Logical Reasoning Capsules - Edwin Jose, CAT DILR 100 Percentiler - Set 7

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DIRECTIONS: Answer the questions on the basis of the information given below.

A class of 1000 students, comprising boys and girls, is divided into three sections, named as A, B and C. The ratio of boys to girls in the class is 9: 11. The following table shows the percentage of boys and girls in each of the sections.

(1) Based on the above information, which of the following is true?
(a) p = q
(b) p < q
(c) p > q
(d) Data Insufficient

(2) If the number of students in section C is 600, then what is the value of 3q + 2p?
(a) 265
(b) 235
(c) 225
(d) Data Insufficient

(3) If the ratio of the number of students in Section A: Section B: Section C is 1: 3: 6, then what is the ratio of the number of girls in Section C: Section B: Section A?
(a) 7 : 6 : 2
(b) 4 : 12 : 39
(c) 78 : 24 : 8
(d) None of these

Solutions

(1) Option B
The ratio of boys to girls in the class is 9 : 11.
So the percentage of boys is 45% and the percentage of girls is 55% in the class.
As the overall percentage of boys is 45% and in sections A and B it is 60% each, the value of p < 45.
Similarly, as the overall percentage of girls is 55% and in sections A and B it is 40% each, the value of q > 55.
∴p < q

(2) Option A
Number of students in section C = 600
∴ the number of students in sections A and B together is 400.
The ratio of the number of student in
(Section C)/((Section A Section B ))=3/2

Value of 3q + 2p = q + 2(p + q) = q + 2 × 100= 200 + q
By alligation:

(55-40)/(q-55)=3/2
3q = 195
q = 65
3q + 2p = 200 + q = 265

(3) Option C
Number of girls in:
Section A = 40
Section B = 120
Section C = 390
∴ The ratio of girls in Section C : Section B : Section A
= 39 : 12 : 4
= 78 : 24 : 8

Directions: Answer the following questions on the basis of information given below:

There are six people Akhil, Beena, Chetan, Dheeraj, Ekta and Feroz who are to be seated on six chairs numbered 1 to 6, each facing North, with 1 being the chair lying on the extreme left and 6 on the extreme right. Some other information is also given regarding their seating plan.

Chetan is sitting to the right of Akhil and Ekta.
Beena is sitting to the left of Dheeraj.
Ekta is sitting immediately to the left of Feroz.
Dheeraj is not sitting in any of the two rightmost positions.

(1) How many positions are possible for Akhil?
(a) 2
(b) 3
(c) 4
(d) 5

(2) If there are exactly two people between Beena and Feroz, who is sitting second from the left?
(a) Beena
(b) Dheeraj
(c) Either (a) or (b)
(d) None of these

A, C, E and F can be arranged amongst themselves in two ways:
A EF C ----------(1)
EF A C ----------(2)
Now when B and D are also put into these two arrangements, there would be 3 cases in each arrangement.
Now when B and D are also put into these two arrangements, there would be 3 cases in each arrangement.
B D A E F C ................ 1a
B A D E F C ................ 1b
A B D E F C ................ 1c
B D E F A C ................ 2a
B E F D A C ................ 2a
E F B D A C ................ 2c

(1) Option C
Akhil can sit in 4 different positions - 1, 2, 3, 5 (from the left).

(2) Option C
There are two such cases - 1c and 2a.