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![If [x] denotes the greatest integer function and the value of [x] is t](/forum/styles/gmatclub_light/imageset/icon_post_target_unread.svg "If [x] denotes the greatest integer function and the value of [x] is t"){kind=icon}
13 Apr 2020, 11:59
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B
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If \([x]\) denotes the greatest integer function and the value of [x] is the greatest integer less than or equal to x, then, what is the value of \([-2.5] + [3.5]\)?
- A. \(– 1\)
B. \(0\)
C. \(1\)
D. \(5\)
E. \(6\)
13 Apr 2020, 22:07
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Enchanting
We are looking at GREATEST integer, but less than x..
\([-2.5]=-3.............. [3.5]=3\)..
\([-2.5] + [3.5]=-3+3=0\)
B
14 Apr 2020, 01:49
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[x] denotes the greatest integer function. This means that the function will give the output as an integer which is the biggest integer that is less than OR equal to x.
When dealing with the greatest integer function, you need to be cognizant of the following:
1) If x is an integer, the function will yield the value of x as the output.
2) If x is a fraction, the function will yield the output as the biggest integer that is LESS THAN x.
A very simple way of dealing with this situation is the following.
If the value of x is an integer, the result will be the same integer.
If the value of x is a positive/negative fraction, plot the number on the number line and pick the closest integer that is on the LEFT side of x.
For example, if we need to find [1.7], we will plot 1.7 on the number line. When we do this, we see that the integer 1 is the closest integer ON the LEFT side of 1.7. Therefore, [1.7] = 1.
Let’s use this technique to find out the values of [-2.5] and [3.5].
When we plot -2.5 on the number line, since -2.5 is a negative fraction, we pick the closest integer ON the LEFT side of -3.5 i.e. -3. Therefore, [-2.5] = -3.
When we plot 3.5 on the number line, since 3.5 is a positive fraction, we pick the closest integer ON the LEFT side of 3.5 i.e. 3. Therefore, [3.5] = 3.
Therefore, [-2.5] + [3.5] = -3 + 3 = 0.
The correct answer option is B.
Hope that helps!
When dealing with the greatest integer function, you need to be cognizant of the following:
1) If x is an integer, the function will yield the value of x as the output.
2) If x is a fraction, the function will yield the output as the biggest integer that is LESS THAN x.
A very simple way of dealing with this situation is the following.
If the value of x is an integer, the result will be the same integer.
If the value of x is a positive/negative fraction, plot the number on the number line and pick the closest integer that is on the LEFT side of x.
For example, if we need to find [1.7], we will plot 1.7 on the number line. When we do this, we see that the integer 1 is the closest integer ON the LEFT side of 1.7. Therefore, [1.7] = 1.
Let’s use this technique to find out the values of [-2.5] and [3.5].
When we plot -2.5 on the number line, since -2.5 is a negative fraction, we pick the closest integer ON the LEFT side of -3.5 i.e. -3. Therefore, [-2.5] = -3.
When we plot 3.5 on the number line, since 3.5 is a positive fraction, we pick the closest integer ON the LEFT side of 3.5 i.e. 3. Therefore, [3.5] = 3.
Therefore, [-2.5] + [3.5] = -3 + 3 = 0.
The correct answer option is B.
Hope that helps!
