Q.1 Find the next term in the series: 2, 5, 10, 17, ...
Detailed Analysis:
In this series, the difference between consecutive terms increases by 3 each time. The differences between the terms are: 5 - 2 = 3, 10 - 5 = 5, 17 - 10 = 7. So, the next difference should be 9. Adding 9 to the last term, we get: 17 + 9 = 26.
Therefore, the next term in the series is 26.
Q.2 Direction for Q2-5: According to a coding scheme the sentence
Peacock is designated as the national bird of India
is coded as
5688999 35 1135556678 56 458 13666689 1334 79 13366
This coding scheme has the following rules:
1. The scheme is case-insensitive (does not distinguish between upper case and lower case letters).
2. Each letter has a unique code which is a single digit from among 1,2,3, …, 9.
3. The digit 9 codes two letters, and every other digit codes three letters.
4. The code for a word is constructed by arranging the digits corresponding to its letters in a non-decreasing sequence.
Detailed Analysis:
Given 'peacock is designated as the national bird of India' is coded as ' 5688999 35 1135556678 56 458 13666689 1334 79 13366'
9 is the code for o and c from the words peacock and of.
F is coded as 7 from the word of.
I is coded as either 3 or 6 from the word India, but from the word 'is' and 'designated' code for 'I' is 3.
S is coded as 5 from the word is.
A is coded as 6 from the word 'as'.
N is coded as 6 from the word national.
Thus D is coded as 1 from the word India.
E is coded as 5 from the word designated.
T is coded as 8 from the word 'the' and 'National'.
Thus H is coded as 4 from the word 'the'. G is coded as 7. L is coded as 1 from the word 'National'.
P and K are coded as 8 from the word 'peacock'. B and R are coded as 3 and 4 many order from the word 'bird'.
We get the codes as follows
. 
B and R is coded as 3 or 4.
Q.3 What best can be concluded about the code for the letter B?
A. 1 or 3 or 4
B. 3
C. 1
D. 3 or 4
Detailed Analysis:
Given 'peacock is designated as the national bird of India' is coded as ' 5688999 35 1135556678 56 458 13666689 1334 79 13366'
9 is the code for o and c from the words peacock and of.
F is coded as 7 from the word of.
I is coded as either 3 or 6 from the word India, but from the word 'is' and 'designated' code for 'I' is 3.
S is coded as 5 from the word is.
A is coded as 6 from the word 'as'.
N is coded as 6 from the word national.
Thus D is coded as 1 from the word India.
E is coded as 5 from the word designated.
T is coded as 8 from the word 'the' and 'National'.
Thus H is coded as 4 from the word 'the'. G is coded as 7. L is coded as 1 from the word 'National'.
P and K are coded as 8 from the word 'peacock'. B and R are coded as 3 and 4 many order from the word 'bird'.
We get the codes as follows
.
B and R is coded as 3 or 4.
Q.4 For how many digits can the complete list of letters associated with that digit be identified?
Detailed Analysis:
Given 'peacock is designated as the national bird of India' is coded as ' 5688999 35 1135556678 56 458 13666689 1334 79 13366'
9 is the code for o and c from the words peacock and of.
F is coded as 7 from the word of.
I is coded as either 3 or 6 from the word India, but from the word 'is' and 'designated' code for 'I' is 3.
S is coded as 5 from the word is.
A is coded as 6 from the word 'as'.
N is coded as 6 from the word national.
Thus D is coded as 1 from the word India.
E is coded as 5 from the word designated.
T is coded as 8 from the word 'the' and 'National'.
Thus H is coded as 4 from the word 'the'. G is coded as 7. L is coded as 1 from the word 'National'.
P and K are coded as 8 from the word 'peacock'. B and R are coded as 3 and 4 many order from the word 'bird'.
We get the codes as follows
.
B and R is coded as 3 or 4.
Q.5 Which set of letters CANNOT be coded with the same digit?
A. S,U,V
B. I,B,M
C. X,Y,Z
D. S,E,Z
Detailed Analysis:
Given 'peacock is designated as the national bird of India' is coded as ' 5688999 35 1135556678 56 458 13666689 1334 79 13366'
9 is the code for o and c from the words peacock and of.
F is coded as 7 from the word of.
I is coded as either 3 or 6 from the word India, but from the word 'is' and 'designated' code for 'I' is 3.
S is coded as 5 from the word is.
A is coded as 6 from the word 'as'.
N is coded as 6 from the word national.
Thus D is coded as 1 from the word India.
E is coded as 5 from the word designated.
T is coded as 8 from the word 'the' and 'National'.
Thus H is coded as 4 from the word 'the'. G is coded as 7. L is coded as 1 from the word 'National'.
P and K are coded as 8 from the word 'peacock'. B and R are coded as 3 and 4 many order from the word 'bird'.
We get the codes as follows
.
B and R is coded as 3 or 4.
Q.6 Direction for Q6-8: When Ram will be as old as Ram's father is now, Ram will be five times as old as Ram's son is now. But at that time Ram's son will be eight years older than Ram is now. At present, the sum of the ages of Ram's father and Ram is 100 years.
How old is Ram's son?
