BTGmoderatorDC wrote:If k is a positive integer and the tens digit of k + 5 is 4, what is the tens digit of k?
(1) k > 35
(2) The units digit of k is greater than 5
OA B
Source: GMAT Prep
Let's take each statement one by one.
(1) k > 35
Case 1: Say k = 36, then k + 5 = 41, ensuring that the tens digit of k + 5 is 4. We see that the tens digit of k = 3.
Case 2: Say k = xx44 (x is any digit), then k + 5 = xx49, ensuring that the tens digit of k + 5 is 4. We see that the tens digit of k = 4.
No unique answer. Insufficient.
(2) The units digit of k is greater than 5.
Say the units digit of k = 6 (minimum value), thus, k = xxx6; and k + 5 = xxx6 + 5 = xx(x + 1)1. We know that the tens digit of k + 5 is 4, thus, x + 1 = 4. Thus, x = 3. Thus, the tens digit of k is 3.
Even if we assume the units digit of k = 9 (maximum value), we would get that the tens digit of k is 3. Sufficient.
The correct answer:
B
Hope this helps!
-Jay
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