Question Bank - Number Theory - Hemant Malhotra


  • Director at ElitesGrid | CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975


    Number of Questions: 100
    Topic: Number Theory
    Answer key available? : No
    Source: Elite's Grid forum


  • Director at ElitesGrid | CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975


    Q1) If a! + (a+1)! has 19 zeroes at the end , what is the value of a
    a) 77
    b) 78
    c) 79
    d) 80
    e) CBD


  • Director at ElitesGrid | CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975


    Q2) How many sets of two or more consecutive positive integers have a sum of 15?


  • Director at ElitesGrid | CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975


    Q 3) How many four-digit positive integers have at least one digit that is a 2 or a 3?
    a) 2439
    b) 4096
    c) 5416
    d) 4896


  • Director at ElitesGrid | CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975


    Q 4) For prime numbers a and b , a + b = 102 and a > b. What is the least possible value of a - b


  • Director at ElitesGrid | CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975


    Q 5) A randomly selects two distinct numbers from the set { 1, 2, 3, 4, 5 }, and B randomly selects a number from the set { 1, 2, ..., 10 } . What is the probability that B's number is larger than the sum of the two numbers chosen by A?


  • Director at ElitesGrid | CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975


    Q 6) How many four-digit numbers, which are divisible by 15, are there such that the number 15 occurs in them?


  • Director at ElitesGrid | CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975


    Q 7) Sarah intended to multiply a two-digit number and a three-digit number, but she left out the multiplication sign and simply placed the two-digit number to the left of the three-digit number, thereby forming a five-digit number. This number is exactly nine times the product Sarah should have obtained. What is the sum of the two-digit number and the three-digit number?


  • Director at ElitesGrid | CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975


    Q8) x = 1/10 + 1/40 + 1/88 + ... + 1/(90298)
    a) 50/151
    b) 25/151
    c) 100/151
    d) 1/11


  • Director at ElitesGrid | CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975


    Q9) How many integers can be expressed as a sum of three distinct numbers if chosen from the set {4, 7,10,13, ..., 46}?


  • Director at ElitesGrid | CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975


    Q 10) ABC is a 3 digit natural number such that ABC=5 * (AB + BC + CA). Find total number of possible values for ABC


  • Director at ElitesGrid | CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975


    Q 11) What is the largest possible number of elements in a subset P of S = {1, 2, 3, ... , 9} such that the sum of every pair of distinct elements in P is different


  • Director at ElitesGrid | CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975


    Q12) A = 5^56,
    B = 10^51,
    C =17^35,
    D = 31^28.
    which is largest number ?
    (1) A
    (2) B
    (3) C
    (4) D
    (5) 2 numbers are equal


  • Director at ElitesGrid | CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975


    Q13) Let P be the prime number greater than 3.Find the remainder when P^2 + 17 is divided by 12 ?


  • Director at ElitesGrid | CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975


    Q14) If a and b are two real numbers which satisfy a + b − ab = 1 and a is not an integer, then b
    (a) is never an integer
    (b) must be some positive integer
    (c) must be some negative integer
    (d) must be equal to 0
    (e) may either be an integer or a non-integer


  • Director at ElitesGrid | CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975


    Q15) Find eight digit numbers which is formed by doubling the first four digits (for example, 12341234) divisible by 137.


  • Director at ElitesGrid | CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975


    Q16) Find the sum of all 8 digit number that can be formed with the digits 1, 1, 1, 5, 5, 7, 8 and 9


  • Director at ElitesGrid | CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975


    Q17) Find the number of two digit numbers where the product of the digits is greater than the sum of the digits.


  • Director at ElitesGrid | CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975


    Q18) Find the maximum possible remainder if (104)^n is divided by 51, given that n is a natural number greater than 8


  • Director at ElitesGrid | CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975


    Q19) Find the smallest positive number with 21 divisors.


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