A. 8 years
B. 13 years
C. 16 years
D. 19 years
Detailed Analysis:
Let the present age of Ram = x years. The present age of his son = y years. The present age of Ram's father = z years. By the question, x + z = 100 x = 100 - z ...(i)
Again, z = 5y ...(ii)
and y + (z - x) = x + 8 y + z = 2x + 8.
Putting the value of x from equation (i) we get,
y + z = 2 (100 - z) + 8 y + 3z = 208. Putting the value of z from equation (ii) we get,
y + 3(5y) = 208 = 16y = 208. y = 13, from equation (ii), z = 65 and from (i) x = 35.
Age of son = 13 years. Ans.(2)
Q.7 How old would Ram have been 5 years ago?
A. 30 years
B. 33 years
C. 38 years
D. 45 years
Detailed Analysis:
Let the present age of Ram = x years. The present age of his son = y years. The present age of Ram's father = z years. By the question, x + z = 100 x = 100 - z ...(i)
Again, z = 5y ...(ii)
and y + (z - x) = x + 8 y + z = 2x + 8.
Putting the value of x from equation (i) we get,
y + z = 2 (100 - z) + 8 y + 3z = 208. Putting the value of z from equation (ii) we get,
y + 3(5y) = 208 = 16y = 208. y = 13, from equation (ii), z = 65 and from (i) x = 35.
Age of Ram 5 years ago = 35 - 5 = 30 years. Ans.(1)
Q.8 After 10 years, how old will Ram's father be?
A. 56 years
B. 65 years
C. 75 years
D. 66 years
Detailed Analysis:
Let the present age of Ram = x years. The present age of his son = y years. The present age of Ram's father = z years. By the question, x + z = 100 x = 100 - z ...(i)
Again, z = 5y ...(ii)
and y + (z - x) = x + 8 y + z = 2x + 8.
Putting the value of x from equation (i) we get,
y + z = 2 (100 - z) + 8 y + 3z = 208. Putting the value of z from equation (ii) we get,
y + 3(5y) = 208 = 16y = 208. y = 13, from equation (ii), z = 65 and from (i) x = 35.
After 10 years, age of Ram's father = 65 + 10 = 75 years. Ans.(3)
Q.9 Direction for Q9-10: Students in a college are discussing two proposals --
A: a proposal by the authorities to introduce dress code on campus, and
B: a proposal by the students to allow multinational food franchises to set up outlets on college campus.
A student does not necessarily support either of the two proposals.
In an upcoming election for student union president, there are two candidates in fray: Sunita and Ragini. Every student prefers one of the two candidates.
A survey was conducted among the students by picking a sample of 500 students. The following information was noted from this survey.
1. 250 students supported proposal A and 250 students supported proposal B.
2. Among the 200 students who preferred Sunita as student union president, 80% supported proposal A.
3. Among those who preferred Ragini, 30% supported proposal A.
4. 20% of those who supported proposal B preferred Sunita.
5. 40% of those who did not support proposal B preferred Ragini.
6. Every student who preferred Sunita and supported proposal B also supported proposal A.
7. Among those who preferred Ragini, 20% did not support any of the proposals.
What percentage of the students surveyed who supported both proposals A and B preferred Sunita as student union president?
Detailed Analysis:
The set of students who like Sunita and Ragini are disjoint sets.
Hence, the Venn diagram can be drawn as follows
There are 500 students in all.
From statement (2)
Sunita = 200. Hence, Ragini = 300.
From statement (1) A (Sunita) + A (Ragini) = 250 and B (Sunita) + B (Ragini) = 250.
From (2), A (Sunita) = 160. Hence, A (Ragini) = 90.
From (4), B (Sunita) = 20 % of 250 = 50. Hence, B (Ragini) = 200.
From (6), g (Sunita) = 50 and hence, b (Sunita) = 0 and a (Sunita) = 110. Hence, n (Sunita) = 40.
From (7), n (Ragini) = 60
It is given that 250 support B, hence the other 250 do not support B.
From (5), (a + n) of Ragini = 40 % of 250 = 100. Hence, a (Ragini) = 40.
Thus, the final solution is as follows.
Q.10 How many of the students surveyed supported proposal B, did not support proposal A and preferred Ragini as student union president?
A. 200
B. 150
C. 210
D. 40
Detailed Analysis:
The set of students who like Sunita and Ragini are disjoint sets.
Hence, the Venn diagram can be drawn as follows
There are 500 students in all.
From statement (2)
Sunita = 200. Hence, Ragini = 300.
From statement (1) A (Sunita) + A (Ragini) = 250 and B (Sunita) + B (Ragini) = 250.
From (2), A (Sunita) = 160. Hence, A (Ragini) = 90.
From (4), B (Sunita) = 20 % of 250 = 50. Hence, B (Ragini) = 200.
From (6), g (Sunita) = 50 and hence, b (Sunita) = 0 and a (Sunita) = 110. Hence, n (Sunita) = 40.
From (7), n (Ragini) = 60
It is given that 250 support B, hence the other 250 do not support B.
From (5), (a + n) of Ragini = 40 % of 250 = 100. Hence, a (Ragini) = 40.
Thus, the final solution is as follows.
