Number Theory Previous Year Questions (CAT)  Set 0002

Previous years`s CAT questions: Number Theory
Post your solutions as reply to respective questions below.

Question 1
What values of x satisfy the equation x^{2/3} + x^{1/3} – 2 ≤ 0?
(1) – 8 ≤ x ≤ 1
(2) – 1 ≤ x ≤ 8
(3) 1 < x < 8
(4) 1 ≤ x ≤ 8
(5) – 8 ≤ x ≤ 8 (CAT 2006)

Answer: Option 1

Question 2
An airline has a certain free luggage allowance and charges for excess luggage at a fixed rate per kg. Two passengers, Raja and Praja, have 60 kg of luggage between them, and are charged Rs. 1200 and Rs. 2400 respectively for excess luggage. Hand the entire luggage to one of them, the excess luggage charge would have been Rs. 5400.
Q1) What is the weight of Praja‘s luggage?
(1) 20 kg
(2) 25 kg
(3) 30 kg
(4) 35 kg
(5) 40 kg
Q2) What is the free luggage allowance?
(1) 10 kg
(2) 15 kg
(3) 20 kg
(4) 25 kg
(5) 30 kg (CAT 2006)

Answer: Option 4 Option 2

Question 3
(CAT 2003 Retest)

Answer: Option 3

Question 4
When you reverse the digits of the number 13, the number increases by 18. How many other two digit numbers increase by 18 when their digits are reversed?
(1) 5
(2) 6
(3) 7
(4) 8
(5) 10 (CAT 2006)

Answer: Option 2

Question 5
The number of employees in Obelix Menhir Co. is a prime number and is less than 300. The ratio of the number of employees who are graduates and above, to that of employees who are not, can possibly be:
(1) 101:88
(2) 87:100
(3) 110:111
(4) 85:98
(5) 97:84 (CAT 2006)

Answer: Option 5

Question 6
The price of Darjeeling tea (in rupees per kilogram) is 100 + 0.10 n, on the nth day of 2007 (n = 1, 2, ..., 100), and then remains constant. On the other hand, the price of Ooty tea (in rupees per kilogram) is 89 + 0.15n, on the nth day of 2007 (n = 1, 2, ..., 365). On which date in 2007 will the prices of these two varieties of tea be equal?
(1) May 21
(2) April 11
(3) May 20
(4) April 10
(5) June 30 (CAT 2007)

Answer: Option 3

Question 7
(CAT 2002)Â

Answer: Option 1

Question 8
Shabnam is considering three alternatives to invest her surplus cash for a week. She wishes to guarantee maximum returns on her investment. She has three options, each of which can be utilized fully or partially in conjunction with others.
Option A: Invest in a public sector bank. It promises a return of + 0.10%
Option B: Invest in mutual funds of ABC Ltd. A rise in the stock market will result in a return of + 5%, while a fall will entail a return of – 3%
Option C: Invest in mutual funds of CBA Ltd. A rise in the stock market will result in a return of – 2.5%, while a fall will entail a return of + 2%Q1) The maximum guaranteed return to Shabnam is
(1) 0.25%
(2) 0.10%
(3) 0.20%
(4) 0.15%
(5) 0.30%
Q2) What strategy will maximize the guaranteed return to Shabnam?
(1) 100% in option A
(2) 36% in option B and 64% in option C
(3) 64% in option B and 36% in option C
(4) 1/3 in each of the three options
(5) 30% in option A, 32% in option B and 38% in option C (CAT 2007)

Answer: Q1) Option 3 Q2) Option 2

Question 9
In a tournament, there are n teams T1 , T2 ....., Tn with n > 5. Each team consists of k players, k > 3. The following pairs of teams have one player in common: T1 & T2 , T2 & T3 ,......, Tn − 1 & Tn , and Tn & T1. No other pair of teams has any player in common. How many players are participating in the tournament, considering all the n teams together?
(1) n(k – 1)
(2) k(n – 1)
(3) n(k – 2)
(4) k(k – 2)
(5) (n – 1)(k – 1) (CAT 2007)

Answer: Option 1

Question 10
Consider four digit numbers for which the first two digits are equal and the last two digits are also equal. How many such numbers are perfect squares?
(1) 3
(2) 2
(3) 4
(4) 0
(5) 1 (CAT 2007)