BTGModeratorVI wrote: ↑

Sat Jun 27, 2020 6:50 am

What is the value of the three-digit integer t if t is divisible by 9 ?

(1) The tens digit and the hundreds digit of t are both 7.
(2) The units digit of t is less than both the tens digit and the hundreds digit.

Answer: A
Source: Princeton Review

----ASIDE------
Key Property: If an integer is divisible by 9, then the sum of its digits will be divisible by 9
For example, 576 is divisible by 9. Notice that 5 + 7 + 6 = 18, and 18 is divisible by 9
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Given: t is a 3-digit integer that is divisible by 9
From the above property we can conclude that the SUM of t's three digits must be divisible by 9

Target question: What is the value of t?

Statement 1: The tens digit and the hundreds digit of t are both 7.
So, t = 77k , where k = the unknown units digit
Since the SUM of t's three digits must be divisible by 9, we know that 7 + 7 + k must equal some value that is divisible by 9.
Since k is a single-digit, it MUST be the case that k equals 4. (when k = 4, we see that t = 774, which is divisible by 9)
The answer to the target question is t = 774
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: The units digit of t is less than both the tens digit and the hundreds digit.
There are several 3-digit integers that satisfy statement 2 (and the given condition that t is divisible by 9). Here are two:
Case a: t = 621. In this case, the answer to the target question is t = 621
Case b: t = 630. In this case, the answer to the target question is t = 630
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent