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

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

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09 Aug 2009, 12:22
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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.
[Reveal] Spoiler: OA

Last edited by Bunuel on 17 Jun 2015, 02:30, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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Re: If the units digit of the three-digit positive integer k is nonzero [#permalink]

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09 Aug 2009, 12:35
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tarek99 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.

thanks!

Consider Statement 1:pick numbers to resolve it, if unit digit of k takes from 1 to 9, then adding nine would increase the tens digit by 1, hence it should be 2..sufficient to answer the question

Consider statement 2: if unit digit takes anything between 1 t0 5 , then on adding 4 tens digit remains the same. so in this case it would be 2, but if unit digit take from 6 to 9, tens digit would increase by 1, so this case its 1.

hence statement 1 alone is sufficient but not 2
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Re: If the units digit of the three-digit positive integer k is nonzero [#permalink]

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10 Aug 2009, 00:40
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Lets say k=x,y,z.

All of x, y and z are in the range of 1-9 (Given). Find Tens Digit ie y.

Stmt 1 Says: K + 9 = gives a number with 3 as the tens digit.
With that we can safely say that the Tens digit of k has to be 2. For eg let k be 121. Adding 9 will give 130. Similiarly, if k = 129, adding 9 will give 138. If we have k = 111, adding 9 will give 120 which goes against the stmt.

Stmt 2 : Not Suff as explained by alwynjoseph.

Hence, A.
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Re: If the units digit of the three-digit positive integer k is nonzero [#permalink]

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10 Aug 2009, 00:45
[quote="tarek99"]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.

k= xyz , z is not 0 what is y??

from 1
xyz
+ 009
-------
z is not 0 thus surely we carried one to add to y thus y = 2...suff

from 2
xyz
+ 004
-------

if 0<z<6 y = 3 if 6<=z<=9 thus y = 2 .............insuff

A, hi Tarek , i think it is easier to visualize it this way, hope it helps.
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Re: If the units digit of the three-digit positive integer k is nonzero [#permalink]

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17 Oct 2009, 20:28
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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.

Last edited by Bunuel on 23 May 2013, 04:51, edited 2 times in total.
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Re: If the units digit of the three-digit positive integer k is nonzero [#permalink]

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17 Oct 2009, 20:44
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We know the following:

(a) k is a 3 digit positive integer
(b) The units digit of k is NOT zero

Statement 1: The tens digit of k + 9 is 3.

If k + 9 has a tens digit of X, the only way k has a tens digit of X as well is if the units digit of k is zero. Since we know the units digit of k is NOT zero, the tens digit of k MUST be 2.

Sufficient.

Statement 2: Then tens digit of k+4 is 2.

The tens digit of k can be 1 or 2. Insufficient.
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Re: If the units digit of the three-digit positive integer k is nonzero [#permalink]

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18 Oct 2009, 01:01
will go with A

Lets consider k = 100x + 10y +z where z is units digit and y is tens digit
we know z is not equal to zero i.e z is b/w 1 and 9 inclusive
we need to find y

1. tens digit of k + 9 is 3 ie z+9 will give the new value of y
since z+9 gives y = 3 then y=2 before 9 is added to z (z is 1 to 9 inclusive) . hence suff

2. tens digit of k + 4 is 2
now if z= 6 or 7 or 8 or 9 then on adding 4, y value will get incremented by 1 so value of y (before adding 4 ) is 1
but if z is b/w 1 to 5 (inclusive) then value of y will not change and y will be equal to 2
hence insuff
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Re: If the units digit of the three-digit positive integer k is nonzero [#permalink]

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09 Dec 2009, 11:06
Consider

x y z
+ + 9

Minimum value of z is 1. Maximum value of z is 9
In both cases if 9 is added to z, it will produce 1 as carry over to y (tens digit)
If y becomes 3 after the addition, then it was 2 before the addition

Statement 1-----sufficient

Statement 2 is clearly insufficient, as we could have a carry from the Units digit and not have a carry (with the addition of 4). Each will give different result

Hope this is simply put
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Re: If the units digit of the three-digit positive integer k is nonzero [#permalink]

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27 Mar 2010, 09:58
nsp007 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.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

Pls. explain..

Unit digit has to be atleast 1.
1: k+9 so there will be a carry of 1 in tens digit always hence tens digit in original number is 2 hence sufficient.
2: k+4 can't say on carry to tens digit as unit digit of original number can be >6 or <6 hence insufficient.

Therefor A.
Whats the OA.
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Re: If the units digit of the three-digit positive integer k is nonzero [#permalink]

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30 Mar 2010, 08:33
bangalorian2000 wrote:
nsp007 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.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

Pls. explain..

