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If x,y are numbers >0 and 2^x*5^y=400

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If x,y are numbers >0 and 2^x*5^y=400 [#permalink] New post 04 May 2013, 12:42
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If \(x,y\) are numbers \(>0\) and \(2^x*5^y=400\), what could be the value of \(x\)?

I)2
II)3
III)4

A)Only I
B)Only II
C)I and II
D)Only III
E)I, II and III

Hi guys, this is my first PS question hope you like it, any feedback is appreciated.

Click here for the OE
(BTW: it's not as easy as it seems, it mays tricks you...)
[Reveal] Spoiler: OA

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Re: If x,y are numbers >0 and 2^x*5^y=400 [#permalink] New post 04 May 2013, 17:32
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Zarrolou wrote:
If \(x,y\) are numbers \(>0\) and \(2^x*5^y=400\), what could be the value of \(x\)?

I)2
II)3
III)4

A)Only I
B)Only II
C)I and II
D)Only III
E)I, II and III

Hi guys, this is my first PS question hope you like it, any feedback is appreciated.

I'll post the OA and the OE after some discussion. Kudos to the first ones who got it right!
(BTW: it's not as easy as it seems, it mays tricks you...)


I am getting E

You can make it into \sqrt{2^x} * \sqrt{5^y} =20

given that all numbers are >0

Therefor x=2 x^2*5^1=20 2 works

and when x=4 gives you 16*25=400

if x=3 it comes out to 2\sqrt{2}*5\sqrt{2}=400
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Re: If x,y are numbers >0 and 2^x*5^y=400 [#permalink] New post 04 May 2013, 20:42
Zarrolou wrote:
If \(x,y\) are numbers \(>0\) and \(2^x*5^y=400\), what could be the value of \(x\)?

I)2
II)3
III)4

A)Only I
B)Only II
C)I and II
D)Only III
E)I, II and III

Hi guys, this is my first PS question hope you like it, any feedback is appreciated.

I'll post the OA and the OE after some discussion. Kudos to the first ones who got it right!
(BTW: it's not as easy as it seems, it mays tricks you...)


First we represent 400 in its prime factored form.
\(400 = 4 * 100 = 2^2 * 2^2 * 5^2 = 2^4 * 5^2\)
Hence \(x = 4\) is the only possible value.
Correct option is D :)
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Re: If x,y are numbers >0 and 2^x*5^y=400 [#permalink] New post 04 May 2013, 21:48
Zarrolou wrote:
If \(x,y\) are numbers \(>0\) and \(2^x*5^y=400\), what could be the value of \(x\)?

I)2
II)3
III)4

A)Only I
B)Only II
C)I and II
D)Only III
E)I, II and III


\(2^x*5^y=400\)
Substituting x=2,3,4 in the given equation
I) 2 --> \(2^2*5^y=400\); \(5^y=100\) --> Not possible
II) 3 --> \(2^3*5^y=400\); \(5^y=50\) --> Not possible
III) 4 --> \(2^4*5^y=400\); \(5^y=25\) , so y =2--> Correct

IMO Answer: D
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Re: If x,y are numbers >0 and 2^x*5^y=400 [#permalink] New post 04 May 2013, 23:15
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Good job hfbamafan!

Official Explanation

If x,y are numbers >0 and \(2^x*5^y=400\), what could be the value of x?

I)2
II)3
III)4


Read the question carefully! I said numbers not integers

\(2^x*5^y=2^4*5^2\)

III is true for sure. But pay attention that y (because could be a non integer) makes all the possible answers correct:

I)\(2^2*5^y=2^4*5^2\), \(5^y=2^2*5^2\), \(5^y=100\), so y is a number \(2<y<3\)
II)\(2^3*5^y=2^4*5^2\), \(5^y=2^1*5^2\), \(5^y=50\) , \(2<y<3\)

The correct answer is E) I, II and III
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Re: If x,y are numbers >0 and 2^x*5^y=400 [#permalink] New post 21 Jul 2015, 07:47
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Re: If x,y are numbers >0 and 2^x*5^y=400 [#permalink] New post 21 Jul 2015, 07:57
\(2^x * 5^y = 400\)

(i) if \(x = 2\), then \(5^y = \frac{400}{2^2} = 100\). So, \(5^y = 100\) => \(2 < y < 3\).

(ii) if \(x = 3\), then \(5^y = \frac{400}{2^3} = 50\). So, \(5^y = 50\) => \(2 < y < 3\).

(iii) if \(x = 4\), then \(5^y = \frac{400}{2^4} = 25\), hence \(y = 2\).

All three cases are possible. Hence Ans (E).
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Re: If x,y are numbers >0 and 2^x*5^y=400   [#permalink] 21 Jul 2015, 07:57
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