GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 23 Oct 2019, 13:53

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# If F is a function defined in the positive integers, such that F(k) is

Author Message
TAGS:

### Hide Tags

GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 935
If F is a function defined in the positive integers, such that F(k) is  [#permalink]

### Show Tags

10 Mar 2019, 08:09
00:00

Difficulty:

55% (hard)

Question Stats:

59% (01:42) correct 41% (01:27) wrong based on 39 sessions

### HideShow timer Statistics

GMATH practice exercise (Quant Class 14)

If F is a function defined in the positive integers, such that F(k) is a positive integer for each positive integer k, what is the value of F(8)?

(1) F(n+1) = (n+1)*F(n), for every positive integer n.
(2) F(1)*F(1) = F(1)

_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
Manager
Joined: 21 Feb 2019
Posts: 125
Location: Italy
If F is a function defined in the positive integers, such that F(k) is  [#permalink]

### Show Tags

10 Mar 2019, 11:51
Statement 1: $$F(7+1) = 8 * F(7)$$

Going backwards, such as $$F (6 +1) = 7 * F (6)$$ we notice that we aren't able to define F(1). $$F(1) = 1 * F(0)$$, whereas $$0$$ is a neutral number and $$F$$ is not defined. Discard this option.

Statement 2: we have $$F(1) = 1$$. Alone is insufficient, because it doesn't say anything else about how to compute F(8).

Since from statement 1 we lacked of $$F(1)$$ value, combined together these two statements lead to solution. Hence, C.
_________________
If you like my post, Kudos are appreciated! Thank you.

MEMENTO AUDERE SEMPER
GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 935
Re: If F is a function defined in the positive integers, such that F(k) is  [#permalink]

### Show Tags

10 Mar 2019, 16:20
1
fskilnik wrote:
GMATH practice exercise (Quant Class 14)

If F is a function defined in the positive integers, such that F(k) is a positive integer for each positive integer k, what is the value of F(8)?

(1) F(n+1) = (n+1)*F(n), for every positive integer n.
(2) F(1)*F(1) = F(1)

$$F\left( k \right) \ge 1\,\,{\mathop{\rm int}} \,\,\,\,{\rm{for}}\,\,{\rm{each}}\,\,\,k \ge 1\,\,\,\,\left( * \right)$$

$$? = F\left( 8 \right)$$

$$\left( 1 \right)\,\,F\left( {n + 1} \right) = \left( {n + 1} \right) \cdot F\left( n \right)\,\,\,{\rm{for}}\,{\rm{each}}\,\,\,n \ge 1\,\,{\mathop{\rm int}}$$

$$\left. {\matrix{ {F\left( 2 \right) = 2 \cdot F\left( 1 \right)\,\,} \hfill \cr {F\left( 3 \right) = 3 \cdot F\left( 2 \right) = 3 \cdot 2 \cdot F\left( 1 \right)} \hfill \cr {\,\,\, \vdots } \hfill \cr {? = F\left( 8 \right) = 8 \cdot 7 \cdot 6 \cdot \ldots \cdot 3 \cdot 2 \cdot F\left( 1 \right)\,\,\,} \hfill \cr } } \right\}\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\left\{ {\matrix{ {\,{\rm{Take}}\,\,F\left( 1 \right) = 1\,\,\,\, \Rightarrow \,\,\,? = 8!\,\,} \hfill \cr {\,{\rm{Take}}\,\,F\left( 1 \right) = 2\,\,\,\, \Rightarrow \,\,\,? = 2 \cdot 8!} \hfill \cr } } \right.$$

$$\left( 2 \right)\,\,F\left( 1 \right) \cdot F\left( 1 \right) = F\left( 1 \right)\,\,\,\,\mathop \Rightarrow \limits^{\,:\,\,F\left( 1 \right)\,\, \ne \,0\,\,\left( * \right)} \,\,\,F\left( 1 \right) = 1$$

$$\left\{ {\matrix{ {\,{\rm{Take}}\,\,F\left( n \right) = 1\,\,\,{\rm{for}}\,{\rm{each}}\,\,\,n \ge 1\,\,{\mathop{\rm int}} \,\,\,\,\, \Rightarrow \,\,\,? = 1\,\,} \hfill \cr {\,{\rm{Take}}\,\,F\left( n \right) = \left( {n + 1} \right) \cdot F\left( n \right)\,\,\,{\rm{for}}\,{\rm{each}}\,\,\,n \ge 1\,\,{\mathop{\rm int}} \,\,\,\,\, \Rightarrow \,\,\,? = 8!\,\,} \hfill \cr } } \right.$$

$$\left( {1 + 2} \right)\,\,\,\,? = 8!\,\,\,\,\, \Rightarrow \,\,\,\,\left( {\rm{C}} \right)$$

We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
Re: If F is a function defined in the positive integers, such that F(k) is   [#permalink] 10 Mar 2019, 16:20
Display posts from previous: Sort by