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If k is a positive integer and the tens digit of k+5 is 4,

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Source: — Data Sufficiency |

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by Jay@ManhattanReview » Mon Nov 18, 2019 9:01 pm
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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