Data Sufficiency

S9-25 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 s and t.

1. r=3s=2t=6u

2. r*u=s*t

If you consider the first statement, r should be divided by 6.

Take r as 6,

u=1; s=2; t=3

6*1 = 2*3

So, r=6

x=0.6231

Statement 1 is enough.
We have that r = 6u, and we have that all r, s, t, u are non-zero digits, i.e. in the range from 1 to 9 (both inclusive). There is only one such combination: u = 1 (because if u = 2, r becomes 12, which is not possible). And since we know the unique value of u, we know that x = 0.6231.

Statement 2 is not eough.
We have that r * u = s * t.
Thus 1 * 1 = 1 * 1, i.e. x = 0.1111
OR 1 * 2 = 2 * 1, i.e. x = 1122.

Thus option A.

Should we consider r, s, t, and u as different digits or same digits? In some questions, I have seen that if the variables are different (for example: x and y), then we consider different numeric values for those variables (for example: x=2 and y=3 (NOT x=2 and y=2))?

In this question, the answer does not change wether we assign same or different numeric values to the variables. My query is about what GMAT expect us to considerif there is no explicit mention that the variables are different.

Thanks!

pharmxanthan wrote:Should we consider r, s, t, and u as different digits or same digits? In some questions, I have seen that if the variables are different (for example: x and y), then we consider different numeric values for those variables (for example: x=2 and y=3 (NOT x=2 and y=2))?

In this question, the answer does not change wether we assign same or different numeric values to the variables. My query is about what GMAT expect us to considerif there is no explicit mention that the variables are different.

Thanks!

I am no Expert,
But i don't think there is any combination possible with similar digits
Considering any statements condition is applied........

if you have combination of numbers please share that, then only there will be ambiguity in the question , if there is no such combination available there is nothing with the question.........

mehravikas wrote:S9-25 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 s and t.

[1] If r, s, t, and u each represent a nonzero digit of x, then u can be nothing EXCEPT 1; and once any of the r, s, t, and u is found, the question is answered. Sufficient

[2] If r × u = s × t, then r, s, t, and u are in proportion; we could have more than one assignments to r, s, t, and u, including, may be they are all same. [spoiler]Insufficient

A[/spoiler]

pharmxanthan wrote:Should we consider r, s, t, and u as different digits or same digits? In some questions, I have seen that if the variables are different (for example: x and y), then we consider different numeric values for those variables (for example: x=2 and y=3 (NOT x=2 and y=2))?

In this question, the answer does not change wether we assign same or different numeric values to the variables. My query is about what GMAT expect us to considerif there is no explicit mention that the variables are different.

Thanks!

The stem element "r, s, t, and u each represent a nonzero digit" is not sufficient for us to take r, s, t, and u as all different only. No more than the insertion of [1] can make us believe so.