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

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.

Since r, s, t and u each represent a nonzero digit, then for 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 cannot be zero as given that all unknowns are nonzero).
Thus, 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.

Answer: A.

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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).

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)

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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(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

Answer A

There are times when you can find the question confusing, the underlying math principles escape you, you just can't clear your head about how to tackle the question, or some combination of all three.

At those times, "Brute Force" method comes in handy. Don't use any formulas or cleaver methods to solve. Just apply what the question tells you.

(1) r = 6u: Well there are only two single digit numbers that have that relationship 6 and 1. So, r = 6 and u = 1. Which means s = 2 and t = 3.
SUFFICIENT

(2) r*u = s*t: Can we think of more than one example where that can be true. There's the example above 6, 2, 3 ,1 and there's also 8, 4, 2, 1. But not only that, we can rearrange the numbers to be 1, 3, 2, 6 and 1, 2, 4, 8.
INSUFFICIENT

Bunuel

when solving for statement 2, is it a valid assumption that RSTU digits can be same digits since question states that they are only non-zero digits?

I addressed similar doubt in this post above. Let me know if that doesn't clear things up!
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