Number Theory Previous Year Questions (CAT)  Set 0001

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

Question 1
Which among 2^{1/2}, 3^{1/3}, 4^{1/4}, 6^{1/6}, 12^{1/12 }is the largest?
a. 2^{ 1/2}
b. 3^{ 1/3}
c. 4^{ 1/4}
d. 6^{ 1/6}
e. 12^{ 1/12}
(CAT 2006)

Answer: Option b

Question 2
If x = − 0.5, then which of the following has the smallest value?
a. 2 ^{1/x}
b. 1/x
c. 1/x^{2}
d. 2^{ x}
e. 1/ √x
(CAT 2006)

Answer: Option b

Question 3
If a/b = 1/3, b/c = 2, c/d = 1/2, d/e = 3 and e/f = 1/4
then what is the value of abc/def
(1) 3/8
(2) 27/8
(3) 3/4
(4) 27/4
(5) 1/4
(CAT 2006)

Answer: Option 1

Question 4
Consider a sequence, where the nth term is t_{n} = n/ (n+2) , n = 1, 2….
The value of t_{3} * t_{4 }* t_{5 }* … t_{53} is
(1) 2/495
(2) 2/477
(3) 12/55
(4) 1/1485
(5) 1/2970
(CAT 2006)

Answer: Option 1

Question 5
A group of 630 children is arranged in rows for a group photograph session. Each row contains three fewer children than the row in front of it. What number of rows is not possible?
(1) 3
(2) 4
(3) 5
(4) 6
(5) 7
(CAT 2006)

Answer: Option 4

Question 6
What are the values of x and y that satisfy both the equations?
2^{ 0.7x} * 3 ^{1.25y} = 8 √6 / 27
4 ^{0.3x} * 9^{ 0.2y} = 8 * (81)^{1/5}
(1) x = 2, y = 5
(2) x = 2.5, y = 6
(3) x = 3, y = 5
(4) x = 3, y = 4
(5) x = 5, y = 2
(CAT 2006)

Answer: Option 5

Question 7
(CAT 2005)

Answer: Option 3

Question 8
The sum of four consecutive two digit odd numbers, when divided by 10, becomes a perfect square. Which of the following can possibly be one of these four numbers?
(1) 21
(2) 25
(3) 41
(4) 67
(CAT 2006)

Answer: Option 3

Question 9
(CAT 2003 Retest)

Answer: Option 3

Question 10
Consider the set S = {1, 2, 3, …., 1000}. How many arithmetic progressions can be formed from the elements of S that start with 1 and with 1000 and have at least 3 elements?
(1) 3
(2) 4
(3) 6
(4) 7
(5) 8
(CAT 2006)