x is a 4digit positive integer whose digits are all the integer n
.Which of the following must be true?
i. The sum of the digits of x is even.
ii. The product of the digits of x is even.
iii. It is not divisible by 12.
Data Sufficiency
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So the number x is of the format nnnn
1) Sum of the digits = 4n (which is divisible by 4, hence even)
2) Product of the digits = \(n^4\)
If n=even, product will be even. If n=odd, product will be odd. So, we can't be sure of this one.
3) To be divisible by 12, the number must be divisible by both 3 and 4.
To be divisible by 4, last 2 digits must be divisible by 4. Since the digits are same and number is positive, only two possibilities here > 4444 and 8888
Both of these numbers aren't divisible by 3
Hence, x is not divisible by 12
To summarise, only 1) and 3) must be true!
Drop a thanks if this helps!
1) Sum of the digits = 4n (which is divisible by 4, hence even)
2) Product of the digits = \(n^4\)
If n=even, product will be even. If n=odd, product will be odd. So, we can't be sure of this one.
3) To be divisible by 12, the number must be divisible by both 3 and 4.
To be divisible by 4, last 2 digits must be divisible by 4. Since the digits are same and number is positive, only two possibilities here > 4444 and 8888
Both of these numbers aren't divisible by 3
Hence, x is not divisible by 12
To summarise, only 1) and 3) must be true!
Drop a thanks if this helps!
1) Sum of the digits = 4n
Hence it's divisible by 4.
2) Product of the digits = n^4
For even or odd, it depends whether n is even or odd
3) To be divisible by 12, the number must be divisible by both 3 and 4.
Only possible numbers divisible by 4 will be 4444 and 8888, and none of them is divisible by 3
So, x is not divisible by 12
Hence it's divisible by 4.
2) Product of the digits = n^4
For even or odd, it depends whether n is even or odd
3) To be divisible by 12, the number must be divisible by both 3 and 4.
Only possible numbers divisible by 4 will be 4444 and 8888, and none of them is divisible by 3
So, x is not divisible by 12