term
in a college. Each of the 300 students enrolled had
chosen just one elective from among these seven.
However, before the start of the term, E7 was withdrawn
as the instructor concerned had left the college. The
students who had opted for E7 were allowed to join any
of the remaining electives, Also, the students who had
chosen other electives were given one chance to change
their choice. The table below captures the movement
of the students from one elective to another during this
process. Movement from one elective to the same
elective simply means no movement. Some numbers
in the table got accidentally erased; however, it is known
that these were either 0 or 1.
Further, the following are known:
1. Before the change process there were 6 more
students in E1 than in E4, but after the reshuffle, the
number of students in E4 was 3 more than that in E1.
2. The number of students in E2 increased by 30 after
the change process.
3. Before the change process, E4 had 2 more students
than E6, while E2 had 10 more students than E3.
Q. 7 After the change process, which course among E1
to E6 had the largest change in its enrollment as a
percentage of its original enrollment?
Question Numbers : (5 to 8) : There were seven
elective courses - E1 to E7 - running in a specific term
in a college. Each of the 300 students enrolled had
chosen just one elective from among these seven.
However, before the start of the term, E7 was withdrawn
as the instructor concerned had left the college. The
students who had opted for E7 were allowed to join any
of the remaining electives, Also, the students who had
chosen other electives were given one chance to change
their choice. The table below captures the movement
of the students from one elective to another during this
process. Movement from one elective to the same
elective simply means no movement. Some numbers
in the table got accidentally erased; however, it is known
that these were either 0 or 1.
Further, the following are known:
1. Before the change process there were 6 more
students in E1 than in E4, but after the reshuffle, the
number of students in E4 was 3 more than that in E1.
2. The number of students in E2 increased by 30 after
the change process.
3. Before the change process, E4 had 2 more students
than E6, while E2 had 10 more students than E3.
Q. 8 Later, the college imposed a condition that if after
the change of electives, the enrollment in any
elective (other than E7) dropped to less than 20
students, all the students who had left that course
will be required to reenroll for that elective.
Which of the following is a correct sequence of
electives in decreasing order of their final
enrollments?
After reshuffling E1 has 18 students which is less
than 20. E1 + (5 + 10 + 1 + 4 + 2) = 18 + 22 = 40
From E1 to E2 = 5 students
E2 – 5 = (76 – 5) students = 71
From E1 to E3 = 10 students
E3 – 10 = (79 – 10) students = 69
From E1 to E4 = 1 students
E4 – 1 = 21 – 1 = 20 students
From E1 to E5 = 4 students
E5 – 4 = 45 – 4 = 41 students
From E1 to E6 = 2 students
E6 – 2 = (61 – 2) = 59 students
Decreasing order
E2 > E3 > E6 > E5 > E1 > E4.
Question Numbers (9 to 12) : An old woman had the
following assets:
(a) Rs.70 lakh in bank deposits
(b) 1 house worth Rs.50 lakh
(c) 3 flats, each worth Rs.30 lakh
(d) Certain number of gold coins, each worth Rs.1 lakh
She wanted to distribute her assets among her three
children; Neeta, Seeta and Geeta.
The house, any of the flats or any of the coins were not
to be split. That is, the house went entirely to one child;
a flat went to one child and similarly, a gold coin went to
one child.
Q. 9 Among the three, Neeta received the least amount
in bank deposits, while Geeta received the highest.
The value of the assets was distributed equally
among the children, as were the gold coins.
How much did Seeta receive in bank deposits (in
lakhs of rupees)?
Q. 10 Among the three, Neeta received the least amount
in bank deposits, while Geeta received the highest.
The value of the assets was distributed equally
among the children, as were the gold coins.
How many flats did Neeta receive?
Q. 11 The value of the assets distributed among Neeta,
Seeta and Geeta was in the ratio of 1 : 2 : 3, while
the gold coins were distributed among them in the
ratio of 2 : 3 : 4. One child got all three flats and she
did not get the house. One child, other than Geeta,
got Rs.30 lakh in bank deposits.
How many gold coins did the old woman have?
Q. 12 The value of the assets distributed among Neeta,
Seeta and Geeta was in the ratio of 1 : 2 : 3, while
the gold coins were distributed among them in the
ratio of 2 : 3 : 4. One child got all three flats and she
did not get the house. One child, other than Geeta,
got Rs.30 lakh in bank deposits.
How much did Geeta get in bank deposits (in lakhs
of rupees)?
Question Numbers (13 to 16) : At a management
school, the oldest 10 dorms, numbered 1 to 10, need to
be repaired urgently. The following diagram represents
the estimated repair costs (in Rs. Crores) for the 10
dorms. For any dorm, the estimated repair cost (in Rs.
Crores) is an integer. Repairs with estimated cost Rs. 1
or 2 Crores are considered light repairs, repairs with
estimated cost Rs. 3 or 4 are considered moderate
repairs and repairs with estimated cost Rs. 5 or 6 Crores
are considered extensive repairs.
