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The three-digit positive integer x has the hundreds,

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The three-digit positive integer x has the hundreds, [#permalink] New post 15 Nov 2013, 07:00
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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
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Re: The three-digit positive integer x has the hundreds, [#permalink] New post 15 Nov 2013, 07:09
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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.

Answer: C.
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Re: The three-digit positive integer x has the hundreds, [#permalink] New post 15 Nov 2013, 07:13
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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.

Answer: C.


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.
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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.


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Re: The three-digit positive integer x has the hundreds, [#permalink] New post 01 Dec 2014, 12:06
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Re: The three-digit positive integer x has the hundreds, [#permalink] New post 01 Dec 2014, 23:11
Hi Brunel,
Can you please explain the right side of this equation :)
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The three-digit positive integer x has the hundreds, [#permalink] New post 02 Dec 2014, 01:00
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

Answer = C
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Re: The three-digit positive integer x has the hundreds, [#permalink] New post 09 Dec 2014, 07:58
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.

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.
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Re: The three-digit positive integer x has the hundreds, [#permalink] New post 09 Dec 2014, 08:03
Expert's post
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.

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^{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.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

GMAT Club Premium Membership - big benefits and savings

Re: The three-digit positive integer x has the hundreds,   [#permalink] 09 Dec 2014, 08:03
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