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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # If x = 0.rstu, where r, s, t, and u each represent a nonzero digit of

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Math Expert V
Joined: 02 Sep 2009
Posts: 64101
If x = 0.rstu, where r, s, t, and u each represent a nonzero digit of  [#permalink]

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2
18 00:00

Difficulty:   35% (medium)

Question Stats: 70% (01:43) correct 30% (02:05) wrong based on 694 sessions

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If x = 0.rstu, where r, s, t, and u each represent a nonzero digit of x, what is the value of x ?

(1) r = 3s = 2t = 6u
(2) The product of r and u is equal to the product of sand t.

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Math Expert V
Joined: 02 Sep 2009
Posts: 64101
Re: If x = 0.rstu, where r, s, t, and u each represent a nonzero digit of  [#permalink]

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SOLUTION

If x = 0.rstu, where r, s, t and u each represent a nonzero digit of x, what is the value of x?

(1) r = 3s = 2t = 6u --> as r, s, t and u each represent a nonzero digit then r, which equals to 6u, to be nonzero digit u must be 1 (if u is 2 or more then r is no more a digit, and u also can not be zero as given that all unknowns are nonzero) --> r=6, s=2, t=3, and u=1 --> x=0.6231. Sufficient.

(2) The product of r and u is equal to the product of s and t --> multiple values of x are possible: x=0.1111, x=2222, x=2211, ... Not sufficient.

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Re: If x = 0.rstu, where r, s, t, and u each represent a nonzero digit of  [#permalink]

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Given that x = 0.rstu, we can infer from the statements that r,s,t & u are non-zero integers(meaning that they range from 1 to 9) and also these numbers need not be distinct.

1) r = 3s = 2t = 6u
If we start by giving a low value for u(eg., 1), we can immediately find out that only one set of numbers fit in.
u=1, t=3, s=2, r=6

Note that u cannot be >=2 since it will give a double-digit value. Therefore, A is sufficient.

2)ru = st
From this, we cannot infer which number has a specific value. Therefore, insufficient.

Ans is (A).
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Re: If x = 0.rstu, where r, s, t, and u each represent a nonzero digit of  [#permalink]

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Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

If x = 0.rstu, where r, s, t, and u each represent a nonzero digit of x, what is the value of x ?

(1) r = 3s = 2t = 6u
(2) The product of r and u is equal to the product of sand t.

Statement 1) we know r,s,t and u can represent only digit, so the 1st set of values which satisfies would be
u = 1, t = 3, s = 2 and r = 6. As this is a ratio, we can increase it by multiplying by 2, but in that case, r cannot be a single digit anymore. So Sufficient.
Statement 2) we cannot determine the values. It can be 1,1,1,1 or 2,2,2,2. Not Sufficient
Hence A)
Intern  Joined: 23 Aug 2014
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Re: If x = 0.rstu, where r, s, t and u each represent a nonzero  [#permalink]

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The examples for the S2 included 0.2211, 0.1111...above. That would mean that the digits assigned for r,s,t and u repeat. Is that allowed? The question says 'each represent a nonzero digit of x', so that does leave open the possibility for repetition, i guess. But when various variables are assigned, does that not mean that they are all different?
Math Expert V
Joined: 02 Sep 2009
Posts: 64101
Re: If x = 0.rstu, where r, s, t and u each represent a nonzero  [#permalink]

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1
deeuk wrote:
The examples for the S2 included 0.2211, 0.1111...above. That would mean that the digits assigned for r,s,t and u repeat. Is that allowed? The question says 'each represent a nonzero digit of x', so that does leave open the possibility for repetition, i guess. But when various variables are assigned, does that not mean that they are all different?

r, s, t and u each represent a nonzero digit means that neither is 0, it does not mean that they are distinct.

Generally, unless it is explicitly stated otherwise, different variables CAN represent the same number.
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Re: If x = 0.rstu, where r, s, t, and u each represent a nonzero digit of  [#permalink]

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(1) s = r/3; t = r/2; u = r/6
r must be 6; so s = 2; t = 3; u = 1
x = 0.6231
Sufficient

(1) ru = st
r = u = s = t = 1
x = 0.1111
r = u = s = t = 2
x = 0.2222
Insufficient

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Re: if x=0.rstu, where r,s,t,u each represent a non-zero digit  [#permalink]

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_________________ Re: if x=0.rstu, where r,s,t,u each represent a non-zero digit   [#permalink] 10 May 2020, 04:35

# If x = 0.rstu, where r, s, t, and u each represent a nonzero digit of  