Further, the following are known:
1. Odd-numbered dorms do not need light repair; evennumbered
dorms do not need moderate repair and
dorms, whose numbers are divisible by 3, do not
need extensive repair.
2. Dorms 4 to 9 all need different repair costs, with
Dorm 7 needing the maximum and Dorm 8 needing
the minimum.
Q. 13 Which of the following is NOT necessarily true?
Question Numbers (13 to 16) : At a management
school, the oldest 10 dorms, numbered 1 to 10, need to
be repaired urgently. The following diagram represents
the estimated repair costs (in Rs. Crores) for the 10
dorms. For any dorm, the estimated repair cost (in Rs.
Crores) is an integer. Repairs with estimated cost Rs. 1
or 2 Crores are considered light repairs, repairs with
estimated cost Rs. 3 or 4 are considered moderate
repairs and repairs with estimated cost Rs. 5 or 6 Crores
are considered extensive repairs.
Further, the following are known:
1. Odd-numbered dorms do not need light repair; evennumbered
dorms do not need moderate repair and
dorms, whose numbers are divisible by 3, do not
need extensive repair.
2. Dorms 4 to 9 all need different repair costs, with
Dorm 7 needing the maximum and Dorm 8 needing
the minimum.
Q. 14 What is the total cost of repairing the odd-numbered
dorms (in Rs. Crores)?
Question Numbers (13 to 16) : At a management
school, the oldest 10 dorms, numbered 1 to 10, need to
be repaired urgently. The following diagram represents
the estimated repair costs (in Rs. Crores) for the 10
dorms. For any dorm, the estimated repair cost (in Rs.
Crores) is an integer. Repairs with estimated cost Rs. 1
or 2 Crores are considered light repairs, repairs with
estimated cost Rs. 3 or 4 are considered moderate
repairs and repairs with estimated cost Rs. 5 or 6 Crores
are considered extensive repairs.
Further, the following are known:
1. Odd-numbered dorms do not need light repair; evennumbered
dorms do not need moderate repair and
dorms, whose numbers are divisible by 3, do not
need extensive repair.
2. Dorms 4 to 9 all need different repair costs, with
Dorm 7 needing the maximum and Dorm 8 needing
the minimum.
Q. 15 Suppose further that:
(1) 4 of the 10 dorms needing repair are women’s
dorms and need a total of Rs.20 Crores for repair.
(2) Only one of Dorms 1 to 5 is a women’s dorm.
What is the cost for repairing Dorm 9 (in Rs.
Crores)?
Question Numbers (13 to 16) : At a management
school, the oldest 10 dorms, numbered 1 to 10, need to
be repaired urgently. The following diagram represents
the estimated repair costs (in Rs. Crores) for the 10
dorms. For any dorm, the estimated repair cost (in Rs.
Crores) is an integer. Repairs with estimated cost Rs. 1
or 2 Crores are considered light repairs, repairs with
estimated cost Rs. 3 or 4 are considered moderate
repairs and repairs with estimated cost Rs. 5 or 6 Crores
are considered extensive repairs.
Further, the following are known:
1. Odd-numbered dorms do not need light repair; evennumbered
dorms do not need moderate repair and
dorms, whose numbers are divisible by 3, do not
need extensive repair.
2. Dorms 4 to 9 all need different repair costs, with
Dorm 7 needing the maximum and Dorm 8 needing
the minimum.
Q. 16 Suppose further that:
(1) 4 of the 10 dorms needing repair are women’s
dorms and need a total of Rs.20 Crores for repair.
(2) Only one of Dorms 1 to 5 is a women’s dorm.
Which of the following is a women’s dorm?
Question Numbers (17 to 20) : A tea taster was assigned
to rate teas from six different locations - Munnar,
Wayanad, Ooty, Darjeeling, Assam and Himachal. These
teas were placed in six cups, numbered 1 to 6, not
necessarily in the same order The tea taster was asked
to rate these teas on the strength of their flavour on a
scale of 1 to 10. He gave a unique integer rating to each
tea. Some other information is given below:
1. Cup 6 contained tea from Himachal.
2. Tea from Ooty got the highest rating, but it was not
in Cup 3.
3. The rating of tea in Cup 3 was double the rating of
the tea in Cup 5.
4. Only two cups got ratings in even numbers.
5. Cup 2 got the minimum rating and this rating was
an even number.
6. Tea in Cup 3 got a higher rating than that in Cup 1.
7. The rating of tea from Wayanad was more than the
rating of tea from Munnar, but less than that from
Assam.
Question Numbers : (21 to 24) : In an 8 × 8 chessboard
a queen placed anywhere can attack another piece if
the piece is present in the same row, or in the same
column or in any diagonal position in any possible 4
directions, provided there is no other piece in between
in the path from the queen to that piece.
