M13-31

Question

If the function  f(x)  rounds  x  to the nearest integer, and the function  g(x)  returns the largest integer less than or equal to  x , what is the value of  f(2.501) - g(-1.8) - g(-0.25) ?

A. 2
B. 3
C. 4
D. 5
E. 6

Bunuel · Answer

Official Solution:

If the function  f(x)  rounds  x  to the nearest integer, and the function  g(x)  returns the largest integer less than or equal to  x , what is the value of  f(2.501) - g(-1.8) - g(-0.25) ?

A. 2
B. 3
C. 4
D. 5
E. 6

f(2.501) = 3 , as 3 is the nearest integer to 2.501.
 
 g(-1.8) = -2 , as -2 is the largest integer less than -1.8.
 
 g(-0.25) = -1 , as -1 is the largest integer less than -0.25.
 
Thus,  f(2.501) - g(-1.8) - g(-0.25) = 3 + 2 + 1 = 6 .

Answer: E

RenanBragion · Answer

I think this is a  high-quality  question and I agree with explanation.

Bunuel · Answer

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

12doodle · Answer

I did not quite understand the solution. in gase of g  the larger integer shouldnt be -1 instead of -2 and same with g  ?

Bunuel · Answer

Your confusion is understandable, but here's the key:

The function g(x) is the  floor  function. It gives the  largest integer less than or equal to x ,  not  the closest integer or the smallest integer greater than x.

So:

g(-1.8)  = the largest integer ≤ -1.8 =  -2  
  g(-0.25)  = the largest integer ≤ -0.25 =  -1

Think of it as always  rounding down , even for negative numbers.

errorsit · Answer

I did not quite understand the solution. not sure what g(x) means

Bunuel · Answer

Check  here . Hope it helps.

aashnaag · Answer

Hi, I don't quite understand the case of -0.25; the question says less than or EQUAL to x, so in this case, why was it not rounded to 0? .25 is too less of a number to be rounded down, in this case, -1

Bunuel · Answer

For g(-0.25), we’re looking for the largest integer that is less than or equal to -0.25.

0 is greater than -0.25, so it doesn't qualify. 
 The next integer below -0.25 is -1, so that's the correct value.

So g(-0.25) = -1, not 0.

This is also explained in the discussion above.

jchonkar · Answer

I like the solution - it’s helpful.

Natalylamounier · Answer

I like the solution - it’s helpful. The question though could be a bit better written, it is quite confusing.

Bunuel · Answer

Glad you found the solution helpful! Could you clarify what exactly you feel could be better written in the question? The wording is actually quite precise and aligned with GMAT style, so I’m curious what part you think creates confusion. Also, keep in mind that “confusing” doesn’t necessarily mean “incorrect”, sometimes GMAT questions are deliberately written in a way that forces closer reading. What part do you feel needs improvement?

Natalylamounier · Answer

Hi! Thanks for the reply

Maybe it could be my bad English, but when I first read 'the function f(x) rounds x' it seems that the variable inside the function is rounded: f(2.5) = f(3). And in g(x) returns the largest integer less than or equal to x, it seems it is mentioned the same x as used in f(x). Again, maybe it was my poor understanding when I first read it. But once I understood the question, it was indeed very clever!

Achillee · Answer

I like the solution - it’s helpful.

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