tricky digits problem: units digit of a three digit number

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tonebeeze: Master | Next Rank: 500 Posts; Posts: 158; Joined: Mon Nov 02, 2009 5:49 pmFollowed by: 3 members; Thanked: 2 times

by tonebeeze » Tue Apr 26, 2011 3:23 pm

Confused. Please help.

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

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Source: Beat The GMAT — Data Sufficiency | Tue Apr 26, 2011 3:23 pm

vineeshp: Legendary Member; Posts: 965; Joined: Thu Jan 28, 2010 12:52 amFollowed by: 34 members; Thanked: 156 times; GMAT Score:720

by vineeshp » Tue Apr 26, 2011 4:44 pm

1) Sufficient.
if unit's digit is non zero, then the number ends with one of 1-9.

If the tens digit of k + 9 is 3, then k+9 is between 30-38.
k is between 21-29.

Hence tens digit is 2.
(even if you take 121,221 etc, the argument still holds good.)

2) Insufficient.
k + 4 has tens digit as 2.

say k ends in 18, then k + 4 would have tens digit 2.
say k ends in 22, then k + 4 would have tens digit 2.

So we cant predict the tens digit of k.

Vineesh,
Just telling you what I know and think. I am not the expert.

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Wed Apr 27, 2011 4:51 am

tonebeeze wrote:Confused. Please help.

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

Let k = XYZ, so that Z is non zero.

(1) The tens digit of k + 9 is 3 implies tens digit of (XYZ + 9) = 3
The minimum digit of Z can be 1 (as it non-zero). Then XY1 + 9 implies the units digit will be 0, with a carry over of 1 to tens place. And since tens digit of k + 9 is 3, so Y = 2.
The maximum digit of Z can be 9. Then XY9 + 9 implies units digit will be 8, with a carry over of 1 to tens place. So, again Y = 2.
So, the tens digit of k is 2.
Hence, (1) is SUFFICIENT.

(2) The tens digit of k + 4 is 2 implies tens digit of (XYZ + 4) = 2
If Z = 2, then (X22 + 4) = X26, here tens digit of k = 2
If Z = 8, then (X18 + 4) = X22, here tens digit of k = 1
We don't get a definite answer.
Hence, (2) is NOT SUFFICIENT.

The correct answer is A.

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Wed Apr 27, 2011 6:14 am

tonebeeze wrote:Confused. Please help.

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

Statement 1: The tens digit of k+9 is 3.
Between 100 and 200:
k+9 could be 130 through 139.
Thus, k could be 130-9 = 121 through 139-9 = 130.
Since the units digit of k must be nonzero, k cannot be 130.
Thus, k = {121...129}.
Using this same logic, between 200 and 300:
k = {221...229}.
And so on.
In every case, the tens digit of k is 2.
Sufficient.

Statement 2: The tens digit of k + 4 is 2.
Between 100 and 200:
k+4 could be 120 through 129.
Thus, k could be 120-4 = 116 through 129-4 = 125 (excluding 120, since the units of k must be nonzero).
Thus, the tens digit of k could be 1 or 2.
Insufficient.

The correct answer is A.

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