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Updated on: 08 Jul 2014, 02:35
Originally posted by imhimanshu on 21 May 2013, 08:23.
Last edited by Bunuel on 08 Jul 2014, 02:35, edited 3 times in total.
Last edited by Bunuel on 08 Jul 2014, 02:35, edited 3 times in total.
Renamed the topic and edited the question.
Kudos
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
45% (02:54) correct
55%
(02:41)
wrong
based on 259
sessions
History
Date
Time
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Not Attempted Yet
The Least Common multiple of 2^6-1 and 2^9-1 is:
A. \(2^{12}+27*2^9-217\)
B. \(2^{12} +63*2^3-1\)
C. \(2^{12}+5^{29}-1\)
D. \(2^{12}+9*2^8 -1\)
E. None of these.
A. \(2^{12}+27*2^9-217\)
B. \(2^{12} +63*2^3-1\)
C. \(2^{12}+5^{29}-1\)
D. \(2^{12}+9*2^8 -1\)
E. None of these.
21 May 2013, 10:35
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Factoralization (refer herefor the formulas)
\(2^6-1=(2^3+1)(2^3-1)=9*7=3*3*7\)
\(2^9-1=(2^3-1)(2^6+2^3+1)=7*73\)
\(LCM=9*7*73=(2^3+1)(2^3-1)(2^6+2^3+1)=(2^6-1)(2^6+2^3+1)=2^{12}+2^3(2^6-1)-1\)
b) \(2^ {12} +63*2^3-1\)
\(2^6-1=(2^3+1)(2^3-1)=9*7=3*3*7\)
\(2^9-1=(2^3-1)(2^6+2^3+1)=7*73\)
\(LCM=9*7*73=(2^3+1)(2^3-1)(2^6+2^3+1)=(2^6-1)(2^6+2^3+1)=2^{12}+2^3(2^6-1)-1\)
b) \(2^ {12} +63*2^3-1\)
21 May 2013, 21:18
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imhimanshu
Responding to a pm:
The best approach in my opinion is what Zarrolou has suggested above.
LCM * GCF = Product of the numbers = \((2^6-1)*(2^9-1) = (2^3 - 1)(2^3 + 1) * (2^3 - 1)(2^6 + 1 + 2^3)\)
Notice that the only common factor between them is \((2^3 - 1)\) so this must be the GCF. Hence LCM will be the rest of the product.
\(LCM = (2^3 + 1) * (2^3 - 1)(2^6 + 1 + 2^3) = (2^6 - 1)(2^6 + 1 + 2^3)\)
Now how do you get it in the format in the options? Almost all options have \(2^{12}\) and 1 so retain those two and club everything else together.
\(LCM = 2^{12} - 1 + (2^6 + 2^9 - 2^6 - 2^3) = 2^{12} - 1 + 2^3(2^6 - 1) = 2^{12} - 1 + 2^3*63\)
Answer (B)
Note that option 'none of these' makes it more complicated since you cannot try some more esoteric methods e.g. last digit etc. GMAT doesn't give you this option. Also, GMAT doesn't expect you to know a^3 - b^3 = (a-b)(a^2 + ab + b^2). Of course, you should be able to arrive at the LHS, given the RHS.
Hence, there are very few CAT questions which will actually be GMAT relevant. If you are practicing for GMAT, try to stick to a GMAT source, especially if you have limited time.
