Question Bank  Number Theory  Shashank Prabhu, CAT 100 Percentiler

Number of Questions  100
Topic  Number Theory
Answer Key Available ? : Yes
Source : Learningroots forum

Q 6) The sum of squares of first 15 positive integers is 1240. What is the sum of squares of the next 15 positive integers (16^2 + 17^2 + ... + 30^2)
a. 2480
b. 3490
c. 6785
d. 8215
e. 9255[OA: Option d]

Q 8) How many natural numbers are factors of 7560 and multiples of 14?
a) 20
b) 22
c) 24
d) 28[OA: Option c]

Q 9) Which of the following numbers is a perfect square?
a) 64! × 65!
b) 124! × 125!
c) 120! × 121!
d) 121! × 122![OA: Option c]

Q 10) If first 23 terms of the series 1, 11, 111, .. are added together, what digit would occupy the thousands place?
a) 3
b) 0
c) 9
d) 2[OA: Option d]

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 lefthand side of a fivedigit number, you get a sixdigit number. This sixdigit number is four times the sixdigit number that you get when you put 9 in righthand side of the original fivedigit number. What is the sum of the digits of the fivedigit 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 eightdigit 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 twodigit 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?