Number System – Set 1

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Number System – Set 1

Dear ! This is Number System – Set 1 Quiz and it contains 50 questions.

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1) The difference between the square of two consecutive odd integers is always divisible by :

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2) The difference between two numbers is 1365. When the large number is divided by the smaller one, the quotient is 6 and the remainder is 15. What is the smaller number ?

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3) The value of 52 + 62 + …. + 102 + 202 is :

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4) If (12n + 1) is divisible by 13, then n is :

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5) Which is not a prime number ?

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6) Let S be the set of prime numbers greater than or equal to 2 and less than 100. Multiply all the elements of S. With how many consecutive zeros will the product end ?

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7) If (a2 – b2) ÷ (a + b) = 25, then (a – b) = ?

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8) When 10025 – 25 is written in decimal notation, the sum of its digits is :

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9) A number when divided by 3 leaves a remainder 1. When the quotient is divided by 2, it leaves a remainder 1. What will be the remainder when numbers is divided by 6 ?

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10) Unit’s digit in (784)126 + (784)127 is :

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11) Which is the greatest 5-digit number exactly divisible by 279 ?

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12) If m and n are natural numbers such that 2m – 2n = 960, what is the value of m ?

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13) The number of digits in the smallest number, which when multiplied by 7 yields all nines, is :

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14) If p,q,r are all real numbers then (p – q)3 + (q – r)3 + (r – p)3 is equal to :

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15) The unit’s digit in the product 274 × 318 × 577 × 313 is :

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16) A number when divided by three consecutive numbers 9, 11, 13 leaves the remainders 8, 9 and 8 respectively. If the order of divisors is reversed, the remainders will be :

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17) (719 + 2) is divided by 6. The remainder is :

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18) How many 3-digit numbers are there in between 100 and 300, having first and the last digit as 2 ?

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19) The number of terms between 11 and 200 which are divisible by 7 but not by 3 are :

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20) If n is a whole number greater than 1, then n2 (n2 – 1) is always divisible by :

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21) The sum of digits of a two-digit number is 12 and the difference between the two-digits of the two-digit number is 6. What is the-digit number ?

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22) Let a number of three digits have for its middle digit the sum of the other two digits. Then it is a multiple of :

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23) Which one of the following numbers is divisible by 15 ?

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24) A 4-digit number is formed by repeating a 2-digit number such as 2525, 3232 etc. Any number of this form is exactly divisible by :

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25) How many numbers will be there between 300 and 500, where 4 comes only one time ?

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26) The product of any three consecutive natural numbers is always divisible by :

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27) Find the least 6-digit number which is exactly divisible by 349 ?

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28) If x and y are positive integers such that (3x + 7y) is a multiple of 11, then which of the followings is also a multiple of 11 ?

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29) The smallest 4-digit number exactly divisible by 7 is :

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30) 111, 111, 111, 111 is divisible by :

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31) The sum of the digits of a natural number (10n – 1) is 4707, where n is a natural number. The value of n is :

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32) The smallest number that must be added to 803642 in order to obtain a multiple of 11 is :

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33) In a division sum, the divisor is 12 times the quotient and 5 times the remainder. If the remainder is 48, then the dividend is :

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34) The numbers 2272 and 875 are divided by a three-digit numbers N, giving the same remainder. The sum of the digits of N is :

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35) A boy multiplies 987 by a certain number and obtains 559981 as his answer. If in the answer both 9’s are wrong but the other digits are correct, then the correct answer will be :

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36) 7386038 is divisible by :

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37) The divisor is 25 times the quotient and 5 times the remainder. If the quotient is 16, then the dividend is :

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38) The remainder when 784 is divided by 342 is :

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39) The remainder when (1523 + 2323) is divided by 19, is :

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40) If m and n are integers divisible by 5, which of the following is not necessarily true ?

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41) If n is any positive integer, 34n – 43n is always divisible by :

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42) By how many of the following numbers is 212 – 1 divisible ? 2, 3, 5, 7, 10, 11, 13, 14

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43) 136 × 12 × 8 = ?

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44) If (6767 + 67) is divided by 68, the remainder is :

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45) A number when divided by 136 leaves remainder 36. If the same number is divided by 17, the remainder will be :

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46) The smallest 6-digit number exactly divisible by 111 is :

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47) The difference between the squares of any two consecutive integers is equal to :

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48) If 11,109,999 is divided by 1111, then what is the remainder ?

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49) The least number of five digit is exactly divisible by 88 is :

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50) If a number 774958A96B is divisible by 8 and 9, the respective values of A and B will be :

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