Math Exam - 1 (Number Theory)

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  • 1/10 Questions

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

    • 4
    • 12
    • 13
    • 21
    • None of these
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About This Quiz

This Math Exam - 1 focuses on Number Theory, including problems on divisibility, consecutive integers, and properties of prime numbers.

Math Exam - 1 (Number Theory) - Quiz

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  • 2. 

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

    • (a-b)/c

    • (a-c)/b

    • (b-c)/a

    • (c-b)/a

    • None of these

    Correct Answer
    A. (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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  • 3. 

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

    • 8x+7

    • 9x-3

    • 11x-4

    • 13x+1

    • 13x

    Correct Answer
    A. 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. 

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

    • N/9

    • N/10

    • N/14

    • N/19

    • None of these

    Correct Answer
    A. 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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  • 5. 

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

    • 3

    • 4

    • 7

    • 8

    • 12

    Correct Answer
    A. 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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  • 6. 

    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.

    • 4

    • 3

    • 2

    • 1

    • None of these

    Correct Answer
    A. 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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  • 7. 

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

    • 56

    • 57

    • 58

    • 60

    • None of these

    Correct Answer
    A. 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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  • 8. 

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

    • 3Q

    • Q

    • 3

    • Q+3

    • None of these

    Correct Answer
    A. 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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  • 9. 

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

    • A-20

    • A-12

    • A-9

    • A-10

    • None of these

    Correct Answer
    A. 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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  • 10. 

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

    • Q(P+1)

    • 2P+3Q

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

    • P2Q3

    • None of these

    Correct Answer
    A. 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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  • Current Version
  • May 22, 2024
    Quiz Edited by
    ProProfs Editorial Team
  • Feb 25, 2016
    Quiz Created by
    Mjhjoy1
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