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

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tarek99
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 Q49  V35
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If the units digit of the three-digit positive integer k is nonzero [#permalink] New post   Updated on: 17 Jun 2015, 02:30
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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.
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A

Originally posted by tarek99 on 09 Aug 2009, 12:22.
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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If the units digit of the three-digit positive integer k is nonzero [#permalink] New post   30 Mar 2010, 17:58
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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.

Answer: A.

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

please show your solving.

thanks!



The answer is A.

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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bhanushalinikhil
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Re: If the units digit of the three-digit positive integer k is nonzero [#permalink] New post   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] New post   21 Jul 2018, 10:46
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Hi Bunuel, for statement 1, why can't b = 4?
How do I know that there is a carry forward of 1 from the units to the tens digit? Thanks!

Bunuel wrote:
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.

Answer: A.

Hope it's clear.
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Re: If the units digit of the three-digit positive integer k is nonzero [#permalink] New post   21 Jul 2018, 12:15
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roastedchips wrote:
Hi Bunuel, for statement 1, why can't b = 4?
How do I know that there is a carry forward of 1 from the units to the tens digit? Thanks!

Bunuel wrote:
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.

Answer: A.

Hope it's clear.


Because we are told that c is non-zero and anything other than 0 when added to 9 gives a carry over 1.
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Re: If the units digit of the three-digit positive integer k is nonzero [#permalink] New post   31 Mar 2023, 03:09
K = abc

What is b is the question??? And c cannot be 0

S1:

tens digit of K + 9 = a3c

abc + 9 = a3c

values that satisfy this

121+ 9 = 130 (wont work cause C = / 0)

122+9 = 131

Or

222+ 9 = 231
223 + 9 = 232 and so on...we know that b will always = 2

For the tens digit to be 3, from k + 9 = a3c is for the tens digit to be 2 in k=abc therefore b = 2


Statement 2:

Tens digit of k + 4 = 2 therefore a2c

K=abc

120 + 4 = 124

125 + 4 = 129

But

117 + 4 = 121

118+ 4 = 122

b can be either 1 or 2 so Statement 2 is not sufficient
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Re: If the units digit of the three-digit positive integer k is nonzero [#permalink] New post   10 Jan 2024, 02:51
yannichc wrote:
K = abc

What is b is the question??? And c cannot be 0

S1:

tens digit of K + 9 = a3c

abc + 9 = a3c

values that satisfy this

121+ 9 = 130 (wont work cause C = / 0)

122+9 = 131

Or

222+ 9 = 231
223 + 9 = 232 and so on...we know that b will always = 2

For the tens digit to be 3, from k + 9 = a3c is for the tens digit to be 2 in k=abc therefore b = 2


Statement 2:

Tens digit of k + 4 = 2 therefore a2c

K=abc

120 + 4 = 124

125 + 4 = 129

But

117 + 4 = 121

118+ 4 = 122

b can be either 1 or 2 so Statement 2 is not sufficient


thanks for this, now it makes more sense with all these examples...
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Re: If the units digit of the three-digit positive integer k is nonzero [#permalink]
10 Jan 2024, 02:51
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Bunuel
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