Author 
Message 
TAGS:

Hide Tags

Senior Manager
Joined: 03 Dec 2012
Posts: 339

The threedigit positive integer x has the hundreds, [#permalink]
Show Tags
15 Nov 2013, 08:00
2
This post received KUDOS
7
This post was BOOKMARKED
Question Stats:
85% (02:34) correct
15% (02:11) wrong based on 291 sessions
HideShow timer Statistics
The threedigit positive integer x has the hundreds, tens, and units digits of a, b, and c, respectively. The threedigit positive integer y has the hundreds, tens, and units digits of k, l, and m, respectively. If (2^a)(3^b)(5^c) = 12(2^k)(3^l)(5^m), what is the value of x – y? A) 21 B) 200 C) 210 D) 300 E) 310
Official Answer and Stats are available only to registered users. Register/ Login.



Math Expert
Joined: 02 Sep 2009
Posts: 39662

Re: The threedigit positive integer x has the hundreds, [#permalink]
Show Tags
15 Nov 2013, 08:09
1
This post received KUDOS
Expert's post
6
This post was BOOKMARKED
mohnish104 wrote: The threedigit positive integer x has the hundreds, tens, and units digits of a, b, and c, respectively. The threedigit positive integer y has the hundreds, tens, and units digits of k, l, and m, respectively. If (2^a)(3^b)(5^c) = 12(2^k)(3^l)(5^m), what is the value of x – y?
A) 21 B) 200 C) 210 D) 300 E) 310 x = abc, where a, b, and c, are the hundreds, tens, and units digits, respectively. y= klm, where k, l, and m, are the hundreds, tens, and units digits, respectively. \((2^a)(3^b)(5^c) = 12(2^k)(3^l)(5^m)\) > \(2^{ak}*3^{bl}*5^{cm}=2^2*3\) > \(ak=2\), \(bl=1\), and \(cm=0\) > \(xy=210\). Answer: C.
_________________
New to the Math Forum? Please read this: 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



Math Expert
Joined: 02 Sep 2009
Posts: 39662

Re: The threedigit positive integer x has the hundreds, [#permalink]
Show Tags
15 Nov 2013, 08:13
Bunuel wrote: mohnish104 wrote: The threedigit positive integer x has the hundreds, tens, and units digits of a, b, and c, respectively. The threedigit positive integer y has the hundreds, tens, and units digits of k, l, and m, respectively. If (2^a)(3^b)(5^c) = 12(2^k)(3^l)(5^m), what is the value of x – y?
A) 21 B) 200 C) 210 D) 300 E) 310 x = abc, where a, b, and c, are the hundreds, tens, and units digits, respectively. y= klm, where k, l, and m, are the hundreds, tens, and units digits, respectively. \((2^a)(3^b)(5^c) = 12(2^k)(3^l)(5^m)\) > \(2^{ak}*3^{bl}*5^{cm}=2^2*3\) > \(ak=2\), \(bl=1\), and \(cm=0\) > \(xy=210\). Answer: C. Similar questions to practice: kandlareeachfourdigitpositiveintegerswiththousands126646.htmlthefunctionfisdefinedforeachpositivethreedigit100847.htmlforanyfourdigitnumberabcdabcd3a5b7c11d126522.htmlHope this helps.
_________________
New to the Math Forum? Please read this: 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



GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15961

Re: The threedigit positive integer x has the hundreds, [#permalink]
Show Tags
01 Dec 2014, 13:06
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources



Manager
Joined: 13 Dec 2013
Posts: 55
GPA: 2.71

Re: The threedigit positive integer x has the hundreds, [#permalink]
Show Tags
02 Dec 2014, 00:11
Hi Brunel, Can you please explain the right side of this equation



SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1857
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)

The threedigit positive integer x has the hundreds, [#permalink]
Show Tags
02 Dec 2014, 02:00
2
This post received KUDOS
1
This post was BOOKMARKED
x = 100a + 10b + c ........... (1) y = 100k + 10l + m ............ (2) We require to find xy (1)  (2) \(2^a* 3^b * 5^c = 12 * 2^k* 3^l * 5^m\) \(2^a * 3^b * 5^c = 2^{k+2} * 3^{l+1} * 5^m\) Equating powers a = k+2; b = l+1; c = m Substituting the above values in equation (1) 100k + 200 + 10l + 10 + c  (100k + 10l + m) = 210 Answer = C
_________________
Kindly press "+1 Kudos" to appreciate



