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

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If the units digit of the three-digit positive integer k is [#permalink]

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05 Aug 2008, 11:09
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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.

This is a DS question and I am not clear on how to solve this problem
Thanks a lot for your help

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Re: Properties Question [#permalink]

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05 Aug 2008, 11:13
A

1) Sufficient.

We know that the units digit is NOT 0. So if it is 1, and you add 9 to that, then you know that the units will become 0 (it's ok to have this as zero, just not k) and there will be a carry over to the tens column, therefore, the tens column must have been 2, or the carry over would not make the tens digit 3.

2) Insufficient. We know that units digit of k is not 0, so it could be anything between 1 and 9 inclusive. If you add 4 to the units column, when the units column is 1, 2, 3, 4, or 5, the tens digit stays the same. If the units digit is 6, 7, 8 or 9, then the tens digit would have to be 1 in order for the carry over to be 2. because there are multiple possibilities with this statement, it is insufficient.

Because one of the answers was sufficient alone, we do not need to consider the statements together.

rnemani wrote:
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.

This is a DS question and I am not clear on how to solve this problem
Thanks a lot for your help

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Re: Properties Question [#permalink]

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05 Aug 2008, 13:06
rnemani wrote:
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.

This is a DS question and I am not clear on how to solve this problem
Thanks a lot for your help

(1) since unit digit of K>0 unit digit must be any of numbers 1...9 . If you add 9 to any of these 9 numbers lead to >=10 .. so
tens digit must be 2.
suffcient.
(2) tens digit of k + 4 is 2 --> tens digit of K can be 1 or 2
e.g 118+4 --> 222
e.g 323+4 --> 327

insufficient.

Will go with A.
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Last edited by x2suresh on 05 Aug 2008, 13:46, edited 2 times in total.

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Re: Properties Question [#permalink]

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05 Aug 2008, 13:13
I am bit confused on the explanation.
If the question is asking for the tens digit.
FOr
The tens digit of k + 9 is 3.

I did not understand the explanation
since unit digit of K>0 it can 1...9 . If you add 9 to any of these 9 numbers lead to >=10 .. so
10 the digit must be 2

How is 10 digit must be 2

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Re: Properties Question [#permalink]

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05 Aug 2008, 13:55
rnemani wrote:
I am bit confused on the explanation.
If the question is asking for the tens digit.
FOr
The tens digit of k + 9 is 3.

I did not understand the explanation
since unit digit of K>0 it can 1...9 . If you add 9 to any of these 9 numbers lead to >=10 .. so
10 the digit must be 2

How is 10 digit must be 2

10 digit -- tens digit.
Sorry for the consufision.

State 1) The tens digit of k + 9 is 3.
K is three digit number say K=XYZ
XYZ + 9 = A3B
units digit of K is non zero (i.e Z>0)
So Z must be 1,2,3,4,5,6,7,8,9
Add 9 to these XYZ (1....9)
XY1 +9 --> A30 ( because tens digit 3 ..)
XY2 +9 --> A31 ( because tens digit 3 ..)
XY9 +9 --> A38 ( because tens digit 3 ..)
here Y must be 2
TRY assume that Y is 3
X3Z+9 --> A3B ( IS this possible???) z>0 its not possible.
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Re: Properties Question [#permalink]

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05 Aug 2008, 14:08
Good explanation guys.

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Re: Properties Question [#permalink]

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05 Aug 2008, 17:20
rnemani wrote:
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.

This is a DS question and I am not clear on how to solve this problem
Thanks a lot for your help

say 100m+10n+p=k

now p>0

(1)k+9 => p+9 gives a carry of 1 =>
10's digit of the number k+9 is n+1 => n+1=3=>n=2 SUFFI
(2) this is not since we dont know whats p and p+4 can or not give a carry INSUFFFI n=2 or n=1 is not clear

IMO A
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Re: Properties Question   [#permalink] 05 Aug 2008, 17:20
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# If the units digit of the three-digit positive integer k is

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