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- Question
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
- Correct Answer
- 1, 2 and 3
- 1. What is the unit place digit in the expansion of 773 ?
Options- A. 1
- B. 3
- C. 7
- D. 9 Discuss
- 2. What is the sum of all prime numbers between 60 and 80?
Options- A. 272
- B. 284
- C. 351
- D. 414 Discuss
- 3. Consider two-digit numbers which remain the same when the digits interchange their positions. What is the average of such two-digit numbers?
Options- A. 33
- B. 44
- C. 55
- D. 66 Discuss
- 4. Given that the polynomial (x2+ ax+ b) leaves that same remainder when by (x ?1) or (x + 1) What are the values of a and b respectively?
Options- A. 4 and 0
- B. 0 and 3
- C. 3 and 0
- D. 0 and any interger Discuss
- 5. A prime number contains the digit X at unit?s place. How many such digits of X are possible?
Options- A. 3
- B. 4
- C. 5
- D. 6 Discuss
- 6. Which one of the following is an irrational number?
Options- A. ?59059
- B. 231/593
- C. 0.454545....
- D. 0.121122111222 Discuss
- 7. 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 Discuss
- 8. 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 Discuss
- 9. 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. Discuss
- 10. 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 Discuss
Numbers problems
Search Results
Correct Answer: 7
Correct Answer: 351
Correct Answer: 55
Explanation:
All such 2 digit numbers are 11,22,33,44....... upto 99
Forms an AP
So sum = n/2(a+l)
= 9/2(11+99)
Average = sum/9 = ½(11+99) = 55
Correct Answer: 0 and any interger
Explanation:
Since x^2+ ax + b when divided by x-1 or x+1 leaves the same remainder
So on putting x=1 and x=-1 we get the same value
1+a+b = 1-a+b
2a=0
a=0
here b can take any value as it will always get cancelled out
Correct Answer: 6
Explanation:
For prime no units place cannot be occupied by even number except for 2
Thus no of digits occupying unit digit of prime numbers = 6 (1,2,3,5,7,9)
Example 2,3,5,7,11,19 in itself are prime numbers
Correct Answer: 0.121122111222
Correct Answer: 5
Correct Answer: 8, 6, 8, 8, 6, 7
Correct Answer: There is only one set of three prime numbers such that there is a gap of 2 between two adjacent prime numbers.
Correct Answer: 5/2
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