Intern
Joined: 23 Sep 2014
Posts: 15

Re: The threedigit positive integer x has the hundreds, [#permalink]
Show Tags
09 Dec 2014, 08:58
Bunuel wrote: mohnish104 wrote: The threedigit positive integer x has the hundreds, tens, and units digits of a, b, and c, respectively. The threedigit positive integer y has the hundreds, tens, and units digits of k, l, and m, respectively. If (2^a)(3^b)(5^c) = 12(2^k)(3^l)(5^m), what is the value of x – y?
A) 21 B) 200 C) 210 D) 300 E) 310 x = abc, where a, b, and c, are the hundreds, tens, and units digits, respectively. y= klm, where k, l, and m, are the hundreds, tens, and units digits, respectively. \((2^a)(3^b)(5^c) = 12(2^k)(3^l)(5^m)\) > \(2^{ak}*3^{bl}*5^{cm}=2^2*3\) > \(ak=2\), \(bl=1\), and \(cm=0\) > \(xy=210\). Answer: C. I am sorry but i dont understand the slightest thing of what's going on here. How does that suddenly translate to 2^2*3? really confused here.



Math Expert
Joined: 02 Sep 2009
Posts: 39662

Re: The threedigit positive integer x has the hundreds, [#permalink]
Show Tags
09 Dec 2014, 09:03
JoostGrijsen wrote: Bunuel wrote: mohnish104 wrote: The threedigit positive integer x has the hundreds, tens, and units digits of a, b, and c, respectively. The threedigit positive integer y has the hundreds, tens, and units digits of k, l, and m, respectively. If (2^a)(3^b)(5^c) = 12(2^k)(3^l)(5^m), what is the value of x – y?
A) 21 B) 200 C) 210 D) 300 E) 310 x = abc, where a, b, and c, are the hundreds, tens, and units digits, respectively. y= klm, where k, l, and m, are the hundreds, tens, and units digits, respectively. \((2^a)(3^b)(5^c) = 12(2^k)(3^l)(5^m)\) > \(2^{ak}*3^{bl}*5^{cm}=2^2*3\) > \(ak=2\), \(bl=1\), and \(cm=0\) > \(xy=210\). Answer: C. I am sorry but i dont understand the slightest thing of what's going on here. How does that suddenly translate to 2^2*3? really confused here. \((2^a)(3^b)(5^c) = 12(2^k)(3^l)(5^m)\); \(\frac{(2^a)(3^b)(5^c)}{(2^k)(3^l)(5^m)} = 12\); \(2^{ak}*3^{bl}*5^{cm}=2^2*3\). Similar questions to practice: kandlareeachfourdigitpositiveintegerswiththousands91004.htmlforanyfourdigitnumberabcdabcd3a5b7c11d126522.htmlkandlareeachfourdigitpositiveintegerswiththousands126646.htmlthefunctionfisdefinedforeachpositivethreedigit100847.htmlforathreedigitnumberxyzwherexyandzarethe59284.htmlHope it helps.
_________________
New to the Math Forum? Please read this: 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



GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15961

Re: The threedigit positive integer x has the hundreds, [#permalink]
Show Tags
20 Mar 2016, 06:19
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources



Senior Manager
Status: Professional GMAT Tutor
Affiliations: AB, cum laude, Harvard University (Class of '02)
Joined: 10 Jul 2015
Posts: 367
Location: United States (CA)
GMAT 1: 770 Q47 V48 GMAT 2: 730 Q44 V47
GRE 1: 337 Q168 V169
WE: Education (Education)

Re: The threedigit positive integer x has the hundreds, [#permalink]
Show Tags
31 Mar 2016, 18:11
1
This post was BOOKMARKED
Attached is a visual that should help.
Attachments
Screen Shot 20160331 at 6.10.08 PM.png [ 137.01 KiB  Viewed 2257 times ]
_________________
Harvard grad and 770 GMAT scorer, offering highquality private GMAT tutoring, both inperson and via Skype, since 2002.
McElroy Tutoring



GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15961

Re: The threedigit positive integer x has the hundreds, [#permalink]
Show Tags
28 Apr 2017, 03:32
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources



Intern
Joined: 14 Jan 2017
Posts: 1

Re: The threedigit positive integer x has the hundreds, [#permalink]
Show Tags
28 Apr 2017, 04:57
what is the next step after this 2a−k∗3b−l∗5c−m=22∗32a−k∗3b−l∗5c−m=22∗3 ? I cant figure it out. can someone break this down well for me please




Re: The threedigit positive integer x has the hundreds,
[#permalink]
28 Apr 2017, 04:57







