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Q.No: 1
Test Name : CAT Paper 2004

If the sum of the first 11 terms of an arithmetic progression equals that of the first 19 terms, then what is the sum of the first 30 terms?

A
0
B
-1
C
1
D
Not unique
Answer key/Solution
Solution:
Q.No: 2
Test Name : CAT Paper 2004

Consider the sequence of numbers a1, a2, a3, ... to infinity where a1 = 81.33 and a2 = –19 and

aj = aj–1 – aj–2 for What is the sum of the first 6002 terms of this sequence?

A
–100.33
B
–30.00
C
62.33
D
119.33
Answer key/Solution
Solution:
Q.No: 3
Test Name : CAT Paper 2008

The integers 1, 2, …, 40 are written on a blackboard. The following operation is then repeated 39 times: In each repetition, any two numbers, say a and b, currently on the blackboard are erased and a new number a + b – 1 is written. What will be the number left on the board at the end?

A
820
B
821
C
781
D
819
E
780
Answer key/Solution
Solution:
Q.No: 4
Test Name : CAT Paper 2008

The number of common terms in the two sequences 17, 21, 25,…, 417 and 16, 21, 26,…, 466 is

A
78
B
19
C
20
D
77
E
22
Answer key/Solution
Solution:
Q.No: 5
Test Name : CAT Paper 2008

Find the sum

A
2008 - 1/2008
B
2007 - 1/2007
C
2007 - 1/2008
D
2008 - 1/2007
E
2008 - 1/2009
Answer key/Solution
Solution:
Q.No: 6
Test Name : CAT Paper 1993
Q58 to 100 : Choose the appropriate answer choice.

Let un+1 = 2un + 1 (n=0,1,2,....)and u0 = 0 Then u10 nearest to

A
1023
B
2047
C
4095
D
8195
Answer key/Solution
Solution:
Q.No: 7
Test Name : CAT Paper 1994
Q51 – 90 : Choose the best alternative.

If the harmonic mean between two positive numbers is to their geometric mean as 12 : 13; then the numbers could be in the ratio

A
12 : 13
B
1/12 : 1/13
C
4 : 9
D
2 : 3
Answer key/Solution
Solution:
Q.No: 8
Test Name : CAT Paper 1994
Q51 – 90 : Choose the best alternative.

Fourth term of an arithmetic progression is 8. What is the sum of the first 7 terms of the arithmetic progression?

A
7
B
64
C
56
D
Cannot be determined
Answer key/Solution
Solution:
Q.No: 9
Test Name : CAT Paper 1994
Q51 – 90 : Choose the best alternative.

Along a road lie an odd number of stones placed at intervals of 10m. These stones have to be assembled around the middle stone. A person can carry only one stone at a time. A man carried out the job starting with the stone in the middle, carrying stones in succession, thereby covering a distance of 4.8 km. Then the number of stones is

A
35
B
15
C
29
D
31
Answer key/Solution
Solution:
Q.No: 10
Test Name : CAT Paper 2001
Directions for questions 1 to 37: Answer the questions independently.

All the page numbers from a book are added, beginning at page 1. However, one page number was added twice by mistake. The sum obtained was 1000. Which page number was added twice?

A
44
B
45
C
10
D
12
Answer key/Solution
Solution:
Q.No: 11
Test Name : CAT Paper 2001
Directions for questions 1 to 37: Answer the questions independently.

For a Fibonacci sequence, from the third term onwards, each term in the sequence is the sum of the previous two terms in that sequence. If the difference in squares of 7th and 6th terms of this sequence is 517, what is the 10th term of this sequence?

A
147
B
76
C
123
D
Cannot be determined
Answer key/Solution
Solution:
Q.No: 12
Test Name : CAT Paper 2003 (L)
DIRECTIONS for Questions 105 to 110: Answer the questions independently of each other.

The sum of 3rd and 15th elements of an arithmetic progression is equal to the sum of 6th, 11th and 13th elements of the same progression. Then which element of the series should necessarily be equal to zero?

A
1st
B
9th
C
12th
D
None of the above
Answer key/Solution
Solution:
Let the 1st term be ‘a’ and common difference be ‘d’
then we have 3rd term = a + 2d
15th term = a + 14d
6th term = a + 5d
11th term = a + 10d
13th term = a + 12d
Since sum of 3rd and 15th term = sum of 6th, 11th and
13th term, therefore we have
2a + 16d = 3a + 27d
⇒ a + 11d = 0
Which is the 12th term.
Q.No: 13
Test Name : CAT Paper 2003 (L)
DIRECTIONS for Questions 126 to 150: Answer the questions independently of each other.

The 288th term of the series a,b,b,c,c,c,d,d,d,d,e,e,e,e,e,f,f,f,f,f,f… is

A
u
B
v
C
w
D
x
Answer key/Solution
Solution:
Q.No: 14
Test Name : CAT Paper 2003 (L)
DIRECTIONS for Questions 126 to 150: Answer the questions independently of each other.

There are 8436 steel balls, each with a radius of 1 centimeter, stacked in a pile, with 1 ball on top, 3 balls in the second layer, 6 in the third layer, 10 in the fourth, and so on. The number of horizontal layers in the pile is

A
34
B
38
C
36
D
32
Answer key/Solution
Solution:
Q.No: 15
Test Name : CAT Paper 2003 (L)
DIRECTIONS for Questions 126 to 150: Answer the questions independently of each other.

If the product of n positive real numbers is unity, then their sum is necessarily

A
a multiple of n
B
C
never less than n
D
a positive integer
Answer key/Solution
Solution:
Q.No: 16
Test Name : CAT Paper 2003 (L)
DIRECTIONS for Questions 126 to 150: Answer the questions independently of each other.

If log3 2, log3 (2x – 5), log3 (2x – 7/2) are in arithmetic progression, then the value of x is equal to

A
5
B
4
C
2
D
3
Answer key/Solution
Solution:
Q.No: 17
Test Name : CAT Paper 2003 (L)
DIRECTIONS for Questions 126 to 150: Answer the questions independently of each other.

In a certain examination paper, there are n questions. For j = 1,2 …n, there are 2n–j students who answered j or more questions wrongly. If the total number of wrong answers is 4095, then the value of n is

A
12
B
11
C
10
D
9
Answer key/Solution
Solution:
Q.No: 18
Test Name : CAT Paper 2003 (R)
Directions for questions 60 to 93: Answer the following questions independently.

A
B
C
D
Answer key/Solution
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Let the 1st term be ‘a’ and common difference be ‘d’
then we have 3rd term = a + 2d
15th term = a + 14d
6th term = a + 5d
11th term = a + 10d
13th term = a + 12d
Since sum of 3rd and 15th term = sum of 6th, 11th and
13th term, therefore we have
2a + 16d = 3a + 27d
⇒ a + 11d = 0
Which is the 12th term.

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