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# x! is defined for all whole numbers x as the product of all the positi

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Math Expert
Joined: 02 Sep 2009
Posts: 51122
x! is defined for all whole numbers x as the product of all the positi  [#permalink]

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07 Jul 2018, 08:29
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Difficulty:

15% (low)

Question Stats:

81% (01:07) correct 19% (01:17) wrong based on 32 sessions

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x! is defined for all whole numbers x as the product of all the positive integers from 1 to x inclusive (where 0!, considered an “empty product,” is defined as 1). For example, 5! = (1)(2)(3)(4)(5). Let two functions be defined over the set of whole numbers as follows:

f(x) = x!
g(x) = the product of all the digits of x.

What is f(g(111,111,114))?

A. 0
B. 1
C. 4
D. 24
E. 362,880

_________________
Math Expert
Joined: 02 Aug 2009
Posts: 7107
Re: x! is defined for all whole numbers x as the product of all the positi  [#permalink]

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07 Jul 2018, 09:19
Bunuel wrote:
x! is defined for all whole numbers x as the product of all the positive integers from 1 to x inclusive (where 0!, considered an “empty product,” is defined as 1). For example, 5! = (1)(2)(3)(4)(5). Let two functions be defined over the set of whole numbers as follows:

f(x) = x!
g(x) = the product of all the digits of x.

What is f(g(111,111,114))?

A. 0
B. 1
C. 4
D. 24
E. 362,880

g(111,111,114)=1*1*1*1*1*1*1*1*4=4..
so f(g(111,111,114))=f(4)=4!=4*3*2*1=24

D
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3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: x! is defined for all whole numbers x as the product of all the positi  [#permalink]

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07 Jul 2018, 10:19
Bunuel wrote:
x! is defined for all whole numbers x as the product of all the positive integers from 1 to x inclusive (where 0!, considered an “empty product,” is defined as 1). For example, 5! = (1)(2)(3)(4)(5). Let two functions be defined over the set of whole numbers as follows:

f(x) = x!
g(x) = the product of all the digits of x.

What is f(g(111,111,114))?

A. 0
B. 1
C. 4
D. 24
E. 362,880

f(g(111,111,114))=f(1*1...(8times)*4)=f(4)=4!=(1)(2)(3)(4)=24

Ans.(D)
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Location: India
Re: x! is defined for all whole numbers x as the product of all the positi  [#permalink]

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07 Jul 2018, 10:56
Bunuel wrote:
x! is defined for all whole numbers x as the product of all the positive integers from 1 to x inclusive (where 0!, considered an “empty product,” is defined as 1). For example, 5! = (1)(2)(3)(4)(5). Let two functions be defined over the set of whole numbers as follows:

f(x) = x!
g(x) = the product of all the digits of x.

What is f(g(111,111,114))?

A. 0
B. 1
C. 4
D. 24
E. 362,880

g(111,111,114) = 1*1*1*1*1*1*1*1*4 = 4

hence f(g(111,111,114)) = f(4) = 4! = 24

Answer D.

Thanks,
GyM
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Re: x! is defined for all whole numbers x as the product of all the positi &nbs [#permalink] 07 Jul 2018, 10:56
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# x! is defined for all whole numbers x as the product of all the positi

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