Math Exam - 1 (Number Theory) - Quiz, Trivia & Questions

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| By Mjhjoy1

Mjhjoy1

Community Contributor

Quizzes Created: 1 | Total Attempts: 164

Questions: 10 | Attempts: 164 | Updated: Mar 19, 2023

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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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Current Version
Mar 19, 2023

Quiz Edited by
ProProfs Editorial Team
Feb 25, 2016

Quiz Created by
Mjhjoy1

Math Exam - 1 (Number Theory)

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

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

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

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

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

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

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

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

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

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.