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

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Manhattan Prep

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

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

OA C

[Brent@GMATPrepNow]

Manhattan Prep

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

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

OA C

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

[Scott@TargetTestPrep]

Manhattan Prep

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

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

OA C

On the number line, for g(x), always choose the first integer to the left of x. Thus, g(1.7) = 1, and g(-1.7) = -2.

On the number line, for h(x), always choose the first integer to the right of x. Thus, h(2.3) = 3, and h(-2.3) = -2.

The product is 1 * 3 * -2 * -2 = 12.

Answer: C