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805+ Level|   Algebra|   Exponents|      
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Bunuel
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If a^x*b^y = 200, where a, b, x, y are positive integers, x + y = ? 14 Jun 2018, 21:13
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

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95% (hard)

Question Stats:

32% (02:09) correct 68% (01:38) wrong based on 68 sessions

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If \(a^x*b^y = 200\), where a, b, x, y are positive integers, x + y = ?


(1) x > y

(2) xy = 6
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E
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If a^x*b^y = 200, where a, b, x, y are positive integers, x + y = ? 14 Jun 2018, 21:26
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IMO it is B.
as per initial q, we can 2^1*100^1,2^3*5^2 or 50^1*2^2 and so on...
(1) x>y
2^3*5^2 [3+2] or 50^1*2^2 [1+2]
(2) xy=6
only one 2^3*5^2 [3+2]

Hence B
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If a^x*b^y = 200, where a, b, x, y are positive integers, x + y = ? 14 Jun 2018, 21:29
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Bunuel
If \(a^x*b^y = 200\), where a, b, x, y are positive integers, x + y = ?


(1) x > y

(2) xy = 6
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Hi Bunuel

I have a doubt.

Do we even need statement I and/or II ?

\(a^x*b^y = 200 = 2^3*5^2\) , as a, b, x, y are positive integers

clearly x=3 and y=2, x+y = 5
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If a^x*b^y = 200, where a, b, x, y are positive integers, x + y = ? 14 Jun 2018, 21:38
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GMATisLovE
Bunuel
If \(a^x*b^y = 200\), where a, b, x, y are positive integers, x + y = ?


(1) x > y

(2) xy = 6

Hi Bunuel

I have a doubt.

Do we even need statement I and/or II ?

\(a^x*b^y = 200 = 2^3*5^2\) , as a, b, x, y are positive integers

clearly x=3 and y=2, x+y = 5
Show more

You missed some of the other possiblities:

\(a^x*b^y = 200 = 8^1*5^2 [x+y=3] or 10^1*20^1 [2]\)
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If a^x*b^y = 200, where a, b, x, y are positive integers, x + y = ? 14 Jun 2018, 22:07
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Statement 1: x > y

2^3 * 5 ^2 = 200

x + y = 5

10^2 * 2^1

X + Y = 3.

No clear solution.


Statement 2: xy = 6

200^1 * 1^6 = 200.

x+y = 7

or

2^3 * 5^2 = 200
x+y = 5

no clear solution.

Combining both also :

we won't have a clear solution as
1^6*200^1 = 200.

x+y = 7

or

2^3 * 5^2 = 200
x+y = 5

In both cases x > y and x*y = 6.

OA - E.
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If a^x*b^y = 200, where a, b, x, y are positive integers, x + y = ? 15 Jun 2018, 09:19
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Bunuel
If \(a^x*b^y = 200\), where a, b, x, y are positive integers, x + y = ?


(1) x > y

(2) xy = 6
Show more

Statement 1:
Example 1: 200 = 100 * 2 = \(10^2 * 2^1\) ---> x+y = 3
Example 2: 200 = 8 * 25 = \(2^3 * 5^2\) -----> x+y = 5

INSUFFICIENT

Statement 2:
Example 1: x =3, y =2 ------> 200 = \(2^3 * 5^2\) ---------> x + y = 5
Example 2: x = 6, y = 1 ------> 200 = \(1^6 * 200^1\) -------> x + y = 7

INSUFFICIENT


Statements 1 & 2 Together:
The two examples from statement 2 work for the two statements combined.

INSUFFICIENT

Answer: E
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If a^x*b^y = 200, where a, b, x, y are positive integers, x + y = ? 15 Jun 2018, 09:42
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should be B.

from 1 we get 2 values of each x and y...
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