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# If a and b are integers, what is the value of (8a^6b − 2)?

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Math Expert
Joined: 02 Sep 2009
Posts: 59590
If a and b are integers, what is the value of (8a^6b − 2)?  [#permalink]

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01 Oct 2018, 04:33
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Difficulty:

35% (medium)

Question Stats:

73% (01:30) correct 27% (01:19) wrong based on 40 sessions

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If a and b are integers, what is the value of $$(8a^{6b} − 2)$$?

(1) $$a^{2b} = 2^4$$

(2) $$ab = 2^2$$

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Re: If a and b are integers, what is the value of (8a^6b − 2)?  [#permalink]

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01 Oct 2018, 04:45
Bunuel wrote:
If a and b are integers, what is the value of $$(8a^{6b} − 2)$$?

(1) $$a^{2b} = 2^4$$

(2) $$ab = 2^2$$

Question: what is the value of $$(8a^{6b} − 2) = 8(a^b)^6-2$$?

To answer this question we only need $$a^b$$

Statement 1: $$a^{2b} = 2^4$$

i.e. $$(a^b)^2 = 16$$

i.e. $$(a^b) = +4 or -4$$ hence

BUT $$8(a^b)^6-2 = 8*4^6-2$$

SUFFICIENT

Statement 2: $$ab = 2^2$$

i.e. a*b = 4
i.e. a=1 and b=4 or a=4 and b=1 hence $$a^b$$ will have multple values hence
NOT SUFFICIENT

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Re: If a and b are integers, what is the value of (8a^6b − 2)?   [#permalink] 01 Oct 2018, 04:45
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