If P is a three digit number where first digit is three times the last digit and no digit is repeate

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11 May 2022 Number System

If P is a three digit number where first digit is three times the last digit and no digit is repeated. How many P are possible which are divisible by 6 ?

OPtion

1) 8
2) 3
3) 5
4) 2
5) 6
6) 1
7) 4
8) 9
9) 7
10) None of these

Solution

Given, 1st digit is 3 times the 3rd digit. .'. The 3-digit number can be of the form 3 _ 1 ; 6 _ 2 ; 9 _ 3
Now, for a number to be divisible by 6, it should be an even number divisible by 2 and 3 both.
.'. Only possible numbers will be even numbers of the form 6 _ 2
So, the numbers are 612, 642, 672, Total 3
Correct Option 2)

Correct Option: 2 Best Solution (1)

Akshitha priya   2 years AGO

given the conditions only possible cases are....1) 3_1
2) 6_2
3) 9_3
no divisible by 6 should be even and the sum should be divisible by 3 .......hence option 1 and 2 rules out as it is odd only possible is 2nd and here also as the sum is already 8 now any number added sum must be divisible by 3 so...only options are...612,642,672,

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