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# Is (4^x)^(5-3x) = 1 ?

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Is (4^x)^(5-3x) = 1 ? [#permalink]  12 Nov 2009, 11:03
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Is $$(4^x)^{(5-3x)}=1$$?

(1) x is an integer.
(2) The product of x and positive integer y is not x.
[Reveal] Spoiler: OA

Last edited by kp1811 on 12 Nov 2009, 11:40, edited 1 time in total.
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Re: Is (4^x)^(5-3x) = 1 ? [#permalink]  12 Nov 2009, 11:33
kp1811 wrote:
Is $$(4^x)^{(5-3x)}=1$$?
(1) x is an integer.
(2) The product of x and positive integer y is not x.

For (4^x)^{(5-3x)}=1, 5x-3x^2=0 i.e x^2=5/3. If "x" is an integer this is not possible. So statement 1 is sufficient.

Statement 2 says that x is not= 0. This is not sufficient.

Hence "A" should be the answer.
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Re: Is (4^x)^(5-3x) = 1 ? [#permalink]  12 Nov 2009, 11:45
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kp1811 wrote:
Is $$(4^x)^{(5-3x)}=1$$?
(1) x is an integer.
(2) The product of x and positive integer y is not x.

First of all $$(4^x)^{(5-3x)}=4^{x*(5-3x)}$$

For this expression to be equal to 1, $$x*(5-3x)$$ must be equal to 0.

$$x*(5-3x)=0$$ --> $$x=0$$ or $$x=\frac{5}{3}$$.

So basically the question asks whether $$x=0$$ or $$x=\frac{5}{3}$$.

(1) x is an integer, hence x is not 5/3. But we don't know whether x is 0 or any other integer. Not sufficient.

(2) $$xy\neq{x}$$, hence x is not equal to 0. But x can be any other number, integer or not integer. Not sufficient.

(1)+(2) x is an integer but not 0. So, x is not 0, not 5/3. Hence $$x*(5-3x)\neq{0}$$, hence $$(4^x)^{(5-3x)}$$ does not equal to 1. Sufficient.

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Re: Is (4^x)^(5-3x) = 1 ? [#permalink]  26 Apr 2014, 00:07
Bunuel wrote:
kp1811 wrote:
Is $$(4^x)^{(5-3x)}=1$$?
(1) x is an integer.
(2) The product of x and positive integer y is not x.

First of all $$(4^x)^{(5-3x)}=4^{x*(5-3x)}$$

This expression to be equal to $$1$$, $$x*(5-3x)$$ must be equal to $$0$$.

$$x*(5-3x)=0$$, $$x=0$$or $$x=\frac{5}{3}$$.

So basically the question asks is $$x=0$$ or $$x=\frac{5}{3}$$.

(1) x is an integer, hence x is not 5/3. But we don't know whether x is 0 or any other integer. Not sufficient.

(2) $$xy\neq{x}$$, hence x is not equal to 0. But x can be any other number, integer or not integer. Not sufficient.

(1)+(2) x is an integer but not 0. So x is not 0, not 5/3. Hence x*(5-3x)#0, hence $$(4^x)^{(5-3x)}$$ does not equal to 1.

Hi Bunuel,
Is it not possible that the expression can be equal to 1 also because 1^1=1.
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Re: Is (4^x)^(5-3x) = 1 ? [#permalink]  26 Apr 2014, 08:58
Expert's post
seabhi wrote:
Bunuel wrote:
kp1811 wrote:
Is $$(4^x)^{(5-3x)}=1$$?
(1) x is an integer.
(2) The product of x and positive integer y is not x.

First of all $$(4^x)^{(5-3x)}=4^{x*(5-3x)}$$

This expression to be equal to $$1$$, $$x*(5-3x)$$ must be equal to $$0$$.

$$x*(5-3x)=0$$, $$x=0$$or $$x=\frac{5}{3}$$.

So basically the question asks is $$x=0$$ or $$x=\frac{5}{3}$$.

(1) x is an integer, hence x is not 5/3. But we don't know whether x is 0 or any other integer. Not sufficient.

(2) $$xy\neq{x}$$, hence x is not equal to 0. But x can be any other number, integer or not integer. Not sufficient.

(1)+(2) x is an integer but not 0. So x is not 0, not 5/3. Hence x*(5-3x)#0, hence $$(4^x)^{(5-3x)}$$ does not equal to 1.

Hi Bunuel,
Is it not possible that the expression can be equal to 1 also because 1^1=1.

We have $$4^{x*(5-3x)}=1$$. The left-hand side is 4 in some power, not 1^1.
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Re: Is (4^x)^(5-3x) = 1 ? [#permalink]  21 Aug 2014, 08:24
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Is (4^x)^(5-3x) = 1?

(1) x is an integer.
(2) The product of x and positive integer y is not x.
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Kudos [?]: 378 [0], given: 47

Re: Is (4^x)^(5-3x) = 1 ? [#permalink]  21 Aug 2014, 09:22
STAT1
x is an integer
If x = 0 then
(4^x)^(5-3x) = (4^0)^(5-3*0) = 1 which is TRUE
If x = 1 then
(4^x)^(5-3x) = (4^1)^(5-3*1) = 16 not equal to 1 so FALSE
So, INSUFFICIENT

STAT2
product of x and y is not x => x is NOT equal to 0
So, x can be 1, then (4^x)^(5-3x) != 1, So, FALSE
Also, x can be fraction
If x= 5/3 then
(4^x)^(5-3x) = (4^5/3)^(5-3*5/3)) = (4^5/3)^0 = 1, So, TRUE
So, INSUFFICIENT

STAT1 and STAT2 together
We know that x is an integer and is not 0
For all values of x, (4^x)^(5-3x) will never be equal to 1 (substitute and check)
So, SUFFICIENT

Hope it helps!

goodyear2013 wrote:
Is (4^x)^(5-3x) = 1?
(1) x is an integer.
(2) The product of x and positive integer y is not x.

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Re: Is (4^x)^(5-3x) = 1 ? [#permalink]  21 Aug 2014, 13:44
Expert's post
goodyear2013 wrote:
Is (4^x)^(5-3x) = 1?

(1) x is an integer.
(2) The product of x and positive integer y is not x.

Merging similar topics. Please refer to the discussion above.
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Exponents and number properties [#permalink]  07 Sep 2014, 08:14
Is$$(4^x)^(5-3x)$$ ?

(1) x is an integer.

(2) The product of x and positive integer y is not x.
Math Expert
Joined: 02 Sep 2009
Posts: 28781
Followers: 4593

Kudos [?]: 47409 [0], given: 7123

Re: Is (4^x)^(5-3x) = 1 ? [#permalink]  07 Sep 2014, 08:21
Expert's post
nitin6305 wrote:
Is$$(4^x)^(5-3x)$$ ?

(1) x is an integer.

(2) The product of x and positive integer y is not x.

Merging similar topics. Please refer to the discussion above.
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Re: Is (4^x)^(5-3x) = 1 ?   [#permalink] 07 Sep 2014, 08:21
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