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

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Math Expert
Joined: 02 Sep 2009
Posts: 60605
The function g(x) is defined as the greatest integer less than or  [#permalink]

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18 Nov 2014, 08:34
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20
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Difficulty:

15% (low)

Question Stats:

78% (01:30) correct 22% (01:53) wrong based on 290 sessions

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Tough and Tricky questions: Number Properties.

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

Kudos for a correct solution.

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Re: The function g(x) is defined as the greatest integer less than or  [#permalink]

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18 Nov 2014, 10:28
1
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.

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Re: The function g(x) is defined as the greatest integer less than or  [#permalink]

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18 Nov 2014, 22:18
1
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

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Re: The function g(x) is defined as the greatest integer less than or  [#permalink]

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19 Nov 2014, 00:03
1

$$Product = 1 * 2 * -2 * -3 = 12$$
Math Expert
Joined: 02 Sep 2009
Posts: 60605
Re: The function g(x) is defined as the greatest integer less than or  [#permalink]

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19 Nov 2014, 07:54
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:
$$g(1.7) \times h(2.3) \times g(-1.7) \times h(-2.3) = 1 \times 3 \times (-2) \times (-2) = 12.$$

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Posts: 60605
Re: The function g(x) is defined as the greatest integer less than or  [#permalink]

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19 Nov 2014, 07:56
1
Bunuel wrote:
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:
$$g(1.7) \times h(2.3) \times g(-1.7) \times h(-2.3) = 1 \times 3 \times (-2) \times (-2) = 12.$$

Check other Rounding Functions Questions in our Special Questions Directory.

Hope it helps.
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Re: The function g(x) is defined as the greatest integer less than or  [#permalink]

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21 Mar 2017, 03:54
Bunuel wrote:

Tough and Tricky questions: Number Properties.

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

Kudos for a correct solution.

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

product = 12
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Re: The function g(x) is defined as the greatest integer less than or  [#permalink]

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24 Aug 2019, 19:43
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Re: The function g(x) is defined as the greatest integer less than or   [#permalink] 24 Aug 2019, 19:43
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