Math Exam - 1 (Number Theory)

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| By Mjhjoy1
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Mjhjoy1
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Quizzes Created: 1 | Total Attempts: 160
Questions: 10 | Attempts: 160

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Math Quizzes & Trivia

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Questions and Answers
  • 1. 

    A certain integer when divided by 5 yields a remainder of 4. Which of these can not be an integer?

    • A.

      N/9

    • B.

      N/10

    • C.

      N/14

    • D.

      N/19

    • E.

      None of these

    Correct Answer
    B. N/10
    Explanation
    n is not divided by 5, how can n be divided by 10? So, n/10 can not be integer ever.

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  • 2. 

    If the average of 5 consecutive odd integer is 55. what is the average of the last two integers?

    • A.

      56

    • B.

      57

    • C.

      58

    • D.

      60

    • E.

      None of these

    Correct Answer
    C. 58
    Explanation
    55 is the average of 5 (which is an odd number) numbers, so 55 is in the middle of those numbers. Hence, 51,53,55,57,59 will those numbers & (57+59)/2=58

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  • 3. 

    When the integers x id divided by 5, the remainder is 2. Which of the following can be multiple of  (x+3) 

    • A.

      8x+7

    • B.

      9x-3

    • C.

      11x-4

    • D.

      13x+1

    • E.

      13x

    Correct Answer
    B. 9x-3
    Explanation
    we have to find out a number divisible by (x+3), Given that the remainder is 2 if x is divided by 5, then we may guess the value of x such as 7 (5+2), 12(5*2+2), 17(5*3+2) ..so on. Then (x+3) means 10(7+3), 15(12+3) & so on. Thus (9x-3)=9*7-3=60 which is divisible by 10 means ( x+3).

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  • 4. 

    P is divisible by 4. Q is divisible by 3. Which of the following is definitely odd? 

    • A.

      Q(P+1)

    • B.

      2P+3Q

    • C.

      ​PQ<sup style="color: rgb(102, 102, 102);">2

    • D.

      P2Q3

    • E.

      None of these

    Correct Answer
    E. None of these
    Explanation
    P is divisible by 4, so P is an even number but Q is divisible by 3, so Q may be odd(3,9,15 etc.) or even (6,12,18 etc.). hence if we think from our concept, we find we can not say about any option definitely.

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  • 5. 

    Q is a prime number larger than 10. What is the smallest positive number (except 1) that 3Q can be equally divided by?

    • A.

      3Q

    • B.

      Q

    • C.

      3

    • D.

      Q+3

    • E.

      None of these

    Correct Answer
    C. 3
    Explanation
    Q is a prime number so it can be divided equally by 3Q, by 1 and by the components of 3 & Q. So the smallest number is 3 except 1.

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  • 6. 

    A can be divided by 11. Which of the following expressions can be divided by 11 leaving a remainder of 1?

    • A.

      A-20

    • B.

      A-12

    • C.

      A-9

    • D.

      A-10

    • E.

      None of these

    Correct Answer
    D. A-10
    Explanation
    Just take the multiples of 11 such as 22,33,44 etc. & replace a by any of them in the choice options.

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  • 7. 

    Turn the odd man out:  4, 9, 10, 12, 13, 18, 21

    • A.

      4

    • B.

      12

    • C.

      13

    • D.

      21

    • E.

      None of these

    Correct Answer
    C. 13
    Explanation
    Only 13 is a prime among them which is odd(strange).

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  • 8. 

    If a, b, and c are nonzero numbers and a+b=c, which of the following is equal to 1?

    • A.

      (a-b)/c

    • B.

      (a-c)/b

    • C.

      (b-c)/a

    • D.

      (c-b)/a

    • E.

      None of these

    Correct Answer
    D. (c-b)/a
    Explanation
    Very simple, just a+b=c, or a=c-b & so (c-b)/a=a/a=1.

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  • 9. 

    When 10 is divided by the positive integer n, the remainder is n-4. Which of the following could be value of n?

    • A.

      3

    • B.

      4

    • C.

      7

    • D.

      8

    • E.

      12

    Correct Answer
    C. 7
    Explanation
    If 10 is being divided by 7, then the remainder is 3 which is 7-4 that means n-4.

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  • 10. 

    When the integer n is divided by 3, the quotient is p and the remainder is 1. When p is divided by 5, the quotient is q and the remainder is 2. What will be the remainder when n is divided by 5.

    • A.

      4

    • B.

      3

    • C.

      2

    • D.

      1

    • E.

      None of these

    Correct Answer
    C. 2
    Explanation
    Here, n=3p+1 = 3(5q+2)+1=15q+6+1=(15q+5)+2; (15q+5) is divisible by 5, so remainder is 2.

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