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

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Is (4^x)^(5-3x) = 1 ? [#permalink]

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12 Nov 2009, 12:03
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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, 12:40, edited 1 time in total.
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Re: Is (4^x)^(5-3x) = 1 ? [#permalink]

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12 Nov 2009, 12:33
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]

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12 Nov 2009, 12:45
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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]

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26 Apr 2014, 01:07
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]

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26 Apr 2014, 09:58
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]

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21 Aug 2014, 09:24
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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]

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21 Aug 2014, 10:22
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]

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21 Aug 2014, 14:44
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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Re: Is (4^x)^(5-3x) = 1 ? [#permalink]

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

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17 Oct 2015, 22:31
Expert's post
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

Is (4 ^x )^ (5−3x) =1 ?

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

If we modify the original condition and the question, we ultimately want to know whether 4^x(5-3x)=1=4^0, x(5-3x)=0, so whether x=0 or x=5/3.
There is only one variable, so we only need one equation, when 2 equations are given from the 2 conditions; there is high chance (D) will be our answer.
For condition 1, the answer becomes 'yes' for x=integer=0, but 'no' when x=1. This condition is insufficient.
For condition 2, on the other hand, we get xy=/=x, x(y-1)=/=0, so likewise, the answer to the question becomes 'yes' for x=5/3 and y=2, but 'no' for x=3 and y=2. This is, again, insufficient.
Combining the 2 conditions, the answer becomes 'no' for all x=1,2,3....... This is sufficient, so the answer becomes (C). This type of question is no longer asked in the test.

For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
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Re: Is (4^x)^(5-3x) = 1 ? [#permalink]

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19 Oct 2015, 05:53
Expert's post
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.

Required: $$(4^x)^{(5-3x)}=1$$
Or simply x*(5-3x) = 0
This can be simplified to x = 0 or 3/5
Hence simply we need to tell if x = 0 or 3/5

Statement 1: x is an integer
We do not know any specific value of x from this statement
INSUFFICIENT

Statement 2: The product of x and positive integer y is not x
x*y ≠ x. Hence x ≠ 0
But we do not know anything else about x
INSUFFICIENT

Combining Statement 1 and Statement 2:
We know that x is an integer, but ≠ 0
Hence x ≠ 0 and x ≠ 3/5
Thus we can say that $$(4^x)^{(5-3x)} ≠ 1$$
SUFFICIENT

Option C
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Re: Is (4^x)^(5-3x) = 1 ?   [#permalink] 19 Oct 2015, 05:53
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