Aptitude - Numbers - Discussion
Discussion Forum : Numbers - General Questions (Q.No. 64)
64.
Which natural number is nearest to 8485, which is completely divisible by 75 ?
Answer: Option
Explanation:
On dividing, we get
75) 8485 (113
75
---
98
75
----
235
225
---
10
---
Required number = (8485 - 10) // Because 10 < (75 - 10)
= 8475.
Discussion:
6 comments Page 1 of 1.
Kinnaboy said:
3 years ago
Standard form of 75 = 5^2 * 3^1.
Therefore the number must be divisible by 25 and 3 (both are coprimes).
For divisibility by 25, the last two digits must be divisible by 25. Here all the numbers are divisible by 25.
Hence what remains is divisibility by 3. For divisibility by 3, the sum of digits must be divisible by 3.
Therefore 8+4+7+5 = 24 i.e. divisible by 3. hence the answer.
Therefore the number must be divisible by 25 and 3 (both are coprimes).
For divisibility by 25, the last two digits must be divisible by 25. Here all the numbers are divisible by 25.
Hence what remains is divisibility by 3. For divisibility by 3, the sum of digits must be divisible by 3.
Therefore 8+4+7+5 = 24 i.e. divisible by 3. hence the answer.
(3)
Vel said:
1 year ago
75/5 = 15.
15 rule is = 3 * 5.
3 rule = sum of digit/3.
Option 1 = 8 + 4 + 7 + 5 = 24/3 = remainder = 0.
Option 2 = 8 + 5 + 0 + 0 = 13/3! = 0.
Option 3 = 8 + 5 + 5 + 0 = 18/3 = remainder = 0.
Option 4 = 8 + 5 + 2 + 5 = 20/3! = 0.
Dividing number is 8475 & 8550 compare the given number.
15 rule is = 3 * 5.
3 rule = sum of digit/3.
Option 1 = 8 + 4 + 7 + 5 = 24/3 = remainder = 0.
Option 2 = 8 + 5 + 0 + 0 = 13/3! = 0.
Option 3 = 8 + 5 + 5 + 0 = 18/3 = remainder = 0.
Option 4 = 8 + 5 + 2 + 5 = 20/3! = 0.
Dividing number is 8475 & 8550 compare the given number.
Ritvik said:
1 decade ago
No need to calculate. Can be solved by looking at the options?
Clearly 8475 is the nearest and to be divisible by 75 it should be divisible 5, 3 and 25 and it is clearly divisible.
Clearly 8475 is the nearest and to be divisible by 75 it should be divisible 5, 3 and 25 and it is clearly divisible.
(1)
Ajeet said:
1 decade ago
Better to play with options 75 = 5*5*3, so the number should be divisible by 5 and 3.
The nearest number to 8485 in option is 8475. Which is clearly divisible by both.
The nearest number to 8485 in option is 8475. Which is clearly divisible by both.
(1)
Srilakshmi m said:
4 years ago
Why the condition 10<(75-10) is given in the explanation?
Please explain about it.
Please explain about it.
(2)
Gaxi said:
3 years ago
Explain the answer clearly.
(2)
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