Number System problems
- 1. How many integers from 1 to 100 exist such that each is divisible by 5 and also has 5 as a digit?
Options- A. 10
- B. 11
- C. 12
- D. 20 Discuss
Correct Answer: 11
Explanation:
5,15,25,35,40,50,55,65,75,85,95
So there are total 11 such type of numbers.
- 2. The sum of the digits of two-digit number is 14 and the difference between the two digits number is 2. What is the product of the two digits of the two-digit number?
Options- A. 56
- B. 48
- C. 45
- D. None of the above Discuss
Correct Answer: 48
Explanation:
Let be the ten's digit be x and unit's digit be y.
So the two digit number = 10x + y ( where x > y )
According to question
x + y = 14 ....(i)
x - y = 2 ....(ii)
Solving Eqs. (i) and (ii), we get
x = 8 and y = 6
? Required product = 8 x 6 = 48
- 3. What number should be added to 231228 to make it exactly divisible by 33?
Options- A. 1
- B. 2
- C. 3
- D. 4 Discuss
Correct Answer: 3
Explanation:
- 4. How many rational numbers are there between 1 and 1000?
Options- A. 998
- B. 999
- C. 1000
- D. infinite Discuss
Correct Answer: infinite
Explanation:
There can be infinite number of rational numbers between 1 and 1000.
- 5. The sum of 5 consecutive even numbers A, B, C, D and E is 130. What is the product of A and E?
Options- A. 720
- B. 616
- C. 660
- D. 672 Discuss
Correct Answer: 660
Explanation:
Let 5 consecutive even number be A = x, B = x+2, C = x+4, D = x + 6 and E = x + 8.
According to question
x + x +2 + x + 4 + x + 6 + x + 8 = 130
? 5x + 20 = 130
? x = 22
? A = 22, E = 22 + 8 = 30.
? Multiplication of A and E = 22 x 30
= 660
- 6. The sum of 5 consecutive numbers is equal to 170. what is the product of largest and smallest numbers?
Options- A. 1512
- B. 1102
- C. 1152
- D. 1210 Discuss
Correct Answer: 1152
Explanation:
Let smallest number = x.
Then, x + x + 1 + x + 2 + x + 3 + x + 4 = 170
? 5x + 10 = 170
? x = 160 / 5
? x = 32
? product of smallest and largest number = 32 x 36
= 1152
- 7. Which of the following number always divides the difference between the square of two consecutive odd numbers?
Options- A. 7
- B. 3
- C. 8
- D. 6 Discuss
Correct Answer: 8
Explanation:
Let the two consecutive odd numbers be 2x+1 and 2x + 3 .
? Difference = ( 2x + 3 )2 - ( 2x + 1 )2
= ( 2x + 3 + 2x + 1 )( 2x + 3 - 2x - 1 )
=( 4x + 4 ) x 2
= 8 (x + 1)
whis is exactly divisible by 8.
- 8. 9856 x 156 + 9856 x 844 =?
Options- A. 9856000
- B. 9836500
- C. 9794560
- D. 9698350 Discuss
Correct Answer: 9856000
Explanation:
9856 x 156 + 9856 x 844 = 9856 x (156 + 844)
= 9856 x 1000
= 9856000
- 9. 6674 x 625 =?
Options- A. 4170160
- B. 4072360
- C. 4171050
- D. 4171250 Discuss
Correct Answer: 4171250
Explanation:
6674 x 625 = 6674 x (5)4
= 6674 x (104/24
= 66740000/16 = 4171250
- 10. 9998 x 999 =?
Options- A. 9997001
- B. 9988002
- C. 9987012
- D. 9898012 Discuss
Correct Answer: 9988002
Explanation:
Exp.= 9998 x 999
= 9998 x (1000-1)
= 9998 x 1000 - 9998 x 1
= 9998000 - 9998 = 9988002
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