For a Positive Number x, {x} is Fractional Part of x GMAT Data Sufficiency

Question: For a positive number x, {x} is fractional part of x. {x} = x – [x], where [x] is the greatest integer less than or equal to x. the fractional part of 12.8, for example is 0.8. what is the value of {z}, if z is positive and has exactly 4 digits after the decimal?

1. z/3 = 0.4175
2. 3z = 0.7575

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.

“For a positive number x, {x} is fractional part of x. {x} = x – [x], where [x] is the greatest integer less than or equal to x. the fractional part of 12.8, for example is 0.8. what is the value of {z}, if z is positive and has exactly 4 digits after the decimal?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Quantitative Review". GMAT Quant section consists of a total of 31 questions. 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.

Answer: D
Solutions and Explanation
Approach Solution (1):

(1) z/3 = 0.4175. This implies that the fractional part of z/3 is 0.4175, thus:

z/3 = integer + 0.4175
z = 3 * integer + 3 * 0.4175
z = 3 * integer + 1.2525
z = (3 * integer + 1) + 0.2525
z = integer + 0.2525

Therefore, {z}, the fractional part of z is 0.2525.
Sufficient

(2) {3z} = 0.7575. This implies that the fractional part of 3z is 0.7575

Thus:

3z = integer + 0.7575
z = integer/3 + 0.2525
z = (multiple of 3)/3 + 0.2525
z = integer + 0.2525

Therefore, {z} the fractional part of z is 0.2525
Sufficient

Correct Option: D

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