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G(x) is the greatest integer less

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by VJesus12 » Thu Dec 28, 2017 5:05 am
G(x) is the greatest integer less than or equal to x and L(x) is the least integer greater than or equal to x. When x is not an integer, which of the following is the value of L(x)-G(x)?

A. -2
B. -1
C. 0
D. 1
E. 2

The OA is the option D.

How can I know the value of L(x)-G(x) without knowing the value of x?

Experts, may you help me here? I'd be thankful.
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by EconomistGMATTutor » Thu Dec 28, 2017 8:51 am
Hello Vjesus12.

Let's take a look at your question.

Let's suppose that x=5.2. Then $$G\left(x\right)=G\left(5.2\right)=5\ ;\ \ and\ \ \ \ L\left(x\right)=L\left(5.2\right)=6.$$ Therefore, $$L\left(x\right)-G\left(x\right)=1.$$ This situation happens every time that x is not an integer.

Hence, the correct solution is option [spoiler]D=1[/spoiler].

I hope this may help you.

Feel free to ask me again if you have a doubt.

Regards.
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by [email protected] » Thu Dec 28, 2017 10:01 am
Hi VJesus12,

We're told that G(X) is the greatest integer LESS THAN OR EQUAL to X and L(X) is the least integer GREATER THAN OR EQUAL to X. When X is NOT an integer, we're asked which of the following is the value of L(X)-G(X).

This question can be solved rather easily by TESTing VALUES (as the other explanation shows). It's also a fairly straight-forward 'concept' question - meaning that you don't have to do much math to answer it if you recognize the concepts involved.

We're told that X is NOT an integer, so the least integer that is GREATER THAN OR EQUAL to X would be the integer that is immediately to the "right" of X on a number line. In that same way, the greatest integer that is LESS THAN OR EQUAL to X would be the integer that is immediately to the 'left' of X on a number line. We're asked to calculate the larger number minus the smaller number - and that will always be 1.

Final Answer: D

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