When the digits of a two digit natural number are interchanged then original…
2018
When the digits of a two digit natural number are interchanged then original number is greater than three times the new number so obtained. How many such natural numbers are there which satisfy the above given condition? Ignore the numbers which have ‘0’ in its unit place.
Answer: B. 6 — Let the two-digit number be 10a + b. After interchange it becomes 10b + a. The condition is 10a + b > 3(10b + a), so 7a > 29b. For b = 1, a can be 5, 6, 7, 8,…
- A.
5
- B.
6
- C.
7
- D.
8
- E.
9
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Correct answer: B
Let the two-digit number be 10a + b. After interchange it becomes 10b + a.
The condition is 10a + b > 3(10b + a), so 7a > 29b.
For b = 1, a can be 5, 6, 7, 8, or 9. For b = 2, only a = 9 works. For b >= 3, no digit a can satisfy the condition.
Therefore 6 two-digit numbers satisfy the condition.