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Is (9^x)^(3 – 2x) = 1? (1) The product of x and positive integer y is

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Bunuel
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Is (9^x)^(3 – 2x) = 1? (1) The product of x and positive integer y is [#permalink] New post   29 Apr 2019, 06:05
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Is \((9^x)^{3 – 2x} = 1\)?

(1) The product of x and positive integer y is not x.
(2) x is a integer.
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chetan2u
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Is (9^x)^(3 – 2x) = 1? (1) The product of x and positive integer y is [#permalink] New post   02 May 2019, 22:42
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Mohammad Ali Khan wrote:
Sorry m unable to get your explanation. Could you please elab.. how to approach these problems.


Is \((9^x)^{3 – 2x} = 1\)?

\((9^x)^{3-2x}=(3^{2x})^{3-2x}=3^{2x(3-2x)}=1..\) Now, when can left hand side become 0.. ONLY when the exponent 2x(3-2x)=0.
That is \(3^{2x(3-2x)}=3^0..\)
Now, WHEN will 2x(3-x) be 0....When 2x =0, that is x=0 OR 3-2x=0, that is x=3/2.
So, the question finally becomes - Is x any one of 0 or 3/2.

(1) The product of x and positive integer y is not x.
\(xy\neq{x}......xy-x\neq{0}......x(y-1)\neq{0}\)... So, x is NOT 0, neither is y equal to 1.
If x=3/2 ans is yes, otherwise No.
Insuff

(2) x is a integer.
Nothing much..
If x is 0, ans is yes, otherwise no..
Insuff

combined..
Now answer is yes, when x is 0 or 3/2, otherwise NO.
Statement I tells us that x is not 0, and statement II tells us that x is not 3/2..
So, answer is NO.
Suff

C
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nick1816
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Is (9^x)^(3 – 2x) = 1? (1) The product of x and positive integer y is [#permalink] New post   Updated on: 02 May 2019, 09:22
Statement 1
x can be any real number except 0 and y can't be 1
Hence x might be 3/2 or not.
Insufficient
Statement 2
x can be 0 or not
Insufficient
combining both statements
x can't be equal to 0 or 3/2
sufficient

Originally posted by nick1816 on 29 Apr 2019, 06:28.
Last edited by nick1816 on 02 May 2019, 09:22, edited 1 time in total.
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Re: Is (9^x)^(3 – 2x) = 1? (1) The product of x and positive integer y is [#permalink] New post   29 Apr 2019, 09:16
Bunuel wrote:
Is \((9^x)^{3 – 2x} = 1\)?

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


#1
y is not given in any relation insufficient
#2
x integer so sufficeint to say \((9^x)^{3 – 2x} = 1\) is NO
IMO B
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Re: Is (9^x)^(3 – 2x) = 1? (1) The product of x and positive integer y is [#permalink] New post   29 Apr 2019, 10:07
At x=0 \((9^x)^{3 – 2x} = 1\)

Archit3110 wrote:
Bunuel wrote:
Is \((9^x)^{3 – 2x} = 1\)?

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


#1
y is not given in any relation insufficient
#2
x integer so sufficeint to say \((9^x)^{3 – 2x} = 1\) is NO
IMO B
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Re: Is (9^x)^(3 – 2x) = 1? (1) The product of x and positive integer y is [#permalink] New post   29 Apr 2019, 10:21
The stem can be reduced to 3^2x. his can be 1 when x =0
Statement 1: (x * y) != x. This means X does not equal to Zero. sufficient.
Statement 2: x is an integer - not mentioned positive or negative - zero is also an integer but neither positive nor negative. Hence
IMO A correct option.
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Re: Is (9^x)^(3 – 2x) = 1? (1) The product of x and positive integer y is [#permalink] New post   01 May 2019, 23:44
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Bunuel wrote:
Is \((9^x)^{3 – 2x} = 1\)?

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



Solution:
(9x)3–2x=1 only if x(3-2x)=0 OR if x=0 or X=3/2
Statement-1:
Xy ≠ x implies that y ≠ 1 and x ≠ 0 But we don’t know about the exact value of x, it could be 3/2, in that case the expression is equal to 1 otherwise not. Insufficient
Statement-2:
X is an integer that means x ≠ 3/2 But we don’t know about the exact value of x, it could be 0, in that case the expression is equal to 1 otherwise not. Insufficient

Combining Statement (1) & (2) x ≠ 0 and x ≠ 3/2. So the Answer is NO. Sufficient
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Re: Is (9^x)^(3 – 2x) = 1? (1) The product of x and positive integer y is [#permalink] New post   02 May 2019, 09:17
ArupRS wrote:
The stem can be reduced to 3^2x. his can be 1 when x =0
Statement 1: (x * y) != x. This means X does not equal to Zero. sufficient.
Statement 2: x is an integer - not mentioned positive or negative - zero is also an integer but neither positive nor negative. Hence
IMO A correct option.


Bunuel and chetan2u

Please help me to understand where was I wrong.