The columns are labelled a to h (left to right) and the
rows are numbered 1 to 8 (bottom to top). The position
of a piece is given by the combination of column and
row labels. For example, position c5 means that the
piece is in cth column and 5th row.
Q. 21 If the queen is at c5, and the other pieces at positions
c2, g1, g3, g5 and a3, how many are under attack
by the queen? There are no other pieces on the
board.
Q. 22 If the other pieces are only at positions a1, a3, b4,
d7, h7 and h8, then which of the following positions
of the queen results in the maximum number of
pieces being under attack?
Q. 24 Suppose the queen is the only piece on the board
and it is at position d5.
In how many positions can another piece be placed
on the board such that it is safe from attack from
the queen?
Question Numbers : (25 to 28) : Eight friends: Ajit,
Byomkesh, Gargi, Jayanta, Kikira, Manik, Prodosh and
Tapesh are going to Delhi from Kolkata by a flight
operated by Cheap Air. In the flight, sitting is arranged
in 30 rows, numbered 1 to 30, each consisting of 6 seats,
marked by letters A to F from left to right, respectively.
Seats A to C are to the left of the aisle (the passage
running from the front of the aircraft to the back), and
seats D to F are to the right of the aisle. Seats A and F
are by the windows and referred to as Window seats, C
and D are by the aisle and are referred to as Aisle seats
while B and E are referred to as Middle seats. Seats
marked by consecutive letters are called consecutive
seats (or seats next to each other). A seat number is a
combination of the row number, followed by the letter
indicating the position in the row; e.g., 1A is the left
window seat in the first row, while 12E is the right middle
seat in the 12th row.
Cheap Air charges Rs.1000 extra for any seats in Rows
1, 12 and 13 as those have extra legroom. For Rows
2-10, it charges Rs.300 extra for Window seats and
Rs.500 extra for Aisle seats. For Rows 11 and 14 to 20,
it charges Rs.200 extra for Window seats and Rs.400
extra for Aisle seats. All other seats are available at no
extra charge.
The following are known:
1. The eight friends were seated in six different rows.
2. They occupied 3 Window seats, 4 Aisle seats and 1
Middle seat.
3. Seven of them had to pay extra amounts, totaling to
Rs. 4600, for their choices of seat. One of them did not
pay any additional amount for his/her choice of seat.
4. Jayanta, Ajit and Byomkesh were sitting in seats
marked by the same letter, in consecutive rows in
increasing order of row numbers; but all of them
paid different amounts for their choices of seat. One
of these amounts may be zero.
5. Gargi was sitting next to Kikira, and Manik was sitting
next to Jayanta.
6. Prodosh and Tapesh were sitting in seats marked
by the same letter, in consecutive rows in increasing
order of row numbers; but they paid different
amounts for their choices of seat. One of these
amounts may be zero.
Question Numbers : (29 to 32) : A high security
research lab requires the researchers to set a pass key
sequence Passed on the scan of the five fingers of their
left hands. When an employee first joins the lab, her
fingers are scanned in an order of her choice, and then
when she wants to re-enter the facility, she has to scan
the five fingers in the same sequence.
The lab authorities are considering some relaxations of
the scan order requirements, since it is observed that
some employees often get locked-out because they
forget the sequence.
Q. 29 The lab has decided to allow a variation in the
sequence of scans of the five fingers so that at most
two scans (out of five) are out of place. For example,
if the original sequence is Thumb (T), index finger
(I), middle finger (M), ring finger (R) and little finger
(L) then TLMRI is also allowed, but TMRLI is not.
How many different sequences of scans are allowed
for any given person’s original scan?
Q. 30 The lab has decided to allow a variations in the
original sequence so that the input of the scanned sequence of five fingers is allowed to vary from the original sequence by one place for any of the fingers. Thus, for example,
if the original sequence is TIMRL then ITRML is also allowed but LIMRT is not.
How many different sequences are allowed for any given person's original scans?
Q. 31 The lab has now decided to require six scans
in the pass key sequence, where exactly one
finger is scanned twice, and the other fingers
are scanned exactly once, which can be done in
any order. For example, a possible sequence is
TIMTRL.
Suppose the lab allows a variation of the original
sequence (of six inputs) where at most two scans
(out of six) are out of place, as long as the finger
originally scanned twice is scanned twice and other
fingers are scanned once.
How many different sequences of scans are allowed
for any given person’s original scan?
Q. 32 The lab has now decided to require six scans in the
pass key sequence, where exactly one finger is
scanned twice, and the other fingers are scanned
exactly once, which can be done in any order. For
example, a possible sequence is TIMTRL.
Suppose the lab allows a variation of the original
sequence (of six inputs) so that input in the form of
scanned sequence of six fingers is allowed to vary
from the original sequence by one place for any of
the fingers, as long as the finger originally scanned
twice is scanned twice and other fingers are scanned
once.
How many different sequences of scans are allowed
if the original scan sequence is LRLTIM?
