x=ab.cd, where a, b, c and d are the tens, units, tenths and hundredth

Question

x=ab.cd, where a, b, c and d are the tens, units, tenths and hundredths digits respectively in the decimal representation of x. If the number obtained when x is rounded to the nearest integer is subtracted from the number 10a+b+1, what is the result?

(1) 10a+b and 10c+d are prime numbers less than 50

(2) When the number 10b+a+d/10+c/100 is rounded to the nearest integer, the result is 10b +a +1

anishgomez · Answer

The Answer is A.
Let's look at the statement X=ab.cd and its mentioned that we need to round to the nearest integer.
So when we round X, we can write X as ab or ab+1 depending on the value of c. 
If c is less than 5 then X will be ab
If c is more than 5 then X will be ab+1
Now we can write 23 as 20 + 3.
The same way we can write ab as 10a + b.
So we just need to know whether c is greater or less than 5.

Statement 1
10a+b and 10c+ d are less than 50 and is a prime number.
Let's just take 10c+d<50. So c<5. Which helps me answer the question.

Statement 2
When 10b+a+d/10+c/100 is rounded to the nearest integer, the result is 10b +a +1.

Here we just need to check for d/10 + c/100.
Here if d>5 then the answer would be rounded to the next integer no matter what the value of c is and so c can be any integer.
So answer is A

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x=ab.cd, where a, b, c and d are the tens, units, tenths and hundredth

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