It is currently 18 Feb 2018, 01:07

### 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
Your Progress

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# If x is a positive integer, what is the value of x ?

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 43787
If x is a positive integer, what is the value of x ? [#permalink]

### Show Tags

18 Nov 2014, 07:38
Expert's post
9
This post was
BOOKMARKED
00:00

Difficulty:

95% (hard)

Question Stats:

38% (01:34) correct 62% (01:25) wrong based on 130 sessions

### HideShow timer Statistics

Tough and Tricky questions: Decimals.

If $$x$$ is a positive integer, what is the value of $$x$$?

(1) The first nonzero digit in the decimal expansion of $$\frac{1}{x!}$$ is in the hundredths place.

(2) The first nonzero digit in the decimal expansion of $$\frac{1}{(x+1)!}$$ is in the thousandths place.

Kudos for a correct solution.
[Reveal] Spoiler: OA

_________________
Manager
Joined: 17 Mar 2014
Posts: 160
Re: If x is a positive integer, what is the value of x ? [#permalink]

### Show Tags

18 Nov 2014, 08:19
1
This post received
KUDOS
Statement 1:

The first nonzero digit in the decimal expansion of $$\frac{{1}}{{x!}}$$ is in the hundredths place.

Let us quickly check few factorials.

$$2! =2$$ ---->$$\frac{1}{2}$$ =.5

$$3!= 6$$ ----> $$\frac{1}{6}$$= .16

$$4! = 24$$ -----> $$\frac{1}{24}$$ = .04 -- first nonzero digit is hundredths place
$$5!= 120$$ -----> $$\frac{1}{120}$$ = .008 ---- Hundredths place is zero.

With increasing value of denominator, place of nonzero digit in decimal expansion will shift to right.

So only $$4!$$has first non zero digit in hundredths place.

Therefore, $$x= 4$$

Statement1 is sufficient.

Statement 2:
The first nonzero digit in the decimal expansion of $$\frac{{1}}{{(x+1)!}}$$ is in the thousandths place.

Let us try some number and check.

$$x= 4$$ ----->$$\frac{1}{(4+1)!}$$ $$=$$ $$\frac{1}{5!}$$ $$=$$ $$0.008$$ after decimal expansion first non zero digit is at thousandths place.

$$x= 5$$ -----> $$\frac{1}{(5+1)!}$$ = $$\frac{1}{6!}$$ $$=$$ $$0.0013$$ after decimal expansion first non zero digit is at thousandths place.

Statement 2 not sufficient.

Answer: A

Regards,
Ammu
Math Expert
Joined: 02 Sep 2009
Posts: 43787
Re: If x is a positive integer, what is the value of x ? [#permalink]

### Show Tags

19 Nov 2014, 06:51
1
This post received
KUDOS
Expert's post
4
This post was
BOOKMARKED
Bunuel wrote:

Tough and Tricky questions: Decimals.

If $$x$$ is a positive integer, what is the value of $$x$$?

(1) The first nonzero digit in the decimal expansion of $$\frac{1}{x!}$$ is in the hundredths place.

(2) The first nonzero digit in the decimal expansion of $$\frac{1}{(x+1)!}$$ is in the thousandths place.

Kudos for a correct solution.

Official Solution:

If $$x$$ is a positive integer, what is the value of $$x$$?

The question does not need rephrasing, although we should note that $$x$$ is a positive integer.

Statement 1: SUFFICIENT. We should work from the inside out by first listing the first several values of $$x!$$ (the factorial of $$x$$, defined as the product of all the positive integers up to and including $$x$$).
$$1! = 1$$
$$2! = 2$$
$$3! = 6$$
$$4! = 24$$
$$5! = 120$$
$$6! = 720$$
$$7! = 5040$$

Now we consider decimal expansions whose first nonzero digit is in the hundredths place. Such decimals must be smaller than $$0.1$$ ($$\frac{1}{10}$$) but at least as large as $$0.01$$ ($$\frac{1}{100}$$). Therefore, for $$\frac{1}{x!}$$ to lie in this range, $$x!$$ must be larger than 10 but no larger than 100. The only factorial that falls between 10 and 100 is $$4! = 24$$, so $$x = 4$$.

(Note that factorials are akin to exponents in the order of operations, so $$\frac{1}{x!}$$ indicates "1 divided by the factorial of $$x$$," not "the factorial of $$\frac{1}{x}$$," which would only have meaning if $$\frac{1}{x}$$ were a positive integer.)

Statement 2: INSUFFICIENT. We consider decimal expansions whose first nonzero digit is in the thousandths place. Such decimals must be smaller than $$0.01$$ ($$\frac{1}{100}$$) but at least as large as $$0.001$$ ($$\frac{1}{1000}$$). Therefore, for $$\frac{1}{(x+1)!}$$ to lie in this range, $$(x+1)!$$ must be larger than 100 but no larger than 1,000.

There are two factorials that fall between 100 and 1,000, namely $$5! = 120$$ and $$6! = 720$$. Thus, $$x+1$$ could be either 5 or 6, and $$x$$ could be either 4 or 5.

Answer: A.
_________________
Non-Human User
Joined: 09 Sep 2013
Posts: 13840
Re: If x is a positive integer, what is the value of x ? [#permalink]

### Show Tags

26 Sep 2017, 23:17
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: If x is a positive integer, what is the value of x ?   [#permalink] 26 Sep 2017, 23:17
Display posts from previous: Sort by

# If x is a positive integer, what is the value of x ?

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.