failatmath
A three digit number A with hundreds digit a, tens digit b and units digit c is written in reverse order to form another three digit number B. If B > A , is B + A > 1200?
(1) B - A is divisible by 8
(2) A is a multiple of 5
Let me help..
Let the hundreds digit be a ,10's digit be b and unit's digit be c.
So A becomes 100*a + 10*b +c .
B is in the reverse order. SO B= c b a = 100*c +10*b + a
B- A = 100*(c-a) + (a-c ) = 99*(c-a)
Statement 1 :-
B-A is divisible by 8.So c and a can be 9 , 1 ( 9 -1 = 8 ) or 8 , 0 (8-0=8)
But 8 and 0 are not possible as then the B will not remain a three digit number.
hence 9 ,1 are possible.
Hence A = 9b1
To maximise A , lets take b = 9 as well..So A= 991
B is in reverse order. B = 199.
So the max. (B+A) = 991 +199 = 1190
So B + A cant be greater than 1200.
Statement 2 : Since A is a multiple of 5 so A = ab5 . A cant be A cant be ab0 as then the B will not remain a two digit number.
SO A = ab5
B = 5ba
Now a has to be lesser than c as B >A.
So the maximum value a can take is 4.
So A = 4b5 = 495
B=5b4 = 594
So the max. B+A = 495+594 = 1089
So B + A cant be greater than 1200.
Hence Each statement is sufficient . Answer is option D.