AAPL wrote: ↑Mon Jan 20, 2020 7:29 am
Princeton Review
Is the four-digit number 4,#58 divisible by 9?
1) The digit # is less than 4.
2) If the tens and hundreds digits were switched, the number 4,#58would be divisible by 3.
OA
C
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
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