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Bunuel
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What is the value of k, if (4^3)(5^8)k = 1,000,0000,000? 06 Jun 2019, 00:37
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

35% (medium)

Question Stats:

67% (01:24) correct 33% (01:41) wrong based on 85 sessions

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What is the value of k, if \((4^3)(5^8)k = 1,000,0000,000\)?

A. 4
B. 40
C. 400
D. 4,000
E. 40,000
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C
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What is the value of k, if (4^3)(5^8)k = 1,000,0000,000? 06 Jun 2019, 00:41
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\(2^6*5^8*k=2^10*5^10\)
\(k=2^4*5^2=400\)

IMO
Ans: C
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What is the value of k, if (4^3)(5^8)k = 1,000,0000,000? 06 Jun 2019, 00:47
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Bunuel
What is the value of k, if \((4^3)(5^8)k = 1,000,0000,000\)?

A. 4
B. 40
C. 400
D. 4,000
E. 40,000
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4^3*5^8 can be written as 10^6*5^2.

10^6*5^2*K = 10,000,000,000 ; will result in 25K=10000; K = 400 IMO option C
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What is the value of k, if (4^3)(5^8)k = 1,000,0000,000? Updated on: 06 Jun 2019, 11:48
Originally posted by eakabuah on 06 Jun 2019, 00:55.
Last edited by eakabuah on 06 Jun 2019, 11:48, edited 1 time in total.
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(4^3)x(5^8)k=10,000,000,000
=(100)(100)(100)(100)
(100)
=(4x5^2)(4x5^2)
(4x5^2)(4x5^2)
(4x5^2).
=4^2x5^2x(4^3)x(5^8)
Hence k=4^2x5^2
=400

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What is the value of k, if (4^3)(5^8)k = 1,000,0000,000? 06 Jun 2019, 11:12
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Observe that the number of zeroes in the number on the RHS of the equation is 10. This means that the number of 5s on the LHS should also be 10; additionally, the number of 2s should also be 10.

\(4^3\) = \(2^6\). Therefore, we need \(2^4\) to make it \(2^{10}\). This has to come from k.

\(5^8\) needs to be multiplied by \(5^2\) to make it \(5^{10}\). Again, this has to come from k. Therefore,

k = \(2^4\) * \(5^2\) = 16 * 25 = 400.

The correct answer option is C.

Answer options A and E can be eliminated straight away because 4 does not have a power of 5 and 40000 will end up giving more zeroes when multiplied with \(4^3\)*\(5^8\).
The other two options can be eliminated basis the analysis done above.

Hope this helps!
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