Question Bank  Number Theory  Shashank Prabhu, CAT 100 Percentiler

Q25)
[OA: 8]

Q26) The sequence 3, 15, 24, 48, contains numbers that are multiples of 3 and one less than a perfect square. Find the remainder when the 1,994th term of the series is divided by 1,000.
[OA: 63]

Q34) 1010101… is a 94digit number. What will be the remainder obtained when this number is divided by 375?
[OA: 260]

Q40) If n = 999 ... 99 is an integer consisting of a string of 2009 nines, then find the sum of digits of n^2.
[OA: 18081]

Q44) (11/3) + (11/8) + (11/15) + (11/24) + (11/35) + ... (11/99) = ?
[OA: 36/5]

Q45) Which of the following can be the number of zeroes at the end of the factorial of a natural number?
a) 156
b) 29
c) 30
d) 155[OA: Option a]

Q46)
[OA: 1]

Q49) What is the largest integer x for which 85! is completely divisible by 42^x?
[OA: 13]

Q51) Find the sum of all positive integers from 1 to 100 which will give a remainder of 2 when divided by 3.
[OA: 1650]

Q58) 1/(1 + 2) + 1/(1 + 2 + 3) + 1/(1 + 2 + 3 + 4) + ... + 1/(1 + 2 + 3 + ... + 2017) = ?
[OA: 1008/1009]

Q71) In the last summer vacation, Akshay was given an assignment of writing down numbers from 100 to 1000. Despite all his brilliance and intelligence, Akshay always gets confused between the digits ‘6’ and ‘9’. As a result, he ends up interchanging them. How many numbers did he write correctly in his assignment?
a) 343
b) 353
c) 448
d) 449[OA: Option d]

Q73) Considering all the natural numbers which lie between 1000 and 7770 (not including either), in which place does the digit 7 appear the most?
a) Units
b) Tens
c) Hundreds
d) Thousands[OA: Option d]

Q74) Find the last two digits of 1! + 2! + 3! + 4! ... + 99! + 100!
[OA: 13]

Q75) A local bank that has 15 branches uses a twodigit code to represent each of its branches. The same integer can be used for both digits of a code, and a pair of twodigit numbers that are the reverse of each other (such as 17 and 71) are considered as two separate codes. What is the fewest number of different integers required for the 15 codes?
[OA: 4]

Q83) N, a natural number less than 30, has odd number of factors. The number of consecutive zeroes at the end of N! cannot be more than
(a) 6
(b) 5
(c) 4
(d) 3[OA: Option a]

Q91) AB + CD = AAA, where AB and CD are twodigit numbers and AAA is a three digit number; A, B, C, and D are distinct positive integers. In the addition problem above, what is the value of C?
[OA: 9]

Q93) The sum of the even numbers between 1 and k is 79 * 80, where k is an odd number, then k=?
[OA: 159]

Q96) Three wheels can complete 60, 36 and 24 revolutions per minute. There is a red spot on each wheel that touches the ground at time zero. After how much time, all these spots will simultaneously touch the ground again?
[OA: 5 seconds]

Q99) (BE)^2 = MPB, where B, E, M and P are distinct integers. Then M = ?
[OA: 3]

Q100) A certain number, when divided by 899, leaves a remainder 63. Find the remainder when the same number is divided by 29.
[OA: 5]