Vincen wrote: ↑Fri Aug 06, 2021 7:09 am
\([y]\) denotes the greatest integer less than or equal to \(y.\) Is \(d < 1?\)
(1) \(d = y - [y]\)
(2) \([d]= 0\)
Answer:
D
Source: Official Guide
First, let's take a moment to get a good idea of what this strange notation means.
A few examples:
[5.1] = 5
[3] = 3
[8.9] = 8
[-1.4] = -2
[-13.6] = -14
IMPORTANT FACT #1:
[y] < y
IMPORTANT FACT #2: The difference between y and [y] is always less than 1. In other words,
y - [y] < 1
Target question: Is d < 1?
Statement 1: d = y - [y]
Take IMPORTANT FACT #1 from above:
[y] < y
Subtract [y] from both sides to get:
0 < y - [y]
Now take IMPORTANT FACT #2 and add it to our inequality to get:
0 < y - [y] < 1
Statement 1 tells us that d = y - [y], so let's replace y - [y] with d to get:
0 < d < 1
PERFECT, we can now be certain that
d < 1
Since we can answer the
target question with certainty, statement 1 is SUFFICIENT
Statement 2: [d] = 0
We're going to use IMPORTANT FACT #2 in our solution.
Take [d] = 0 and add d to both sides to get: [d] + d = d
Subtract [d] from both sides to get: d = d - [d]
From IMPORTANT FACT #2, we know that
d - [d] < 1
Since we just showed that d = d - [d], we can be certain that
d < 1
Since we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer: D
Cheers,
Brent
