1309 : LRDI Reasoning case

Case 80 & 81

There are five machines — A, B, C, D, and E — situated on a straight line at distances of 10 m, 20 m,
30 m, 40 m and 50 m respectively from the origin of the line. A robot is stationed at the origin of the line. The robot serves the machines with raw material whenever a machine becomes idle. All the raw materials are located at the origin. The robot is in an idle state at the origin at the beginning of a day. As soon as one or more machines become idle, they send messages to the robot-station and the robot starts and serves all the machines from which it received messages. If a message is received at the station while the robot is away from it, the robot takes notice of the message only when it returns to the station. While moving, it serves the machines in the sequence in which they are encountered, and then returns to the origin. If any messages are pending at the station when it returns, it repeats the process again. Otherwise, it remains idle at the origin till the next message(s) is(are) received.



80. Suppose on a certain day, machines A and D have sent the first two messages to the origin at the
beginning of the first second, and C has sent a message at the beginning of the 5th second and
B at the beginning of the 6th second, and E at the beginning of the 10th second. How much distance
has the robot travelled since the beginning of the day, when it notices the message of E? Assume
that the speed of movement of the robot is 10 m/s.

a. 140 m b. 80 m c. 340 m d. 360 m

Solution
80. a The robot begins to give material to machine A and then to D, it thus covers 40 m in that time span and takes 4 s. Also then it returns to the origin, and takes 4s, while covering 40 m again. When it arrives at the origin, the messages of B and C are already there, thus it moves to give the material to them, which takes it in total 6 s, and it covers 30 + 30 = 60 m in total. Hence, the distance travelled by the robot will be 40 m+ 40 m + 60 m = 140 m.

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81. Suppose there is a second station with raw material for the robot at the other extreme of the line
which is 60 m from the origin, i.e. 10 m from E. After finishing the services in a trip, the robot returns
to the nearest station. If both stations are equidistant, it chooses the origin as the station to return
to. Assuming that both stations receive the messages sent by the machines and that all the other
data remains the same, what would be the answer to the above question?
a. 120 b. 140 c. 340 d. 70

Solution :
81. a In this question, once the robot has delivered the material to machines A and D, it shall reach the origin 2 (nearest), taking 6 s, and covering 60 m. Then it immediately moves to deliver material to machines C and B covering a distance of 40 m and finally back to the origin (nearest). Thus, it cover a distance of 60 m. Hence, it covers a total distance of 120 m.

1308: Number System - Remainder - CAT 2000

The integers 34041 and 32506, when divided by a three-digit integer n, leave the same remainder.
What is the value of n?

a. 289          b. 367         c. 453     d. 307
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Let r be the remainder. Then 34041 – r and 32506 – r are perfectly divisible by n.
Hence, their difference should also be divisible by the same.
(34041 – r) – (32506 – r) = 1535, which is divisible by only 307.
Answer : D 

1307 : Permutation Combination CAT 2000

One red flag, three white flags and two blue flags are arranged in a line such that:

I. No two adjacent flags are of the same colour
II. The flags at the two ends of the line are of different colours

In how many different ways can the flags be arranged?
   a. 6    b. 4    c. 10   d. 2


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Soln : 63. a The possibilities are W@W@W@ (or) @W@W@W,
where 2 blue and 1 red flag occupy the space marked
as @. Hence, the total permutation is 2(3!/2!) = 6

1305:TSD : Two Pools

A and B are the two opposite ends of a swimming pool and the distance between them is
420 metres. Ankur and Manu start swimming towards each other at the same time from A and B,
with speeds in the ratio 5 : 9 respectively. As soon as any of them reaches an end, he turns back
and starts swimming towards the other end. At what distance (in metres) from A will they meet when
Manu is in his 13th round? Note: A to B is considered one round and B to A another round.

(a) 405 (b) 330 (c) 240 (d) 280


Answer

By the time Manu completes 12 rounds, Ankur will complete × = 5/9 *12 = 6 -2/3 rounds. At this point in time Ankur is moving towards B and is 280 metres away from A whereas Manu is at B.
They will meet at a distance of

9 * (420 -280)/ 5+ 9 = 90 metres from B. This point will be at a distance of 420 – 90 = 330 metres from A.

Answer : B

From Eduventures _Puneet Singh

1304 : Data Sufficiency CAT 2007

Each question is followed by two statements A and B. Indicate your
response based on the following directives.
Mark (1) if the questions can be answered using A alone but not using B alone.
Mark (2) if the question can be answered using B alone but not using A alone.
Mark (3) if the question can be answered using A and B together, but not using either A or B alone.
Mark (4) if the question cannot be answered even using A and B together.


