The function g(x) is defined as the greatest integer less than or

Question

The function  g(x)  is defined as the greatest integer less than or equal to  x , while the function  h(x)  is defined as the least integer greater than or equal to  x . What is the product  g(1.7) 	imes h(2.3) 	imes g(-1.7) 	imes h(-2.3) ?

A. 6
B. 9
C. 12
D. 16
E. 24

revul · Accepted Answer

Some painfully annoying verbage going on here but:

g(x) is round down to nearest integer unless its an integer already
h(x) is round up to nearest integer unless its an integer already

so we have

(1)(3)(-2)(-2) as our equation, negative x negative cancels so 3 x 2 x 2 = 6 x 2 = 12.

C

akumar5 · Answer

Given that 
 g(x)= greatest integer less than or equal to x
 h(x)= least integer greater than or equal to x

g(1.7)* h(2.3)*g(-1.7)*h(-2.3) =?

so g(1.7)=1
 h(2.3)=3
 g(-1.7)=-2
 h(-2.3)=-2

g(1.7)* h(2.3)*g(-1.7)*h(-2.3) =1*3*(-2)*(-2)=12

Answer is C

PareshGmat · Answer

Answer = C = 12

Product = 1 * 2 * -2 * -3 = 12

Bunuel · Answer

Official Solution:

The function  g(x)  is defined as the greatest integer less than or equal to  x , while the function  h(x)  is defined as the least integer greater than or equal to  x . What is the product  g(1.7) 	imes h(2.3) 	imes g(-1.7) 	imes h(-2.3) ?

A. 6
B. 9
C. 12
D. 16
E. 24

In problems involving "decimal functions," which involve rounding decimals up or down to a nearby integer, we must be very careful to follow directions precisely. Here, we have two functions that have similar but distinct definitions.
 
To avoid confusion between the two functions, evaluate just one function's results first.
 
The function  g(x)  is defined as the greatest integer less than or equal to  x . So  g(1.7) = 1 , while  g(-1.7) = -2 . Notice how this function operates on negative numbers. The results are not symmetrical:  g(-1.7)  does not equal the negative of  g(1.7) .
 
Likewise, we have the function  h(x)  defined as the least integer greater than or equal to  x . So  h(2.3) = 3 , while  h(-2.3) = -2 . Again, the results are not symmetrical:  h(-2.3)  does not equal the negative of  h(2.3) .
 
Now we multiply the results together:
  g(1.7) 	imes h(2.3) 	imes g(-1.7) 	imes h(-2.3) = 1 	imes 3 	imes (-2) 	imes (-2) = 12. 
 
Answer: C.

Bunuel · Answer

Check other  Rounding Functions Questions  in our  Special Questions Directory .

Hope it helps.

KrishnakumarKA1 · Answer

g(1.7) = 1
h(2.3) = 3
g(-1.7) = -2
h(-2.3) = -2

product = 12

BrentGMATPrepNow · Answer

Let's first get a better idea of what each function does.

g(x) = the greatest integer less than or equal to x
So, for example, g(3.1) = 3, since 3 is the greatest integer that is less than 3.1 
Likewise, g(8.7) = 8, since 8 is the greatest integer that is less than 8.7
And g(4.2) = 4, f(0.5) = 0 and f(-5.55) = -6

h(x) = the least integer greater than or equal to x
So, for example, h(4.6) = 5, since 5 is the smallest integer that is greater than 4.6 
Likewise, h(10.11) = 11, since 11 is the smallest integer that is greater than 10.11
And h(0.4) = 1, h(-2.33) = -2 and h(-3.5) =-3

So....      = (1)(3)(-2)(-2) = 12

Answer: C

Cheers,
Brent

fauji · Answer

the product g(1.7)×h(2.3)×g(−1.7)×h(−2.3)

=> 1*3*(-2)*(-2) = 12

Option C

mysteriouswoman · Answer

Please help me understand why is g(1.7) 1 and not 2? Similarly how is g(-1.7) -2?

Bunuel · Answer

The function g rounds DOWN a number to the nearest integer. For example  =1 (because 1 is the greatest integer  less  than or equal to 1.5),  =2,  =-2, ...

The function h rounds UP a number to the nearest integer. For example  =2 (because 2 the least integer  greater  than or equal to 1.5),  =2,  =-1, ...

Check other  Rounding Functions Questions  in our  Special Questions Directory .

Hope it helps.

BrushMyQuant · Answer

Given that g(x) = the greatest integer less than or equal to  x  and h(x) = the least integer greater than or equal to x and we need to find the value of  g(1.7) 	imes h(2.3) 	imes g(-1.7) 	imes h(-2.3)

g(1.7) = the greatest integer less than or equal to 1.7 = 1
h(2.3) = the least integer greater than or equal to 2.3 = 3
g(-1.7) = the greatest integer less than or equal to -1.7 = -2
h(-2.3) = the least integer greater than or equal to -2.3 = -2

=>  g(1.7) 	imes h(2.3) 	imes g(-1.7) 	imes h(-2.3)  =  1 	imes 3 	imes -2 	imes -2  = 3*4 = 12

So,  Answer will be C 
Hope it helps!

Watch the following video to learn the Basics of Functions and Custom Characters

https://www.youtube.com/watch?v=b7JoMX0gk8M

bumpbot · Answer

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The function g(x) is defined as the greatest integer less than or

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