Number Theory Previous Year Questions (CAT)  Set 0010

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

Question 1
A student finds the sum 1 + 2 + 3 + ... as his patience runs out. He found the sum as 575. When the teacher declared the result wrong, the student realized that he missed a number. What was the number the student missed?
(1) 16
(2) 18
(3) 14
(4) 20 (CAT 2002)

Answer: Option 4

Question 2
A thief was stealing diamonds from a jewellery store. On his way out, he encountered three guards, each was given half of the existing diamonds and two over it by the thief. In the end, he was left with one diamond. How many did the thief steal?
(1) 40
(2) 36
(3) 42
(4) 38 (CAT 2002)

Answer: Option 2

Question 3
If Xn = (1)^{n} X_{n1} and X_{0} = x and x > 0
(1) X_{n} is positive for n = even
(2) X_{n} is negative for n = even
(3) X_{n} is positive for n = odd
(4) None of these (CAT 2002)

Answer: Option 4

Question 4
In a book store, each of the word of the glowing board "MODERN BOOK STORES" is visible after 5/2, 17/4 and 41/8 seconds respectively. Each of them is put off for 1 second. Find the time after which one person can see a completely visible glowing board.
(1) 73.5 seconds
(2) 79.4 seconds
(3) 68.2 seconds
(4) None of these (CAT 2002)

Answer: Option 1

Question 5
A boy is supposed to put a mango into a basket if ordered 1, an orange if ordered 2 and an apple if ordered 3. He took out 1 mango and 1 orange if ordered 4. He was given the following sequence of orders. 12332142314223314113234
Q1) At the end of the sequence, what will be the number of oranges in the basket?
(1) 2
(2) 3
(3) 4
(4) 6
Q2) At the end of the sequence, what will be the total number of fruits in the basket?
(1) 10
(2) 11
(3) 13
(4) 17 (CAT 2002)

Answer: Option 1 Option 2

Question 6
A red light flashes 3 times per minute and a green light flashes 5 times in two minutes at regular intervals. If both lights start flashing at the same time, how many times do they flash together in each hour?
1. 30
2. 24
3. 20
4. 60 (CAT 2001)

Answer: Option 1

Question 7
Of 128 boxes of oranges, each box contains at least 120 and at most 144 oranges. The number of boxes containing the same number of oranges is at least:
1. 5
2. 103
3. 6
4. Cannot be determined ( CAT 2001 )

Answer: Option 3

Question 8
In a 4digit number, the sum of the first two digits is equal to that of the last two digits. The sum of the first and last digits is equal to the third digit. Finally, the sum of the second and fourth digits is twice the sum of the other two digits. What is the third digit of the number?
1. 5
2. 8
3. 1
4. 4 (CAT 2001)

Answer: Option 1

Question 9
Two men X and Y started working for a certain company at similar jobs on January 1, 1950. X asked for an initial salary of Rs. 300 with an annual increment of Rs. 30. Y asked for an initial salary of Rs. 200 with a rise of Rs. 15 every six months. Assume that the arrangements remained unaltered till December 31, 1959. Salary is paid on the last day of the month. What is the total amount paid to them as salary during the period?
1. Rs. 93,300
2. Rs. 93,200
3. Rs. 93,100
4. None of these (CAT 2001)

Answer: Option 1