# Question Bank - Number Theory - Shashank Prabhu, CAT 100 Percentiler

• Q14) How many positive integers 'n' can we form using the digits 3, 4, 4, 5, 6, 6, 7 if we want 'n' to exceed 6,000,000?
Note that any repetition except for the ones mentioned explicitly in the question is not allowed.

• Q15) If you place 9 in the left-hand side of a five-digit number, you get a six-digit number. This six-digit number is four times the six-digit number that you get when you put 9 in right-hand side of the original five-digit number. What is the sum of the digits of the five-digit number? All the digits are distinct.
a. 18
b. 27
c. 17
d. Data insufficient

• Q16) The auto fare in La La Land has the following formula based upon the meter reading. The meter reading is rounded up to the next higher multiple of 4. For instance, if the meter reading is 37 paise, it is rounded up to 40 paise. The resultant is multiplied by 12. The final result is rounded up to the nearest multiple of 25 paise. If 53 paise is the meter reading, what will be the actual fare?
a. Rs. 6.75
b. Rs. 6.50
c. Rs. 6.25
d. Rs. 7.50

• Q40) Let D be a recurring decimal of the form D=0.a1 a2 a1 a2...., where digits a1 and a2 lie between 0 and 9. Further, at most one of them is zero. Which of the following numbers necessarily produces an integer, when multiplied by D?
a) 18
b) 108
c) 198
d) 288
e) 158

• Q49) Which of the following divides 144^2 + 169^2 + 144*169?
a. 157
b. 144
c. 313
d. None of these

• Q53) In a certain number system, the product of 51 and 22 is 1452. The number 1231 in this number system when converted to the decimal system becomes?

• Q57) If a = sqrt(3) + 1, then the value of a^4 - 6a^2 + 8a is
a. 12a - 3
b. 12a
c. 4a
d. 8a - 3

• Q58) If the eight-digit number N = 76542a3b is divisible by 18, find the number of possible values of N.

• Q66) If N = 1! - 2! + 3! - 4! + 5! ... + 47! - 48! + 49! then what is the unit's place digit of N^N?

• Q67) Two different two digit numbers are written beside each other to form a 4 digit number such that the smaller number is to the right. The difference between these two numbers when subtracted from the 4 digit number so formed is 5481. What is the sum of the two 2 digit numbers?

• Q70) Given that 1/(2!17!) + 1/(3!16!) + 1/(4!15!) + 1/(5!14!) + 1/(6!13!) + 1/(7!12!) + 1/(8!11!) + 1/(9!10!) = N /(1!18!)
Find the greatest integer that is less than N/100. (in numerical value)

• Q72) How many natural numbers exist which divide at least one among 28^12, 18^8 and 21^6?

• Q73) All the two-digit natural numbers whose unit digit is greater than their ten’s digit are selected. If all these numbers are written one after the other in a series, how many digits are there in the resulting number?

• Q74) The set X consists of m consecutive integers such that their sum is 2m. The set Y consists of 2m consecutive integers such that their sum is m. The difference between the largest elements of X and Y is 9. What is the value of m?
a) 17
b) 36
c) 9
d) 21

• Q80) How many natural numbers less than 10000 are present such that the sum of the digits of any such number is 33 and the number is divisible by 6?

• Q84) a and b are two positive numbers such that their sum is less than their product. The product of these two numbers would always be more than?

• Q89) The largest possible number divides four numbers, 5688, 6552, 7848 and 8712 to leave the same remainder in each case. What is the remainder?

• Q92) How many numbers less than 1000 have their sum of digits as 12?

• Q100) What is the remainder when the sum of all the terms in the 1024th row of the pascal triangle is divided by 1000.

• Q4) How many numbers greater than 13000 can be formed using the digits 5, 0, 8, 1 and 7 such that each digit is used exactly once?
[OA: 90]

63

53

22

42

89

47

138

47