Question: 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.

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
4. EACH statement ALONE is sufficient.
5. Statements (1) and (2) TOGETHER are not sufficient.

Solutions and Explanation

Approach Solution : 1

Statement - 1 : r = 3s = 2t = 6u

Since r, s, t, and u all define a nonzero digit, u must be 1 for r to be a nonzero digit since r equals 6u (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)
r = 6, s = 2, t = 3, and u = 1 result in x = 0.6231.
Therefore this statement is sufficient.

Statement - 2 : The product of r and u is equal to the product of sand t.

For x, there are multiple possible values, x = 0.1111, x = 2222, x = 2211,.…
Therefore this statement is not sufficient.

Correct Answer: (A)

Approach Solution : 2

Statement - 1 : r = 3s = 2t = 6u

Given that x = 0.rstu, it follows that r, s, t, and u are non-zero integers (i.e., they range from 1 to 9) and that they are not required to be distinct.
One set of numbers fits in perfectly if we start by providing a low value for u, like 1.
u=1, t=3, s=2, r=6
Note that u cannot be >=2 because that would result in a value with two digits.
Therefore this statement is sufficient.

Statement - 2 : The product of r and u is equal to the product of sand t.

This prevents us from determining which number has a particular value.
Therefore this statement is not sufficient.

Correct Answer: (A)

Approach Solution : 3

There are times when the question can be challenging, the underlying mathematical concepts can elude you, you simply can't think clearly about how to approach the question, or some combination of all three.

The "Brute Force" method is useful in those circumstances. Use no formulas or clever techniques when solving. Just use the information the question provides.

Statement - 1 : r = 3s = 2t = 6u

There are only two single-digit numbers, 6 and 1, that are related to each other.
Hence, r = 6 and u = 1. Consequently, s = 2 and t = 3.
Therefore this statement is sufficient.

Statement - 2 : The product of r and u is equal to the product of sand t.

It states that, r*u = s*t.
We need to come up with several examples where that is possible.
There are two examples, the one given above (6, 2, 3), and another (8, 4, 2).
In addition, the numbers can be rearranged to become 1, 3, 2, 6 and 1, 2, 4, 8.
Therefore this statement is not sufficient.

Correct Answer: (A)

“If x = 0.rstu, where r, s, t, and u each represent a nonzero digit” - is a topic of the GMAT Quantitative reasoning section of GMAT. GMAT Quant section consists of a total of 31 questions. This question was taken from the book “The Official Guide for GMAT Quantitative Review”. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiency comprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

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