Unit digit has to be atleast 1.
1: k+9 so there will be a carry of 1 in tens digit always hence tens digit in original number is 2 hence sufficient.
2: k+4 can't say on carry to tens digit as unit digit of original number can be >6 or <6 hence insufficient.

Therefor A.
Whats the OA.

I am unable to follow your reasoning.Could you please explain in detail ,how you infer that the tens digit is 2 in stmt 1.
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If the units digit of the three-digit positive integer k is nonzero [#permalink]

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30 Mar 2010, 17:58
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Kiski wrote:
I am unable to follow your reasoning.Could you please explain in detail ,how you infer that the tens digit is 2 in stmt 1.

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

k=abc, c not zero, question b=?

(1) The tens digit of k + 9 is 3:
abc
+9
---
a3x

Tens digit of k+9, which is 3, gains 1 unit from c+9 (as c is not zero), hence b+1=3 --> b=2. Sufficient.

(2) The tens digit of k + 4 is 2
abc
+4
---
a2x

Tens digit of k + 4, which is 2, may or may not gain 1 unit from c+4, hence either b+1=2 or b+0=2. Two different values for b. Not sufficient.

Hope it's clear.
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Re: If the units digit of the three-digit positive integer k is nonzero [#permalink]

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30 Mar 2010, 18:55
Thanks Bunuel.. good explanation.
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Re: If the units digit of the three-digit positive integer k is nonzero [#permalink]

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30 Mar 2010, 19:16
Well, I plugged some numbers and got A.
I) If k+9=38 (can't be 39 as k would have 0 as unit digit and also unit digit of k+9 can be from 0 to 8) then k=38-9=29 so the 10th digit for k is 2, that was if unit digit of k+9 is max which is 8. If, I take k+9=30 then k=21 and similarly for k+9=34, k would be 25 so the 10th digit is still 2. Same goes for 130 to 138 and 230 to 238 and so on.
Hence A is sufficient, so cross out answer choices B,C, and E.
Now we are left with options A & D. T check whether D can be an answer or not, we'll have to check out 2nd information.
II) If k+4=28 (can't be 24 as this way we'll get 0 as unit digit for k) then k=24 and 10th digit for k is 2. Now if we take k+4 less than 24 suppose k+4=23 then k=19 and 10th digit for k is 1. So we can't be sure either 10th digit for k is 1 or 2, Hence Insufficient. Same goes for if k+4 is in hundreds or more. Now cross out D option and we are left with only option A.
Hope it helps!
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Re: If the units digit of the three-digit positive integer k is nonzero [#permalink]

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13 Aug 2011, 09:20
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The question is fine I think.

Going by stmt 1: k+9 giving 3 in the tenths place would mean any number with two in the tenths place can give this. Sufficient.
Going by stmt 2: k+4 giving 2 in tenths place would mean any number between 1 and 5 in the hundreds place would return the same number in the tenths place. Any number between 6 and 9 in the hundreds place would return the next value. Therefore insufficient.
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Re: If the units digit of the three-digit positive integer k is nonzero [#permalink]

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14 Aug 2011, 05:47
Hope this helps.
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Re: If the units digit of the three-digit positive integer k is nonzero [#permalink]

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14 Aug 2011, 05:53
i think A is the answer.
if the units digit is non -zero, then no matter what it is, if u plus 9 , u will get 1. 1 +x =3 then the tens digit is 2
st2 cant help us to determine the tens digit
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Re: If the units digit of the three-digit positive integer k is nonzero [#permalink]

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29 Jan 2012, 07:32
Let k =abc (c ≠ 0) question is b= ?

(1) As c ≠ 0, so b+9 means k+9, if k+9 then b = 3. it is possible if b = 2 only
[123 + 9 = 132, 122+9= 131]
sufficient
(2) k+4 = b = 2, 118+4 = 122, b = 1
123 = 127 b= 2
Insufficient.
Ans. A
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Re: If the units digit of the three-digit positive integer k is nonzero [#permalink]

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29 Jan 2012, 07:40
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If the units digit of the three-digit positive integer k is nonzero, what is the tens digit of k?

Given that: k=abc and c is nonzero. Question b=?

(1) The tens digit of k + 9 is 3:
abc
+9
---
a3x

Tens digit of k+9, which is 3, gains 1 unit from c+9 (as c is not zero), hence b+1=3 --> b=2. Sufficient.

(2) The tens digit of k + 4 is 2
abc
+4
---
a2x

Tens digit of k + 4, which is 2, may or may not gain 1 unit from c+4, hence either b+1=2 or b+0=2. Two different values for b. Not sufficient.

Hope it's clear.
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Re: If the units digit of the three-digit positive integer k is nonzero [#permalink]

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

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