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

Question

Is  (9^x)^{3 – 2x} = 1 ?

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

chetan2u · Accepted Answer

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
eq{x}......xy-x
eq{0}......x(y-1)
eq{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

nick1816 · Answer

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

Archit3110 · Answer

#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

nick1816 · Answer

At x=0  (9^x)^{3 – 2x} = 1

ArupRS · Answer

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.

krish9679 · Answer

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

ArupRS · Answer

Bunuel  and  chetan2u

Please help me to understand where was I wrong.

Regards,
Arup Sarkar

chetan2u · Answer

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.

Mohammad Ali Khan · Answer

Sorry m unable to get your explanation. Could you please elab.. how to approach these problems.

ArupRS · Answer

Mistakenly, I have reduced 2x(3-2x) to 2x, but it is 6x-4x^2. 
Thanks for clarifying this.

Aderonke01 · Answer

Posted from my mobile device

bumpbot · Answer

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

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

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