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If x = 0.abcd, where a, b, c, and d each represent a nonzero

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If x = 0.abcd, where a, b, c, and d each represent a nonzero  [#permalink]

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New post 11 Feb 2012, 19:10
5
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A
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E

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  25% (medium)

Question Stats:

76% (01:52) correct 24% (02:15) wrong based on 618 sessions

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If x = 0.abcd, where a, b, c, and d each represent a nonzero digit of x, what is the value of x ?

(1) a/2 = b = 2c = 4d
(2) The product of a and d is equal to the product of b and c.

Struggling to solve this and get A. Can you please let me know the concept behind this?

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Re: value of X?  [#permalink]

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New post 11 Feb 2012, 19:21
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If x = 0.abcd, where a, b, c, and d each represent a nonzero digit of x, what is the value of x ?

(1) a/2 = b = 2c = 4d --> multiply by 2: a=2b=4c=8d --> since each represent a nonzero single digit then d can only be 1 (if it's more than 1 a will be more than 10) --> a=8, b=4, c=2 and d=1. Sufficient.

(2) The product of a and d is equal to the product of b and c --> multiple values of x are possible: 0.1111, 2222, 1221, ... Not sufficient.

Answer: A.

Similar question to practice: if-x-0-rstu-where-r-s-t-and-u-each-represent-a-nonzero-109735.html

Hope it helps.
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Re: If x = 0.abcd, where a, b, c, and d each represent a nonzero  [#permalink]

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New post 18 Nov 2016, 22:48
Great Question
Here x=0.abcd
To get x we need a,b,c,d
Statement 1
a/2=b=2c=4d
multiplying by 2 throughout
a=2b=4c=8d
hence a must be divisible by 8
hence the only possible value of x is 0.8421
hence sufficient

Statement 2
using test cases
x=0.1111
x=0.2424
hence not sufficient

Hence A
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Re: If x = 0.abcd, where a, b, c, and d each represent a nonzero  [#permalink]

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New post 10 Sep 2019, 22:14
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Re: If x = 0.abcd, where a, b, c, and d each represent a nonzero   [#permalink] 10 Sep 2019, 22:14
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