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# If x=1/2^2*3^2*4^2*5^2 is expressed as a decimal, how many

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Joined: 02 Nov 2016
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If x=1/2^2*3^2*4^2*5^2 is expressed as a decimal, how many  [#permalink]

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11 Aug 2019, 05:19
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Difficulty:

35% (medium)

Question Stats:

68% (01:40) correct 32% (02:01) wrong based on 56 sessions

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If $$x$$= $$\frac{1}{2^2*3^2*4^2*5^2}$$ is expressed as a decimal, how many distinct nonzero digits will $$x$$ have?

A. One

B. Two

C. Three

D. Seven

E. Ten

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Joined: 19 Oct 2018
Posts: 1175
Location: India
If x=1/2^2*3^2*4^2*5^2 is expressed as a decimal, how many  [#permalink]

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11 Aug 2019, 20:14
The number of distinct non zero digit in $$\frac{1}{2^2*3^2*4^2*5^2}$$ is equal to that in $$\frac{11111......}{16}$$
$$\frac{11111....}{16}$$=69444......

Option C

If $$x$$= $$\frac{1}{2^2*3^2*4^2*5^2}$$ is expressed as a decimal, how many distinct nonzero digits will $$x$$ have?

A. One

B. Two

C. Three

D. Seven

E. Ten
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Joined: 03 Jun 2019
Posts: 1885
Location: India
If x=1/2^2*3^2*4^2*5^2 is expressed as a decimal, how many  [#permalink]

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11 Aug 2019, 21:13
3
If $$x$$= $$\frac{1}{2^2*3^2*4^2*5^2}$$ is expressed as a decimal, how many distinct nonzero digits will $$x$$ have?

A. One

B. Two

C. Three

D. Seven

E. Ten

Given: $$x$$= $$\frac{1}{2^2*3^2*4^2*5^2}$$ is expressed as a decimal.

Asked: How many distinct nonzero digits will x have?

2*3*4*5 = 120
We can multiply the expression by any power of 10 without changing non-zero digits.
$$\frac{1*1000}{120}= \frac{1000}{120} = \frac{25}{3}$$
But expression is $$\frac{1}{120^2}$$
$$\frac{25^2}{3^2} = \frac{625}{9} = 69 \frac{4}{9} = 69.44444...$$
No of unique non-zero digits = 6,9 & 4 (3 unique non-zero numbers)

IMO C
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Re: If x=1/2^2*3^2*4^2*5^2 is expressed as a decimal, how many  [#permalink]

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21 Aug 2019, 01:49
If $$x$$= $$\frac{1}{2^2*3^2*4^2*5^2}$$ is expressed as a decimal, how many distinct nonzero digits will $$x$$ have?

A. One

B. Two

C. Three

D. Seven

E. Ten

Similar questions to practice:
https://gmatclub.com/forum/if-x-1-2-2-3 ... 00297.html
https://gmatclub.com/forum/if-d-1-2-3-5 ... 44440.html
https://gmatclub.com/forum/if-t-1-2-9-5 ... 29447.html
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Re: If x=1/2^2*3^2*4^2*5^2 is expressed as a decimal, how many  [#permalink]

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24 Aug 2019, 02:08
It's only 1/144 that matters for the question (not 2 and 5).

What's a quick way to solve this? Are we just meant to know the number of digits?
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Joined: 03 Sep 2018
Posts: 252
Location: Netherlands
GMAT 1: 710 Q48 V40
GMAT 2: 780 Q50 V49
GMAT 3: 760 Q49 V44
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Re: If x=1/2^2*3^2*4^2*5^2 is expressed as a decimal, how many  [#permalink]

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17 Nov 2019, 23:54
$$x=\frac{(1*5^4)}{(3^2*2^4*5^4)}=\frac{625}{90000}=0.00694444...$$
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Re: If x=1/2^2*3^2*4^2*5^2 is expressed as a decimal, how many   [#permalink] 17 Nov 2019, 23:54
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