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

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AAPL: Moderator; Posts: 2599; Joined: Sun Oct 29, 2017 2:08 pm; Followed by:2 members

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

by AAPL » Sat Feb 22, 2020 7:24 am

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

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Source: Beat The GMAT — Problem Solving | Sat Feb 22, 2020 7:24 am

GMAT/MBA Expert

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

by Brent@GMATPrepNow » Sat Feb 22, 2020 9:27 am

AAPL wrote: ↑
Sat Feb 22, 2020 7:24 am
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

Brent Hanneson - Creator of GMATPrepNow.com

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

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

by Scott@TargetTestPrep » Sun Mar 01, 2020 1:06 pm

AAPL wrote: ↑
Sat Feb 22, 2020 7:24 am
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

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