Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

 It is currently 24 May 2017, 23:23

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# The three-digit positive integer x has the hundreds,

Author Message
TAGS:

### Hide Tags

Senior Manager
Joined: 03 Dec 2012
Posts: 344
Followers: 1

Kudos [?]: 141 [2] , given: 291

The three-digit positive integer x has the hundreds, [#permalink]

### Show Tags

15 Nov 2013, 08:00
2
KUDOS
7
This post was
BOOKMARKED
00:00

Difficulty:

5% (low)

Question Stats:

85% (02:35) correct 15% (02:07) wrong based on 282 sessions

### HideShow timer Statistics

The three-digit positive integer x has the hundreds, tens, and units digits of a, b, and c, respectively. The three-digit 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
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Sep 2009
Posts: 38859
Followers: 7728

Kudos [?]: 106061 [1] , given: 11607

Re: The three-digit positive integer x has the hundreds, [#permalink]

### Show Tags

15 Nov 2013, 08:09
1
KUDOS
Expert's post
6
This post was
BOOKMARKED
mohnish104 wrote:
The three-digit positive integer x has the hundreds, tens, and units digits of a, b, and c, respectively. The three-digit 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.

$$(2^a)(3^b)(5^c) = 12(2^k)(3^l)(5^m)$$ --> $$2^{a-k}*3^{b-l}*5^{c-m}=2^2*3$$ --> $$a-k=2$$, $$b-l=1$$, and $$c-m=0$$ --> $$x-y=210$$.

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 38859
Followers: 7728

Kudos [?]: 106061 [0], given: 11607

Re: The three-digit positive integer x has the hundreds, [#permalink]

### Show Tags

15 Nov 2013, 08:13
Expert's post
1
This post was
BOOKMARKED
Bunuel wrote:
mohnish104 wrote:
The three-digit positive integer x has the hundreds, tens, and units digits of a, b, and c, respectively. The three-digit 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.

$$(2^a)(3^b)(5^c) = 12(2^k)(3^l)(5^m)$$ --> $$2^{a-k}*3^{b-l}*5^{c-m}=2^2*3$$ --> $$a-k=2$$, $$b-l=1$$, and $$c-m=0$$ --> $$x-y=210$$.

Similar questions to practice:
k-and-l-are-each-four-digit-positive-integers-with-thousands-126646.html
the-function-f-is-defined-for-each-positive-three-digit-100847.html
for-any-four-digit-number-abcd-abcd-3-a-5-b-7-c-11-d-126522.html

Hope this helps.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15433
Followers: 649

Kudos [?]: 207 [0], given: 0

Re: The three-digit 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.
_________________
Manager
Joined: 13 Dec 2013
Posts: 57
GPA: 2.71
Followers: 0

Kudos [?]: 5 [0], given: 21

Re: The three-digit 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)
Followers: 51

Kudos [?]: 2168 [2] , given: 193

The three-digit positive integer x has the hundreds, [#permalink]

### Show Tags

02 Dec 2014, 02:00
2
KUDOS
1
This post was
BOOKMARKED
x = 100a + 10b + c ........... (1)

y = 100k + 10l + m ............ (2)

We require to find x-y

(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

_________________

Kindly press "+1 Kudos" to appreciate

Intern
Joined: 23 Sep 2014
Posts: 15
Followers: 0

Kudos [?]: 0 [0], given: 6

Re: The three-digit positive integer x has the hundreds, [#permalink]

### Show Tags

09 Dec 2014, 08:58
Bunuel wrote:
mohnish104 wrote:
The three-digit positive integer x has the hundreds, tens, and units digits of a, b, and c, respectively. The three-digit 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.

$$(2^a)(3^b)(5^c) = 12(2^k)(3^l)(5^m)$$ --> $$2^{a-k}*3^{b-l}*5^{c-m}=2^2*3$$ --> $$a-k=2$$, $$b-l=1$$, and $$c-m=0$$ --> $$x-y=210$$.

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: 38859
Followers: 7728

Kudos [?]: 106061 [0], given: 11607

Re: The three-digit positive integer x has the hundreds, [#permalink]

### Show Tags

09 Dec 2014, 09:03
Expert's post
1
This post was
BOOKMARKED
JoostGrijsen wrote:
Bunuel wrote:
mohnish104 wrote:
The three-digit positive integer x has the hundreds, tens, and units digits of a, b, and c, respectively. The three-digit 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.

$$(2^a)(3^b)(5^c) = 12(2^k)(3^l)(5^m)$$ --> $$2^{a-k}*3^{b-l}*5^{c-m}=2^2*3$$ --> $$a-k=2$$, $$b-l=1$$, and $$c-m=0$$ --> $$x-y=210$$.

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.

$$(2^a)(3^b)(5^c) = 12(2^k)(3^l)(5^m)$$;

$$\frac{(2^a)(3^b)(5^c)}{(2^k)(3^l)(5^m)} = 12$$;

$$2^{a-k}*3^{b-l}*5^{c-m}=2^2*3$$.

Similar questions to practice:
k-and-l-are-each-four-digit-positive-integers-with-thousands-91004.html
for-any-four-digit-number-abcd-abcd-3-a-5-b-7-c-11-d-126522.html
k-and-l-are-each-four-digit-positive-integers-with-thousands-126646.html
the-function-f-is-defined-for-each-positive-three-digit-100847.html
for-a-three-digit-number-xyz-where-x-y-and-z-are-the-59284.html

Hope it helps.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15433
Followers: 649

Kudos [?]: 207 [0], given: 0

Re: The three-digit 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.
_________________
Senior Manager
Status: Professional GMAT Tutor
Affiliations: AB, cum laude, Harvard University (Class of '02)
Joined: 10 Jul 2015
Posts: 348
Location: United States (CA)
GMAT 1: 770 Q47 V48
GMAT 2: 730 Q44 V47
GRE 1: 337 Q168 V169
WE: Education (Education)
Followers: 59

Kudos [?]: 352 [0], given: 45

Re: The three-digit 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 2016-03-31 at 6.10.08 PM.png [ 137.01 KiB | Viewed 2127 times ]

_________________

Harvard grad and 770 GMAT scorer, offering high-quality private GMAT tutoring, both in-person and via Skype, since 2002.

McElroy Tutoring

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15433
Followers: 649

Kudos [?]: 207 [0], given: 0

Re: The three-digit 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.
_________________
Intern
Joined: 14 Jan 2017
Posts: 1
Followers: 0

Kudos [?]: 0 [0], given: 0

Re: The three-digit 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 three-digit positive integer x has the hundreds,   [#permalink] 28 Apr 2017, 04:57
Similar topics Replies Last post
Similar
Topics:
7 a is the hundreds digit of the three digit integer x, b 7 11 Aug 2016, 07:41
11 If the integer x is rounded to the nearest hundred 6 01 Oct 2016, 14:53
6 A three-digit positive integer is chosen at random. What is 7 13 Sep 2016, 08:07
6 If x is an integer that has exactly three positive divisors 9 05 Jun 2016, 00:19
85 If x represents the sum of all the positive three-digit 18 31 Mar 2017, 01:50
Display posts from previous: Sort by