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If the units digit of the three-digit positive integer k is

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Source: — Data Sufficiency |

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by Jay@ManhattanReview » Thu Jan 09, 2020 10:47 pm

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BTGmoderatorLU wrote:Source: GMAT Prep

If the units digit of the three-digit positive integer k is nonzero, what is the tens digit of k?

1) The tens digit of k + 9 is 3.
2) The tens digit of k + 4 is 2.

The OA is A
Let's take each statement one by one.

1) The tens digit of k + 9 is 3.

Since the units' digit of k is nonzero, the minimum value of the units' digit is 1 and the maximum value of the units' digit is 9. Thus, the sum of units' digit + 9 ≥ 10; thus, there is a carry of 1. This means that the tens digit of k is 3 - 1 = 2. Sufficient.

2) The tens digit of k + 4 is 2.

Case 1: If units' digit of k is between 1 and 5, then the tens digit of k is 2.
Case 2: If units' digit of k is between 6 and 9, then the tens digit of k is 2 - 1 = 1.

No unique answer. Insufficient.

The correct answer: A

Hope this helps!

-Jay
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by Brent@GMATPrepNow » Fri Jan 10, 2020 5:16 am

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BTGmoderatorLU wrote:Source: GMAT Prep

If the units digit of the three-digit positive integer k is nonzero, what is the tens digit of k?

1) The tens digit of k + 9 is 3.
2) The tens digit of k + 4 is 2.

The OA is A
Target question: What is the tens digit of k?

Statement 1: The tens digit of k + 9 is 3
If the units digit of k is not zero, then it must be 1 or 2 or . . .or 8 or 9
So, when we add 9 to k, the tens digit must increase by one.
So, if the tens digit of k + 9 is 3, then the tens digit of k must be 2
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: The tens digit of k + 4 is 2
Consider these two possible values of k:
Case a: k = 17, since the tens digit of k + 4 (aka 21) is 2. In this case, the tens digit of k is 1
Case b: k = 23, since the tens digit of k + 4 (aka 27) is 2. In this case, the tens digit of k is 2
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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