Units Digit of 0

[billyb767]

Hello, For this question, why isn't units digit of 0 allowed? (bolded below)

thank you!



If a and b are positive integers, what is the units digit of b ?

(1) b is 25% greater than a.

(2) If b is decreased by 50%, the result is not an integer.


Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

Both statements TOGETHER are sufficient, but NEITHER one ALONE is sufficient.

EACH statement ALONE is sufficient.

Statements (1) and (2) TOGETHER are NOT sufficient.
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You can use smart numbers or algebraic theory to solve this problem; both approaches are shown below. (You can also mix and match for the different statements.)

Smart Numbers
(1) NOT SUFFICIENT: 25% of a must be an integer, so choose multiples of 4 for a. If a = 4, then b = 5, with units digit 5. If a = 8, then b = 10, with units digit 0. There are at least two possible values for the units digit of b.

(2) NOT SUFFICIENT: If b = 3, then 50% of b is indeed not an integer (1.5). If, on the other hand, b = 4, then 50% of b is still an integer (2). Any even value for b will still result in an integer, so b can’t be even; b must be odd. The units digit of b could be any odd digit (1, 3, 5, 7, or 9).

(1) AND (2) SUFFICIENT: Statement 2 limits the units digit of b to 1, 3, 5, 7, or 9. Statement 1 requires a to be a multiple of 4. If a = 4, then b = 5, with units digit 5. This time, a cannot equal 8, because then b will be 10, but a units digit of 0 isn’t allowed. The next possible value is a =12, in which case b = 15, with units digit 5. Is this a pattern?

Yes, if you try the next couple of values, the only acceptable values will result in b having a units digit of 5. The two statements together are sufficient.

[RonPurewal]

that discussion is for the combination of both statements.

statement 2 basically just says "b is odd". (if you cut an even integer in half, you'll still have an integer. if you cut an odd integer in half, you won't get an integer.)

...so, statement 2 doesn't allow any numbers with units digit 0, because those will be even.

i agree that this isn't the best wording in the whole world -- it would have been better to write something like "...because then b will be 10, which is even and thus disallowed by statement 2."

does that make sense now?