7. The average weight of a class of 100 students is 45 kg. The class consists of two sections, I and II,
each with 50 students. The average weight, I W , of Section I is smaller than the average weight II W ,
of the Section II. If the heaviest student say Deepak, of section II is moved to Section I, and the
lightest student, say Poonam, of Section I is moved to Section II, then the average weights of the
two sections are switched, i.e., the average weight of Section I becomes II W and that of Section II
becomes I W . What is the weight of Poonam?
A: WII – WI = 1.0 .
B: Moving Deepak from Section II to I (without any move I to II) makes the average weights of the
two sections equal.

8. ABC Corporation is required to maintain at least 400 Kilolitres of water at all times in its factory, in
order to meet safety and regulatory requirements. ABC is considering the suitability of a spherical
tank with uniform wall thickness for the purpose. The outer diameter of the tank is 10 meters. Is the
tank capacity adequate to met ABC’s requirements?
A: The inner diameter of the tank is at least 8 meters.
B: The tank weights 30,000 kg when empty, and is made of a material with density of 3 gm/cc.

9. Consider integers x, y, z. What is the minimum possible value of x2 + y2 + z2 ?
A: x + y + z = 89.
B: Among x, y, z two are equal.


10. Rahim plans to draw a square JKLM with point O on the side JK but is not successful. Why is
Rahim unable to draw the square?
A: The length of OM is twice that of OL.
B: The length of OM is 4 cm.



Solution :
7. 3 Using A: WII = 45.5 and WI = 44.5
Using B: Weight of Deepak = 70kg (Only after using
statement A)
This is sufficient to find weight of Poonam using the
data given in the question statement. Hence option (3)
is correct choice.

8. 2 Using A: Inner radius of the tank is atleast 4 m. So volume
4 3
r where 4 r 10
3
= π < <
This volume can be greater as well as smaller than
400 for different r.
Using B: The given data gives the volume of the material of tank, which can be expressed as
4 3 3
(10 r ),
3
π − which will give the value of r which is unique and sufficient to judge if the capacity is
adequate. Hence option (2) is correct choice.

9. 1 Using A: x = 30, y = 30 and z = 29 will give the minimum value.
Using B: Nothing specific can be said about the relation between x, y and z.
Hence option (1) is correct choice.


10. 1 Using A:
OM        2
----  =  -----
OL          1

But if O lies on JK, maximum possible value of (when O lies on K)
OM           sqrt 2
------   =  --------
OL            1

So, Rahim is unable to draw such a square Using B: Nothing specific can be said about the
dimensions of the figure. Hence option (1) is correct choice.

1303 : Arithmetic _CAT 2007

A confused bank teller transposed the rupees and paise when he cashed a cheque for Shailaja.
giving her rupees instead of paise and paise instead of rupees. After buying a toffee for 50 paise,
Shailaja noticed that she was left with exactly three times as much as the amount on the cheque.
Which of the following is a valid statement about the cheque amount?
(1) Over Rupees 13 but less than Rupees 14
(2) Over Rupees 7 but less than Rupees 8
(3) Over Rupees 22 but less than Rupees 23
(4) Over Rupees 18 but less than Rupees 19
(5) Over Rupees 4 but less than Rupees 5


Soln :

Suppose the cheque for Shailaja is of Rs. X and Y paise
As per the question: 3 × (100X + Y) = (100Y + X) – 50
⇒ 299X = 97Y – 50
⇒ Y = 299X + 50 /97

Now the value of Y should be a integer. Checking by options only for X = 18, Y is a integer and
the value of Y = 56

From Puneet Singh (www.bsaitmfbd.com) Eduventures

1302 : Arithmetic : Age (CAT2007)

Ten years ago, the ages of the members of a joint family of eight people added up to 231 years. Three years later, one member died at the age of 60 years and a child was born during the same year. After another three years, one more member died, again at 60, and a child was born during the same year. The current average age of this eight-member joint family is nearest to
(1) 23 years (2) 22 years (3) 21 years (4) 25 years (5) 24 years


Solution:
The total age of all the eight people in the family = 231 As per the information given in the question, the total age of all the people in the family= 231 + 3 × 8 – 60 + 0 = 195
Similarly the total age of the people in the family four years ago= 195 + 3 × 8 – 60 + 0 = 159.
Therefore the current average age of all the people in the family159 + 32 /  24
8 years.