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

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Is (4^x)^(5-3x) = 1 ? [#permalink] New post 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] New post 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] New post 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.

Answer: C.
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Re: Is (4^x)^(5-3x) = 1 ? [#permalink] New post 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.

Answer: C.




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] New post 26 Apr 2014, 08:58
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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.

Answer: C.




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] New post 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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Re: Is (4^x)^(5-3x) = 1 ? [#permalink] New post 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

So, Answer will be C

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] New post 21 Aug 2014, 13:44
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Exponents and number properties [#permalink] New post 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.
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Re: Is (4^x)^(5-3x) = 1 ? [#permalink] New post 07 Sep 2014, 08:21
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Re: Is (4^x)^(5-3x) = 1 ?   [#permalink] 07 Sep 2014, 08:21
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