# Number Theory Previous Year Questions (CAT) - Set 0001

• Previous years`s CAT questions: Number Theory

• Question 1

Which among  21/2,  31/3,  41/4,  61/6,  121/12 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)

• Question 2

If x = − 0.5, then which of the following has the smallest value?

a.   2 1/x

b.   1/x

c.   1/x2

d.   2 x

e.   1/ √-x

(CAT 2006)

• 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)

• Question 4

Consider a sequence, where the nth term is tn = n/ (n+2) , n = 1, 2….

The value of t3 * t4 * t5 * … t53 is

(1) 2/495

(2) 2/477

(3) 12/55

(4) 1/1485

(5) 1/2970

(CAT 2006)

• 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)

• 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)

• Question 7

(CAT 2005)

• 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)

• Question 9

(CAT 2003 Retest)

• 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)

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