Author 
Message 
TAGS:

Hide Tags

VP
Joined: 21 Jul 2006
Posts: 1447

If the units digit of the threedigit positive integer k is nonzero
[#permalink]
Show Tags
Updated on: 17 Jun 2015, 02:30
Question Stats:
65% (01:01) correct 35% (01:29) wrong based on 750 sessions
HideShow timer Statistics
If the units digit of the threedigit 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.
Official Answer and Stats are available only to registered users. Register/ Login.
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.




Math Expert
Joined: 02 Sep 2009
Posts: 47967

If the units digit of the threedigit positive integer k is nonzero
[#permalink]
Show Tags
30 Mar 2010, 17:58
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 threedigit 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.
_________________
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? Extrahard Quant Tests with Brilliant Analytics




Manager
Joined: 17 Dec 2007
Posts: 97

Re: If the units digit of the threedigit positive integer k is nonzero
[#permalink]
Show Tags
09 Aug 2009, 12:35
tarek99 wrote: If the units digit of the threedigit 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




Manager
Joined: 28 Jul 2009
Posts: 116
Location: India
Schools: NUS, NTU, SMU, AGSM, Melbourne School of Business

Re: If the units digit of the threedigit positive integer k is nonzero
[#permalink]
Show Tags
10 Aug 2009, 00:40
Lets say k=x,y,z. All of x, y and z are in the range of 19 (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.
_________________
GMAT offended me. Now, its my turn! Will do anything for Kudos! Please feel free to give one.



Retired Moderator
Joined: 05 Jul 2006
Posts: 1731

Re: If the units digit of the threedigit positive integer k is nonzero
[#permalink]
Show Tags
10 Aug 2009, 00:45
[quote="tarek99"]If the units digit of the threedigit 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.



Manager
Joined: 03 Oct 2009
Posts: 89

Re: If the units digit of the threedigit positive integer k is nonzero
[#permalink]
Show Tags
Updated on: 23 May 2013, 04:51
If the units digit of the threedigit 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.
Originally posted by KocharRohit on 17 Oct 2009, 20:28.
Last edited by Bunuel on 23 May 2013, 04:51, edited 2 times in total.
Added the OA



Manager
Joined: 11 Sep 2009
Posts: 129

Re: If the units digit of the threedigit positive integer k is nonzero
[#permalink]
Show Tags
17 Oct 2009, 20:44
The answer is A.
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.



Manager
Joined: 12 Oct 2009
Posts: 100

Re: If the units digit of the threedigit positive integer k is nonzero
[#permalink]
Show Tags
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



Manager
Joined: 17 Aug 2009
Posts: 202

Re: If the units digit of the threedigit positive integer k is nonzero
[#permalink]
Show Tags
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 1sufficient
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



Manager
Joined: 01 Feb 2010
Posts: 239

Re: If the units digit of the threedigit positive integer k is nonzero
[#permalink]
Show Tags
27 Mar 2010, 09:58
nsp007 wrote: If the units digit of the threedigit 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.



Intern
Joined: 20 Mar 2007
Posts: 48

Re: If the units digit of the threedigit positive integer k is nonzero
[#permalink]
Show Tags
30 Mar 2010, 08:33
bangalorian2000 wrote: nsp007 wrote: If the units digit of the threedigit 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.



Manager
Joined: 16 Apr 2008
Posts: 75

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



Senior Manager
Status: Not afraid of failures, disappointments, and falls.
Joined: 20 Jan 2010
Posts: 278
Concentration: Technology, Entrepreneurship
WE: Operations (Telecommunications)

Re: If the units digit of the threedigit positive integer k is nonzero
[#permalink]
Show Tags
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=389=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. So Answer is A Hope it helps!
_________________
"I choose to rise after every fall" Target=770 http://challengemba.blogspot.com Kudos??



Manager
Joined: 19 Oct 2010
Posts: 215
Location: India
GPA: 3

Re: If the units digit of the threedigit positive integer k is nonzero
[#permalink]
Show Tags
13 Aug 2011, 09:20
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.
_________________
petrifiedbutstanding



Intern
Status: pursuing a dream
Joined: 02 Jun 2011
Posts: 41
Schools: MIT Sloan (LGO)

Re: If the units digit of the threedigit positive integer k is nonzero
[#permalink]
Show Tags
14 Aug 2011, 05:47
Hope this helps.
Attachments
increase.jpg [ 48.6 KiB  Viewed 15120 times ]



Senior Manager
Joined: 23 Oct 2010
Posts: 361
Location: Azerbaijan
Concentration: Finance

Re: If the units digit of the threedigit positive integer k is nonzero
[#permalink]
Show Tags
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
_________________
Happy are those who dream dreams and are ready to pay the price to make them come true
I am still on all gmat forums. msg me if you want to ask me smth



Director
Status: No dream is too large, no dreamer is too small
Joined: 14 Jul 2010
Posts: 549

Re: If the units digit of the threedigit positive integer k is nonzero
[#permalink]
Show Tags
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
_________________
Collections: PSof OG solved by GC members: http://gmatclub.com/forum/collectionpswithsolutionfromgmatclub110005.html DS of OG solved by GC members: http://gmatclub.com/forum/collectiondswithsolutionfromgmatclub110004.html 100 GMAT PREP Quantitative collection http://gmatclub.com/forum/gmatprepproblemcollections114358.html Collections of work/rate problems with solutions http://gmatclub.com/forum/collectionsofworkrateproblemwithsolutions118919.html Mixture problems in a file with best solutions: http://gmatclub.com/forum/mixtureproblemswithbestandeasysolutionsalltogether124644.html



Math Expert
Joined: 02 Sep 2009
Posts: 47967

Re: If the units digit of the threedigit positive integer k is nonzero
[#permalink]
Show Tags
29 Jan 2012, 07:40
If the units digit of the threedigit 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. Answer: A. Hope it's clear.
_________________
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? Extrahard Quant Tests with Brilliant Analytics



Manager
Joined: 07 Jun 2017
Posts: 103

Re: If the units digit of the threedigit positive integer k is nonzero
[#permalink]
Show Tags
16 Aug 2017, 21:16
I miss the nonzero.. be extra aware of the questions



Senior Manager
Joined: 29 Jun 2017
Posts: 493
GPA: 4
WE: Engineering (Transportation)

Re: If the units digit of the threedigit positive integer k is nonzero
[#permalink]
Show Tags
17 Aug 2017, 10:42
1) let number be 121,122,123,124,125,.....129 if 9 is added the tens digit changes to 3 therefore tens digit is 3. A/D 2) let number be 119 then adding 4 makes tens digit 2 but on other hand taking number 121 and adding 4 makes tens digit again 2 so insufficient. A is the answer
_________________
Give Kudos for correct answer and/or if you like the solution.




Re: If the units digit of the threedigit positive integer k is nonzero &nbs
[#permalink]
17 Aug 2017, 10:42



Go to page
1 2
Next
[ 23 posts ]



