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a×b×c=d×e×f=b×g×e

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Joined: 21 Jan 2017
Posts: 10
a×b×c=d×e×f=b×g×e [#permalink]

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New post 28 Jan 2017, 19:25
If
a×b×c=d×e×f=b×g×e
and each one's value is in between 1-9 and distinct. What is the value of g?

(A) 8
(B) 9
(C) 2
(D) 6

Sent from my Lenovo A6020a46 using GMAT Club Forum mobile app
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Joined: 16 Aug 2015
Posts: 5839
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Re: a×b×c=d×e×f=b×g×e [#permalink]

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New post 01 Feb 2017, 17:31
Harshit401 wrote:
If
a×b×c=d×e×f=b×g×e
and each one's value is in between 1-9 and distinct. What is the value of g?

(A) 8
(B) 9
(C) 2
(D) 6

Sent from my Lenovo A6020a46 using GMAT Club Forum mobile app



Hi Harshit401,

5, 7 can't be any variable among a, b, c, ... , f, g, since they are prime numbers and they showed up just once.
Hence a, b, c, ... g are from 1, 2, 3, 4, 6, 8, 9

(axbxc)x(dxexf)x(bxgxe) is the type of 2^(3k) * 3^(3n), but axbxcxdxexfxg = 1x2x3x4x6x8x9 = 2^7 * 3^4.
And so b * e = 2^2 * 3^2 and (axbxc) = (dxexf) = (bxgxe) = 2^3 * 3^2.
Therefore g = 2


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Re: a×b×c=d×e×f=b×g×e   [#permalink] 01 Feb 2017, 17:31
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