Regards,
Arup Sarkar
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Re: Is (9^x)^(3 – 2x) = 1? (1) The product of x and positive integer y is [#permalink] New post   02 May 2019, 09:26
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ArupRS wrote:
ArupRS wrote:
The stem can be reduced to 3^2x. his can be 1 when x =0
Statement 1: (x * y) != x. This means X does not equal to Zero. sufficient.
Statement 2: x is an integer - not mentioned positive or negative - zero is also an integer but neither positive nor negative. Hence
IMO A correct option.


Bunuel and chetan2u

Please help me to understand where was I wrong.

Regards,
Arup Sarkar



The entire term is \((9^x)^{3-2x}=(3^{2x})^{3-2x}..\)
So, you have found one part 3^2x but what if 3-2x=0...X=3/2..
Thus two values possible X as 0 or X as 3/2..
Combined it is not 0 but an integer, so even 3/2 is out.
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Re: Is (9^x)^(3 – 2x) = 1? (1) The product of x and positive integer y is [#permalink] New post   02 May 2019, 22:14
chetan2u wrote:
ArupRS wrote:
ArupRS wrote:
The stem can be reduced to 3^2x. his can be 1 when x =0
Statement 1: (x * y) != x. This means X does not equal to Zero. sufficient.
Statement 2: x is an integer - not mentioned positive or negative - zero is also an integer but neither positive nor negative. Hence
IMO A correct option.


Bunuel and chetan2u

Please help me to understand where was I wrong.

Regards,
Arup Sarkar



The entire term is \((9^x)^{3-2x}=(3^{2x})^{3-2x}..\)
So, you have found one part 3^2x but what if 3-2x=0...X=3/2..
Thus two values possible X as 0 or X as 3/2..
Combined it is not 0 but an integer, so even 3/2 is out.



Sorry m unable to get your explanation. Could you please elab.. how to approach these problems.
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Re: Is (9^x)^(3 – 2x) = 1? (1) The product of x and positive integer y is [#permalink] New post   03 May 2019, 08:41
chetan2u wrote:
Mohammad Ali Khan wrote:
Sorry m unable to get your explanation. Could you please elab.. how to approach these problems.


Is \((9^x)^{3 – 2x} = 1\)?

\((9^x)^{3-2x}=(3^{2x})^{3-2x}=3^{2x(3-2x)}=1..\) Now, when can left hand side become 0.. ONLY when the exponent 2x(3-2x)=0.
That is \(3^{2x(3-2x)}=3^0..\)
Now, WHEN will 2x(3-x) be 0....When 2x =0, that is x=0 OR 3-2x=0, that is x=3/2.
So, the question finally becomes - Is x any one of 0 or 3/2.

(1) The product of x and positive integer y is not x.
\(xy\neq{x}......xy-x\neq{0}......x(y-1)\neq{0}\)... So, x is NOT 0, neither is y equal to 1.
If x=3/2 ans is yes, otherwise No.
Insuff

(2) x is a integer.
Nothing much..
If x is 0, ans is yes, otherwise no..
Insuff

combined..
Now answer is yes, when x is 0 or 3/2, otherwise NO.
Statement I tells us that x is not 0, and statement II tells us that x is not 3/2..
So, answer is NO.
Suff

C


Mistakenly, I have reduced 2x(3-2x) to 2x, but it is 6x-4x^2.
Thanks for clarifying this.
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Re: Is (9^x)^(3 – 2x) = 1? (1) The product of x and positive integer y is [#permalink] New post   14 Nov 2019, 14:34
chetan2u wrote:
Mohammad Ali Khan wrote:
Sorry m unable to get your explanation. Could you please elab.. how to approach these problems.


Is \((9^x)^{3 – 2x} = 1\)?

\((9^x)^{3-2x}=(3^{2x})^{3-2x}=3^{2x(3-2x)}=1..\) Now, when can left hand side become 0.. ONLY when the exponent 2x(3-2x)=0.
That is \(3^{2x(3-2x)}=3^0..\)
Now, WHEN will 2x(3-x) be 0....When 2x =0, that is x=0 OR 3-2x=0, that is x=3/2.
So, the question finally becomes - Is x any one of 0 or 3/2.

(1) The product of x and positive integer y is not x.
\(xy\neq{x}......xy-x\neq{0}......x(y-1)\neq{0}\)... So, x is NOT 0, neither is y equal to 1.
If x=3/2 ans is yes, otherwise No.
Insuff

(2) x is a integer.
Nothing much..
If x is 0, ans is yes, otherwise no..
Insuff

combined..
Now answer is yes, when x is 0 or 3/2, otherwise NO.
Statement I tells us that x is not 0, and statement II tells us that x is not 3/2..
So, answer is NO.
Suff

C


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Re: Is (9^x)^(3 2x) = 1? (1) The product of x and positive integer y is [#permalink] New post   03 Dec 2022, 23:42
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Re: Is (9^x)^(3 2x) = 1? (1) The product of x and positive integer y is [#permalink]
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