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# If n is an integer and f(n) = f(n 1) n, what is the value of

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If n is an integer and f(n) = f(n 1) n, what is the value of [#permalink]  15 Jun 2011, 14:30
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If n is an integer and f(n) = f(n – 1) – n, what is the value of f (4)?

(1) f(3) = 14

(2) f(6) = -1
[Reveal] Spoiler: OA
Current Student
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Re: f(n) = f(n – 1) – n [#permalink]  15 Jun 2011, 15:16
f(4) = f(3) - 4

1) Sufficient, slot straights into above equation.

2)
f(6) = -1 = f(5) - 6
f(5) = 5 = f(4) - 5
f(4) = 10

Sufficient

D.
Intern
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Kudos [?]: 8 [0], given: 3

If n is an integer and f(n) = f(n – 1) – n, what is the [#permalink]  02 Aug 2012, 14:58
If n is an integer and f(n) = f(n – 1) – n, what is the value of f (4)?

(1) f(3) = 14

(2) f(6) = -1

Last edited by Bunuel on 02 Aug 2012, 15:25, edited 1 time in total.
Moved to DS subforum and renamed the topic.
Math Expert
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Kudos [?]: 62239 [0], given: 9445

Re: If n is an integer and f(n) = f(n – 1) – n, what is the [#permalink]  02 Aug 2012, 15:30
Expert's post
If n is an integer and f(n) = f(n – 1) – n, what is the value of f (4)?

(1) f(3) = 14. Since f(n)=f(n-1)-n then: f(4)=f(3)-4 --> f(4)=14-4=10. Sufficient.

(2) f(6) = -1. The same way as above f(6)=f(5)-6 --> -1=f(5)-6 --> f(5)=5 --> f(5)=f(4)-5 --> 5=f(4)-5 --> f(4)=10. Sufficient.

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Intern
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Kudos [?]: 5 [0], given: 51

Re: f(n) = f(n – 1) – n [#permalink]  17 Dec 2012, 20:55
pike wrote:
f(4) = f(3) - 4

1) Sufficient, slot straights into above equation.

2)
f(6) = -1 = f(5) - 6
f(5) = 5 = f(4) - 5
f(4) = 10

Sufficient

D.

I don't understand what you mean slot straights into above equation. When I simplify the f(3) I get -1 and for f(6) I also get -1. Is that why both are sufficient? I don't understand why Statement 1 the f(3)=14. What I supposed to do something else?
VP
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Location: United States (NY)
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Kudos [?]: 988 [0], given: 62

Re: f(n) = f(n – 1) – n [#permalink]  17 Dec 2012, 21:25
Expert's post
dcastan2 wrote:
pike wrote:
f(4) = f(3) - 4

1) Sufficient, slot straights into above equation.

2)
f(6) = -1 = f(5) - 6
f(5) = 5 = f(4) - 5
f(4) = 10

Sufficient

D.

I don't understand what you mean slot straights into above equation. When I simplify the f(3) I get -1 and for f(6) I also get -1. Is that why both are sufficient? I don't understand why Statement 1 the f(3)=14. What I supposed to do something else?

Hii.
See the question gives us the relation: $$f(n)=f(n-1)-n$$ and the question asks the value of $$f(4)$$.

As per the above relation, if we expand $$f(4)$$, we get: $$f(4)=f(3)-4$$---------[a]

Now coming to the statements:
Statement 1 gives us direct $$f(3)$$. We just have to put in equation [a].
Statement 2 gives us $$f(6)=-1$$.
$$f(6)$$ can be expanded as $$f(5)$$-6. Moreover $$f(5)$$ can be expanded as $$f(4)-5$$. Put this value of $$f(5)$$ in the former one. It will become $$f(6)=f(4)-9$$, which will gives the value of $$f(4)$$ as 10.

Both are sufficient.
Hope that helps.
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Re: f(n) = f(n – 1) – n [#permalink]  17 Dec 2012, 23:14
Marcab wrote:
dcastan2 wrote:
pike wrote:
f(4) = f(3) - 4

1) Sufficient, slot straights into above equation.

2)
f(6) = -1 = f(5) - 6
f(5) = 5 = f(4) - 5
f(4) = 10

Sufficient

D.

I don't understand what you mean slot straights into above equation. When I simplify the f(3) I get -1 and for f(6) I also get -1. Is that why both are sufficient? I don't understand why Statement 1 the f(3)=14. What I supposed to do something else?

Hii.
See the question gives us the relation: $$f(n)=f(n-1)-n$$ and the question asks the value of $$f(4)$$.

As per the above relation, if we expand $$f(4)$$, we get: $$f(4)=f(3)-4$$---------[a]

Now coming to the statements:
Statement 1 gives us direct $$f(3)$$. We just have to put in equation [a].
Statement 2 gives us $$f(6)=-1$$.
$$f(6)$$ can be expanded as $$f(5)$$-6. Moreover $$f(5)$$ can be expanded as $$f(4)-5$$. Put this value of $$f(5)$$ in the former one. It will become $$f(6)=f(4)-9$$, which will gives the value of $$f(4)$$ as 10.

Both are sufficient.
Hope that helps.

Yes, thank you! But we don't use the =14 anywhere? What's the purpose of it then?
VP
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Kudos [?]: 988 [0], given: 62

Re: If n is an integer and f(n) = f(n 1) n, what is the value of [#permalink]  17 Dec 2012, 23:41
Expert's post
In statement 1, put f(3)=14. You will get the answer as 10.
In DS, if you know that with the given information a particular question can be solved then rather than trying to find the exact answer, move to the next statement.
In the explanation, I did the same.

Hope that helps.
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Manager
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Kudos [?]: 81 [1] , given: 14

Re: f(n) = f(n – 1) – n [#permalink]  17 Dec 2012, 23:46
1
KUDOS
The equation says f(n) = f(n-1) - n
(1) states f(3)=14 and we need to find f(4)
so as per the equation, f(4) = f(4-1) -4
==> f(4)=f(3)-4
==> f(4)=14-4=10
So (1) is sufficient...Hope explanation for (2) is already clear. And this expalins the use of f(3)=14 as well.
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Shouvik
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Re: f(n) = f(n – 1) – n [#permalink]  18 Dec 2012, 02:13
Expert's post
dcastan2 wrote:
pike wrote:
f(4) = f(3) - 4

1) Sufficient, slot straights into above equation.

2)
f(6) = -1 = f(5) - 6
f(5) = 5 = f(4) - 5
f(4) = 10

Sufficient

D.

I don't understand what you mean slot straights into above equation. When I simplify the f(3) I get -1 and for f(6) I also get -1. Is that why both are sufficient? I don't understand why Statement 1 the f(3)=14. What I supposed to do something else?

Merging similar topics.

Solution is given here: if-n-is-an-integer-and-f-n-f-n-1-n-what-is-the-value-of-136745.html#p1109873
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Re: If n is an integer and f(n) = f(n 1) n, what is the value of [#permalink]  31 Jan 2014, 09:49
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Re: If n is an integer and f(n) = f(n 1) n, what is the value of   [#permalink] 31 Jan 2014, 09:49
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