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

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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, 09:46
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.
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 51233
Re: If the units digit of the three-digit positive integer k is nonzero  [#permalink]

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New post 21 Jul 2018, 11:15
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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Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 51233
Re: If the units digit of the three-digit positive integer k is nonzero  [#permalink]

Show Tags

New post 21 Jul 2018, 11:16
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.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

GMAT Club Bot
Re: If the units digit of the three-digit positive integer k is nonzero &nbs [#permalink] 21 Jul 2018, 11:16

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

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