Problems on Numbers System: Level 01

  1. Which of the following is an odd prime number?
    1. 1
    2. 9
    3. 3
    4. 15

    Answer : Option 3
    Among the given options, 3 is an odd prime number. Therefore, the answer is option 3.
  2. What least digit should come in place of # in the 9 digit number 15549#325, for which the number is divisible by 3?
    1. 0
    2. 1
    3. 2
    4. Any of these

    Answer : Option 3
    A number if divisible by 3 if sum of digits is multiple of 3. In 15549#325,
    Sum of the digits= 1 + 5 + 5 + 4 + 9 + # + 3 + 2 + 5 = 34 + # = 34 + 2 = 36 which is divisible by 3.
  3. What is the product of smallest 15 whole numbers?
    1. 1
    2. 0
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    3. 25
    4. 60

    Answer : Option 2
    Smallest 15 whole numbers are 0, 1, 2, 3, 4,.....14. As these numbers contain a zero, so, product will be zero. So, answer is option 2.
  4. What is the sum of first 10 perfect cubes?
    1. 3025
    2. 5625
    3. 1225
    4. None of these

    Answer : Option 1
    Sum of 1st 10 perfect cubes :- = 13 + 23 + 33 ______ + 103 = (10(10+1)/2)2 = 3025 Hence, the correct answer is option 1
  5. What is the difference between the greatest 5 digit number and the smallest 5 digit number?
    1. 99998
    2. 89999
    3. 89990
    4. 99990

    Answer : Option 2
    The greatest 5 digit number = 99999
    Smallest 5 digit number = 10000.
    The required difference = 99999 – 10000 = 89999
    So, the answer is option 2.
  1. There are 20 people in a party. If every person shakes hand with every other person, what is the total number of handshakes?
    1. 180
    2. 155
    3. 145
    4. 190

    Answer : Option 4
    1st person will shake hand with 19 other persons. 2nd person will shake hand with remaining 18 persons, and so on.
    Therefore, total number of handshakes.
    = 19 + 18 + 17+ ……………………+ 3 + 2 + 1 = Σ19 =(19(19+1)/2) =190
    So, the correct answer is option 4.
  2. A 107 digit number is formed by writing first 58 natural numbers next to each other. Find the remainder when number is divided by 8.
    1. 6
    2. 10
    3. 4
    4. 9

    Answer : Option 1
    To find remainder by 8, we only divide the number formed by the last 3 digit by 8. The last 3 digits would give the number 758. The remainder when 758 is divided by 8 = 6. So, answer is option 1.
  3. The five digit number 7500A8 is divisible by 4. How many values of A are possible?
    1. 0
    2. 3
    3. 5
    4. 4

    Answer : Option 3
    To find divisibility by 4, we need to consider last two digits of the number, these should be divisible by 4. Hence, A can take values equal to 0, 2, 4, 6 and 8. Therefore 5 values are possible. So, the correct answer is option 3.
  4. What is the sum of this series 1 + 1 + 2 + 8 + 3+ 27 + 4 + 64 +_______10 + 1000?
    1. 308
    2. 3008
    3. 3800
    4. 3080

    Answer : Option 4
    Here, we are given a combination of two series
    (1 + 2 + 3 + 4 +.....................+10) + (1 + 8 + 27 + 64 +............+1000)
    = (1 + 2 + 3 + 4 +.....................+10) + (13 +23 +33 +43 +.................+103)
    (10(10+1)/2) + ((10 × 11)/2)2 = 3080. So, correct answer is option 4.
  5. Which one of the following is not a rational number?
    1. 0.2333
    2. 0.56666
    3. √3
    4. 7

    Answer : Option 3
    Here, 0.2333, 0.56666 and 7 are rational numbers as these can be represented in the form p/q.√3 is not a rational number, therefore answer is option 3.
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