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

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

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New post 11 Nov 2019, 03:05
1
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A
B
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D
E

Difficulty:

  95% (hard)

Question Stats:

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

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

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New post 11 Nov 2019, 07:41
3
1
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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New post 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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Re: If 1,485 = a^x*b^y*c^z, then abc = ?  [#permalink]

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

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

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New post 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)

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

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