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

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B
Joined: 18 Apr 2013
Posts: 34
Re: If the units digit of the three-digit positive integer k is nonzero  [#permalink]

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New post 21 Jul 2018, 10:46
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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V
Joined: 02 Sep 2009
Posts: 49271
Re: If the units digit of the three-digit positive integer k is nonzero  [#permalink]

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New post 21 Jul 2018, 12:16
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 know that c is not 0 and anything other than 0 added to 9 creates a carry over 1.
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Re: If the units digit of the three-digit positive integer k is nonzero &nbs [#permalink] 21 Jul 2018, 12:16

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