Number System problems
- 1. The number 6 2n - 1, where n is any positive integer, is always divisible by?
Options- A. 11
- B. 5
- C. 7
- D. Both (B) and (C) Discuss
Correct Answer: Both (B) and (C)
Explanation:
62 -1 = 35, which is divisible by both 5 and 7.
- 2. Which of the following numbers is not a square of any natural number?
Options- A. 34692
- B. 4096
- C. 15129
- D. 15376 Discuss
Correct Answer: 34692
Explanation:
A number that ends in 2 , 3 , 7 or 8 is never a perfect square.
- 3. Of the three numbers, the first is twice the second and is half of the third. if the average of three number is 56. the smallest number is?
Options- A. 24
- B. 36
- C. 40
- D. 48 Discuss
Correct Answer: 24
Explanation:
Let the second number be N.
Then, first number = 2N and third number = 4N
? 2N + N+ 4N/3 = 56
? 7N = 3 x 56
? N = 3 x 56/7 = 24
So, the smallest number is 24.
- 4. The number x is exactly divisible by 5 and the remainder obtained on dividing the number y by 5 is 1. what remainder will be obtained when (x + y) is divided by 5?
Options- A. 0
- B. 1
- C. 2
- D. 3 Discuss
Correct Answer: 1
Explanation:
Let x/5 = p and let y when divided by 5 gives q as quotient and 1 as remainder.
Then, y = 5q + 1
Now x = 5p and y = 5q + 1
? x + y = 5p + 5q + 1 = 5(p + q) + 1
So, required remainder = 1
- 5. If the unit digit in the product 75? x 49 x 867 x 943 be 1, then the value of? is
Options- A. 1
- B. 3
- C. 7
- D. 9 Discuss
Correct Answer: 9
Explanation:
Let the value for ? be N
So N x 9 x 7 x 3 = a number with unit digit 1.
Clearly, the minimum value of N is 9.
- 6. The sum of three numbers is 132, If the first number be twice the second and third number be one-third of the first, then the second number is?
Options- A. 32
- B. 36
- C. 48
- D. 60 Discuss
Correct Answer: 36
Explanation:
Let second number be 3N, then, first one is 6N and the third one is 2N.
From question 3N + 6N + 2N = 132
? 11N = 132
? N = 12
? Second number = 3N = 3 x 12 = 36
- 7. A certain number of two digits is three times the sum of its digits and if 45 be added to it, then digits are reversed. The number is?
Options- A. 32
- B. 72
- C. 27
- D. 23 Discuss
Correct Answer: 27
Explanation:
Let unit digit = x and ten's digit = y
3(x + y)= 10y + x .....(i)
10y + x + 45 = 10x + y ....(ii)
2x - 7y = 0.9x -9y = 45
or x - y = 5 .... (iii)
Solving these equations, we get
x=7, y=2
? Required number = 27
- 8. A fraction becomes 4 when 1 is added to both the numerator and denominator, it becomes 7 When 1 is subtract from both the numerator and denominator. The numerator of the given fractions is?
Options- A. 2
- B. 3
- C. 7
- D. 15 Discuss
Correct Answer: 15
Explanation:
Let the required fraction be p/q.
Then, (p +1) / (q +1) = 4
? p - 4q= 3 ....(i)
And, (p - 1) / (q -1) = 7
? p - 7q = -6 ....(ii)
Solving these equation we get p = 15, q=3
- 9. The sum of squares of two numbers is 68 and the squares of their difference is 36. The product of the two number is?
Options- A. 16
- B. 32
- C. 58
- D. 104 Discuss
Correct Answer: 16
Explanation:
Let the number be a and b .
Then a2 + b2 = 68 ....(i)
and (a - b)2 = 36
Now, (a - b)2 = 36 ....(ii)
? a2 + b2 - 2ab = 36
? 68 - 2ab = 36
? 2ab = 32
? ab = 16 .
- 10. There are two numbers such that the sum of twice the first and thrice the second is 18, while the sum of thrice the first and twice the second is 17. The larger of the two is?
Options- A. 4
- B. 6
- C. 8
- D. 12 Discuss
Correct Answer: 4
Explanation:
Let the numbers be x and y ,
Then, 2x + 3y = 18 ....(i),
3x + 2y = 17 ....(ii)
Solving, we get x =3 , y= 4
? Largest number = 4
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