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# If 1,485 = a^x*b^y*c^z, then abc = ?

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Math Expert
Joined: 02 Sep 2009
Posts: 61549
If 1,485 = a^x*b^y*c^z, then abc = ?  [#permalink]

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11 Nov 2019, 03:05
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Difficulty:

95% (hard)

Question Stats:

30% (02:04) correct 70% (01:49) wrong based on 105 sessions

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If $$1,485= a^x b^y c^z$$, then $$abc=$$ ?

(1) $$1485 = a^3bc$$

(2) $$c = 11$$

Are You Up For the Challenge: 700 Level Questions

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Posts: 8254
Re: If 1,485 = a^x*b^y*c^z, then abc = ?  [#permalink]

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11 Nov 2019, 07:41
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If $$1,485= a^x b^y c^z$$, then $$abc=$$ ?
$$1485=3^3*5*11$$

(1) $$1485 = a^3bc$$

(2) $$c = 11$$

Combined..
We know that c=11, but a and b could be anything as it is NOT given that they are integers..
$$1485=a^3*b*11...a^3b=135=3*3*3*5.$$.
$$a=3$$, and $$b=5...abc=3*5*11$$.
$$a=135^{\frac{1}{3}}$$ and $$b=1.....abc = 135^{\frac{1}{3}}*1*11$$
Insuff

E
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Re: If 1,485 = a^x*b^y*c^z, then abc = ?  [#permalink]

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15 Nov 2019, 05:53
Very tricky. It's not given a b and c are prime , neither it's given that they are integers . Got it wrong :D

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Joined: 08 Aug 2017
Posts: 695
Re: If 1,485 = a^x*b^y*c^z, then abc = ?  [#permalink]

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16 Nov 2019, 20:26
Sometimes it becomes very important to consider 0 and 1 in calculation.
We should give more attention if 0 and 1 could be included in calculation or not.
Intern
Joined: 05 Nov 2015
Posts: 14
Re: If 1,485 = a^x*b^y*c^z, then abc = ?  [#permalink]

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06 Jan 2020, 00:02
chetan2u wrote:
If $$1,485= a^x b^y c^z$$, then $$abc=$$ ?
$$1485=3^3*5*11$$

(1) $$1485 = a^3bc$$

(2) $$c = 11$$

Combined..
We know that c=11, but a and b could be anything as it is NOT given that they are integers..
$$1485=a^3*b*11...a^3b=135=3*3*3*5.$$.
$$a=3$$, and $$b=5...abc=3*5*11$$.
$$a=135^{\frac{1}{3}}$$ and $$b=1.....abc = 135^{\frac{1}{3}}*1*11$$
Insuff

E

This is impossible to think at exam.....it seems we are not giving exam for GMAT its for some CIA OR KGB OR MOSSAD.....Crazy thinking....By the way nice explation.....
Intern
Joined: 27 May 2018
Posts: 17
If 1,485 = a^x*b^y*c^z, then abc = ?  [#permalink]

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10 Jan 2020, 18:53
Bunuel wrote:
If $$1,485= a^x b^y c^z$$, then $$abc=$$ ?

(1) $$1485 = a^3bc$$

(2) $$c = 11$$

Are You Up For the Challenge: 700 Level Questions

Even if its given that a,b,c are integers it can have multiple values

Statement 1
as 1485=3^3x5x11 or 1^3x297x5 or 3^3x55x1 or 1^3x135x11

statement 2
c=11, 1485= 3^3x5x11 or 1^3x135x11

Combining St1 and St 2

so two values satisfying integer conditions (abc=3x5x11 or abc=1x135x11)

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Re: If 1,485 = a^x*b^y*c^z, then abc = ?  [#permalink]

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10 Jan 2020, 22:06
Bunuel wrote:
If $$1,485= a^x b^y c^z$$, then $$abc=$$ ?

(1) $$1485 = a^3bc$$

(2) $$c = 11$$

Are You Up For the Challenge: 700 Level Questions

Prime factorization of 1485 is 3^2 * 5 * 11

Value of abc is required?

(1) 1485 = a^3bc = 3^2 * 5 * 11,
but a, b, c may or may not be integers or prime factors of 1485
possible values of a,b,c are as follows:
a = 3, b = 5, c=11 OR
a = 1, b = 135, c =11
Insufficient

(2) c = 11
Definite values of a, b are unknown. Insufficient

(1)+(2); 1485 = a^3b * 11 = 3^2 * 5 * 11
Value of a and b may or may not be 3 or 5 respectively.
Insufficient.

E is correct
Re: If 1,485 = a^x*b^y*c^z, then abc = ?   [#permalink] 10 Jan 2020, 22:06
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