A number is divisible by 9 if the sum of its digits is divisible by 9. The sum of the number 4,#58 = 17 + #.
If # = 1, the number 4,#58 is divisible by 9, else no.
Let's take each statement one by one.
1) The digit # is less than 4.
Certainly insufficient. # can be any digit 0, 1, 2, or 3.
2) If the tens and hundreds digits were switched, the number 4,#58 would be divisible by 3.
=> 4,5#8 is divisible by 3.
A number is divisible by 3 if the sum of its digits is divisible by 3. The sum of the number 4,5#8 = 17 + #.
# can be 1, 4, or 7. # is not necessarily 1. Insufficient.
(1) and (2) together
# = 1. Thus, the number 4,#58 divisible by 9. Sufficient.
The correct answer: C
Hope this helps!
-Jay
_________________
Manhattan Review
Locations: Manhattan Review Kukatpally | GMAT Prep Jayanagar | GRE Prep Tarnaka | Madhapur GRE Coaching | and many more...
Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.
