Smita04
Shaina's five-distinct-digit locker code is 5A48B. What digit letter A symbolizes in Shaina's locker code?
(1) Shaina's locker code is divisible by all integers 2 through 6.
(2) Shaina's locker code is divisible by 9 and 11.
nice question
(1) says 5A48B is divisible by 2, 3, 4, 5, 6..IF that be so we need to find what does B represents here...since B is divisible by 5 , the value of B can either be 0 or 5...if the value of B is 5, then 5A48B is not divisible by 2,4 and 6 (5A485 is not divisible by 2,4 and 6) thus the value of B is 0 here
so the new term is 5A480..in order for 5A480 to be divisible by 3 or 6( 2 x 3), the total sum of digits should be divisible by 3 so the total makes it 17 + A, now A could be either 1 (total =18) or 4 (total = 21) or 7( total = 24) , thus (1) is not sufficient enough to answer.
lets move to (2) now,
5A48B is divisible by 9 and 11..taking them one by one, to be divisible by 9 , the total should be divisible by 9, the total is 17 + A+B, so A+ B could be either 1( total 18) or 10 ( total 27)
now if the total of A + B is 1, then either A is 0 and B is 1 or A is 1 and B is 0
as we plug them in
the number would be either 50481 or 51480
only 51480 is divisible by 11
so (2) correctly gives the value of A
IMO B
correct me if i am wrong.