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Numbers problems


  • 1. Consider the following statements in respect of two integers p and q (both > 1) which are relatively prime: 1) Both p and q may be prime numbers. 2) Both p and q may be composite numbers 3) one of p and q may be prime and the other composite. Which of the above statements are correct?

  • Options
  • A. 1 and 2 only
  • B. 2 and 3 only
  • C. 1 and 3 only
  • D. 1, 2 and 3
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  • 2. Which one of the following is an irrational number?

  • Options
  • A. ?59059
  • B. 231/593
  • C. 0.454545....
  • D. 0.121122111222
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  • 3. How many pairs (A, B) are possible in the number 479865AB if the number is divisible by 9 and it is given that the last digit of the number is odd?

  • Options
  • A. 5
  • B. 6
  • C. 9
  • D. 11
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  • 4. Consider the multiplication 999 × abc = def132 in decimal notation, where a, b, c, d, e and f are digits. What are the values of a, b, c, d, e and f respectively?

  • Options
  • A. 6, 6, 8, 6, 8, 7
  • B. 8, 6, 8, 6, 7, 8
  • C. 6, 8, 8, 7, 8, 6
  • D. 8, 6, 8, 8, 6, 7
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  • 5. Which of the following statements is not true?

  • Options
  • A. The difference of two prime numbers, both greater than 2, is divisible by 2
  • B. For two different integers m, n and a prime number p, if p divides the product m × n, then p divides either m or n.
  • C. If a number is of the form 6n ?1 (n being a natural number), then its is a prime number.
  • D. There is only one set of three prime numbers such that there is a gap of 2 between two adjacent prime numbers.
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  • 6. Sum of twice a fraction and 5 times its reciprocal is 7. What is the fraction?

  • Options
  • A. 2/5
  • B. 5/4
  • C. 5/2
  • D. 4/5
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  • 7. The 3rd and 6th term of an arithmetic progression are 19 and 37 respectively. What is the 13th term?

  • Options
  • A. 79
  • B. 43
  • C. 45
  • D. 49
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  • 8. Convert binary 10110 to decimal.

  • Options
  • A. 22
  • B. 20
  • C. 18
  • D. 16
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  • 9. What is the reflection of the point (6, -3) in the line y = 2?

  • Options
  • A. (-2 , -3)
  • B. (6 , 7)
  • C. (-6 , 7)
  • D. (-2 , 3)
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  • 10. What least number must be subtracted from 518, so that the sum is completely divisible by 13?

  • Options
  • A. 11
  • B. 10
  • C. 9
  • D. 12
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