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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] New post   11 Feb 2012, 19:10
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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.
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Re: If x = 0.abcd, where a, b, c, and d each represent a nonzero [#permalink] 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] 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] New post   26 Aug 2021, 06:48
Bunuel wrote:
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: https://gmatclub.com/forum/if-x-0-rstu-w ... 09735.html

Hope it helps.


The question has given 4 different variables a, b, c and d. So in (2) shouldn't we be taking different values?:
ad=bc
=> a,d can be either of 3,2 or 6,1. similar with b, c. So we have
x=0.2163,
0.3162,
0.3612,
0.2613, and so on (insufficient)

(not that my query is related directly to the given question but it may help to know about the same when solving other questions)
TIA
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Re: If x = 0.abcd, where a, b, c, and d each represent a nonzero [#permalink] New post   26 Aug 2021, 07:38
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Sarahchol20 wrote:
Bunuel wrote:
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: https://gmatclub.com/forum/if-x-0-rstu-w ... 09735.html

Hope it helps.


The question has given 4 different variables a, b, c and d. So in (2) shouldn't we be taking different values?:
ad=bc
=> a,d can be either of 3,2 or 6,1. similar with b, c. So we have
x=0.2163,
0.3162,
0.3612,
0.2613, and so on (insufficient)

(not that my query is related directly to the given question but it may help to know about the same when solving other questions)
TIA


Unless it is explicitly stated otherwise, different variables CAN represent the same number.
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Re: If x = 0.abcd, where a, b, c, and d each represent a nonzero [#permalink] New post   24 Sep 2023, 05:30
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Re: If x = 0.abcd, where a, b, c, and d each represent a nonzero [#permalink]
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