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# If 5,000 = 2^x5^y and x and y are integers, what is the value of x + y

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Math Expert
Joined: 02 Sep 2009
Posts: 52296
If 5,000 = 2^x5^y and x and y are integers, what is the value of x + y  [#permalink]

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17 Dec 2018, 22:56
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Difficulty:

15% (low)

Question Stats:

89% (00:29) correct 11% (01:28) wrong based on 37 sessions

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If $$5,000 = 2^x5^y$$ and x and y are integers, what is the value of $$x + y$$?

A. 3
B. 4
C. 5
D. 6
E. 7

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Joined: 04 Jun 2014
Posts: 11
Location: United States
GPA: 3.31
WE: Other (Military & Defense)
Re: If 5,000 = 2^x5^y and x and y are integers, what is the value of x + y  [#permalink]

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17 Dec 2018, 23:36
5000 can be prime factored to 100 x 50.

100 --> 50x2 --> 25x2x2--> 5x5x2x2
50 --> 25x2 --> 5x5x2

5^4 and 2^3 -->> 4+3=7.

The prime factorization of 5000 can be written as 2^3 5^4

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Director
Joined: 31 Oct 2013
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Concentration: Accounting, Finance
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Re: If 5,000 = 2^x5^y and x and y are integers, what is the value of x + y  [#permalink]

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18 Dec 2018, 02:27
Bunuel wrote:
If $$5,000 = 2^x5^y$$ and x and y are integers, what is the value of $$x + y$$?

A. 3
B. 4
C. 5
D. 6
E. 7

$$5000 = 5 *1000 = 5 * 10 * 100 = 5 *10 * 10 *10 = 5 * 5*2 *5*2 *5*2 = 5^4 2^3$$

$$5,000 = 2^x5^y$$

x =3
y=4

x + y = 3 + 4 = 7.

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Re: If 5,000 = 2^x5^y and x and y are integers, what is the value of x + y  [#permalink]

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18 Dec 2018, 03:25
Bunuel wrote:
If $$5,000 = 2^x5^y$$ and x and y are integers, what is the value of $$x + y$$?

A. 3
B. 4
C. 5
D. 6
E. 7

5000= 2^3*5^4
2^3*5^4 =2^x*5^y
or say x+y= 7

IMO E
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Re: If 5,000 = 2^x5^y and x and y are integers, what is the value of x + y &nbs [#permalink] 18 Dec 2018, 03:25
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