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QuantMadeEasy
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If f(x) = |x| + [x] where [x] is the greatest integer less than 31 Jan 2020, 21:38
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

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15% (low)

Question Stats:

81% (01:25) correct 19% (01:29) wrong based on 98 sessions

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If f(x) = |x| + [x] where [x] is the greatest integer less than or equal to x, the value of f(-0.5) + f(2.5) is

A. -2
B. 2
C. 3
D. 4
E. -3
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D
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BrentGMATPrepNow
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If f(x) = |x| + [x] where [x] is the greatest integer less than 01 Feb 2020, 07:56
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kapil1
If f(x) = |x| + [x] where [x] is the greatest integer less than or equal to x, the value of f(-0.5) + f(2.5) is
a. -2
b. 2
c. 3
d. 4
e. -3
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ASIDE---------------------
Let's make sure we understand what this [] symbol means.

Here are a few examples:
[3.1] = 3
[5.8] = 5
[0.7] = 0
[-0.9] = -1
[-4.6] = -5
--------------------------

So, [-0.5] = -1 and [2.5] = 2

So, f(-0.5) = |-0.5| + [-0.5]
= 0.5 + (-1)

And f(2.5) = |2.5| + [2.5]
= 2.5 + 2

This means: f(-0.5) + f(2.5) = [0.5 + (-1)] + [2.5 + 2] = 4

Answer: D

Cheers,
Brent
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If f(x) = |x| + [x] where [x] is the greatest integer less than 31 Jan 2020, 23:52
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kapil1
If f(x) = |x| + [x] where [x] is the greatest integer less than or equal to x, the value of f(-0.5) + f(2.5) is
a. -2
b. 2
c. 3
d. 4
e. -3
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Solution


    • \(f(x) = |x| + [x]\) where |x| is mod value of x and [x] is the greatest integer less than or equal to x.
    • Now, \(f (-0.5) = |-0.5|+ [-0.5] \)
      o Since, \(-1 < -0.5 < 0\), so the greatest integer less than -0.5 or [-0.5] = -1.
      o Hence, \(f (-0.5) = 0.5 + (-1) = -0.5 ……………Eq. (1)\)
    • And, \(f (2.5) = |2.5| + [2.5] \)
      o Since, \(2 < 2.5 < 3\), so the greatest integer less than 2.5 or [2.5] = 2.
      o Hence, \(f (2.5) = 2.5 + 2 = 4.5 ……………Eq. (2)\)
    • On adding Eq. (1) and Eq. (2) we get:
      o \(f (-0.5) +f (2.5) = -0.5+4.5 =4\)
Thus, the correct answer is Option D.
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If f(x) = |x| + [x] where [x] is the greatest integer less than 15 Nov 2023, 12:15
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Hi Brent and everyone,

Could someone give more insight into how square brackets work? I do not understand their principle.

Thank you in advance for you help!!!
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If f(x) = |x| + [x] where [x] is the greatest integer less than 17 Nov 2023, 09:11
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Marc.duquene
If f(x) = |x| + [x] where [x] is the greatest integer less than or equal to x, the value of f(-0.5) + f(2.5) is

A. -2
B. 2
C. 3
D. 4
E. -3

Hi Brent and everyone,

Could someone give more insight into how square brackets work? I do not understand their principle.

Thank you in advance for you help!!!
Show more

The square brackets in this question represent the 'floor function', which rounds down a number to the closest integer less than or equal to that number. Here's how it works:

[4.7] = 4, because 4 is the greatest integer less than or equal to 4.7;
[7] = 7, because 7 is the greatest integer less than or equal to 7;
[-12.1] = -13, because -13 is the greatest integer less than or equal to -12.1;
[-8] = - 8, because -8 is the greatest integer less than or equal to -8.

For more information, you can check out these links:

13. Functions



For more check below:
ALL YOU NEED FOR QUANT ! ! !
Ultimate GMAT Quantitative Megathread
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