digits

sumasajja wrote:each of the following numbers has 2 digits blotted out.which of the numbers could be the number of hours in x days, where x is an integer?
a]25 , 06
b]50 , 26
c]56 , 02
d]62 , 50
e]65 , 20

If x is an integer, then in x days there will be 24x hours which is also an integer. Thus, the correct option must be divisible by 24 and hence by 4 also.

Now a number is divisible by 4 only if the number formed by the last two digits of the number is divisible by 4. In this case, we know last two digits of all the options and we can easily find that only option E will be divisible by 4.

Hence, only option E could be divisible by 24.

The correct answer is E.

gmatdriller wrote:well, we know the number has to be divisible by 24 hrs per day.
But factors of 24 includes 3, 6, and 8. What motivates the choice of 4
and not 3?

Because,

• 1. To check whether a number is divisible by 3, we have to check whether the sum of the digits of the number is divisible by 3 or not. As we don't all the digits of the numbers, we cannot check for divisibility by 3.
  2. To check whether a number is divisible by 6, we have to check whether the number is even and sum of the digits of the number is divisible by 3 or not. We can check whether the number is even by looking at last digit of the numbers but we cannot check for divisibility by 3.
  3. To check whether a number is divisible by 8, we have to check whether the number formed by the last three digits of the number is divisible by 8 or not. As we don't know the last three digits of the numbers, we cannot check for divisibility by 8.

But, to check whether a number is divisible by 4, we have to check whether the number formed by the last two digits of the number is divisible by 4 or not. As we know the last two digits of each of the numbers, we can easily check for divisibility by 4.