104 Number Theory Problems PDF

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Download : 104 Number Theory Problems PDF

Few problems:

1.If both 112 and 33 are factors of the number a * 43 * 62 * 1311, what is the smallest possible value of ‘a’?

  1. 121
  2. 3267
  3. 363
  4. 33
  5. 37

Correct Answer: Choice (3). The smallest possible value of ‘a’ is 363.

 

2.Find the largest five digit number that is divisible by 7, 10, 15, 21 and 28.

  1. 99,840
  2. 99,900
  3. 99,960
  4. 99,990
  5. 99,970

Correct Answer: Choice (3). 99960

 

3.Anita had to multiply two positive integers. Instead of taking 35 as one of the multipliers, she incorrectly took 53. As a result, the product went up by 540. What is the new product?

  1. 1050
  2. 540
  3. 1440
  4. 1520
  5. 1590

Correct Answer – 1590. Choice (5)

 

4.Let x, y and z be distinct integers. x and y are odd and positive, and z is even and positive. Which one of the following statements cannot be true?

  1. (x – z)2 y is even
  2. (x – z) y2 is odd
  3. (x – z) y is odd
  4. (x – y)2 z is even
  5. (x + y)3 z is even

 

Correct Answer – (x – z)2 y is even. Choice (1)

 

5.When a number is divided by 36, it leaves a remainder of 19. What will be the remainder when the number is divided by 12?

  1. 10
  2. 7
  3. 19
  4. 192
  5. None of these

Correct Answer – 7. Choice (2)

 

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