ABA represents a three-digit number having digits A and B; BC3 represe

Hi All,

This DS question is built around a few Number Property rules, but even if you don't spot those pattern you can still get the correct answer with a little 'brute force' arithmetic.

We're told that A, B and C are DIGITS in the three-digit numbers ABA and BC3. This means that each of those variables can only be the numbers 0-9 inclusive. We're asked for the value of B.

1 )ABA x 3 = BC3

There are only 10 possible values for A - and Fact 1 gives us an equation that tells us that when we multiply A by 3, we get a number that ENDS in a 3. Could A = 5? NO - because multiplying a number that ends in 5 by 3 will gives us a number that ends in a 5. How long would it take you to multiply each possible digit by 3 and see what happens? You'll find that there's just ONE possibility that 'fits'... A = 1. With that value 'locked in', we have...

1B1 x 3 = BC3

From here, we can take the same approach to figure out the possible value(s) of B. Could B = 1? NO - because 111 x 3 = 333 (not 1C3). How long would it take to work through the other possibilities (hint: you won't have to work for very long). You'll find that B = 3 and B = 4 are both possibilities.

131 x 3 = 393
141 x 3 = 423
Fact 1 is INSUFFICIENT.

2) A, B, and C are distinct non-zero digits.

Fact 2 lets us know that the three variables are all different from one another, but there's still no way to determine the exact value of B.
Fact 2 is INSUFFICIENT.

Combined, we still end up with two possible outcomes (A=1, B=3, C=9 and A=1, B=4, C=3).
Combined, INSUFFICIENT.

Final Answer:

GMAT assassins aren't born, they're made,
Rich

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