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

Answer = C = 12

\(Product = 1 * 2 * -2 * -3 = 12\)

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 \(g(1.7) \times h(2.3) \times g(-1.7) \times h(-2.3)\)?

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:
\(g(1.7) \times h(2.3) \times g(-1.7) \times h(-2.3) = 1 \times 3 \times (-2) \times (-2) = 12.\)

Answer: C.

Check other Rounding Functions Questions in our Special Questions Directory.

Hope it helps.

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

product = 12

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.... [g(1.7)][h(2.3)][g(-1.7)][h(-2.3)] = (1)(3)(-2)(-2) = 12

Answer: C

Cheers,
Brent

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

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

Option C

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

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


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

Check other Rounding Functions Questions in our Special Questions Directory.

Hope it helps.

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 \(g(1.7) \times h(2.3) \times g(-1.7) \times h(-2.3)\)

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

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

So, Answer will be C
Hope it helps!

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

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.