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

 It is currently 20 Aug 2018, 15:42

### 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 x^2 < x and x is written as a terminating decimal,does x

Author Message
TAGS:

### Hide Tags

Director
Joined: 25 Apr 2012
Posts: 701
Location: India
GPA: 3.21
If x^2 < x and x is written as a terminating decimal,does x  [#permalink]

### Show Tags

27 Jul 2014, 11:54
3
35
00:00

Difficulty:

95% (hard)

Question Stats:

34% (01:07) correct 66% (00:49) wrong based on 497 sessions

### HideShow timer Statistics

If $$x^{2} < x$$ and x is written as a terminating decimal, does x have a nonzero hundredths digit?

(1) 10x is not an integer.

(2) 100x is an integer.

_________________

“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”

Math Expert
Joined: 02 Sep 2009
Posts: 48067
If x^2 < x and x is written as a terminating decimal,does x  [#permalink]

### Show Tags

27 Jul 2014, 14:20
11
14
If $$x^{2} < x$$ and x is written as a terminating decimal, does x have a nonzero hundredths digit?

$$x^{2} < x$$ means that $$0<x<1$$.

(1) 10x is not an integer. This only means that x is NOT 0.1, 0.2, ...., 0.9. Now, if x=0.01, then the answer is YES but if x=0.001, then the answer is NO. Not sufficient.

(2) 100x is an integer. This means that x is 0.01, 0.02, ..., 0.10, ..., 0.99. The hundredths digit could be 0 as well as nonzero. Not sufficient.

(1)+(2) From (1) 0.10, 0.20, 0.30, 0.40, 0.50, 0.60, 0.70, 0.80 and 0.90 are excluded, thus from (2) only those decimals are left which have a nonzero hundredths digit: 0.01, 0.02, ..., 0.09, 0.11, ..., 0.19, ..., 0.21, ..., 0.99. Sufficient.

Hope it's clear.
_________________
##### General Discussion
Manager
Joined: 03 Jul 2013
Posts: 89
Schools: ISB '17 (A), IIMC (A)
GMAT 1: 660 Q48 V32
Re: If x^2 < x and x is written as a terminating decimal,does x  [#permalink]

### Show Tags

08 Oct 2014, 01:51
Hi. Suppose i choose two numbers 0.23 and 0.03 for both of them x^2<x

Both number satisfy both the statements:

x=0.23 10x=2.3, not an integer
x=0.23 100X=23 is an integer

x=0.03 10x=0.3 is not an integer
x=0.03 100x=3 is an integer

in case 1 100 digit is 2 and in case 2 100 digit is 0.

_________________

Sometimes standing still can be, the best move you ever make......

Math Expert
Joined: 02 Sep 2009
Posts: 48067
Re: If x^2 < x and x is written as a terminating decimal,does x  [#permalink]

### Show Tags

08 Oct 2014, 01:57
3
3
Hi. Suppose i choose two numbers 0.23 and 0.03 for both of them x^2<x

Both number satisfy both the statements:

x=0.23 10x=2.3, not an integer
x=0.23 100X=23 is an integer

x=0.03 10x=0.3 is not an integer
x=0.03 100x=3 is an integer

in case 1 100 digit is 2 and in case 2 100 digit is 0.

In both cases the hundredths digit is 3: 0.23 and 0.03.

1234.567

1 - THOUSANDS
2 - HUNDREDS
3 - TENS
4 - UNITS
. - decimal point
5 - TENTHS
6 - HUNDREDTHS
7 - THOUSANDTHS

Hope it helps.
_________________
Intern
Joined: 06 Nov 2013
Posts: 31
Re: If x^2 < x and x is written as a terminating decimal,does x  [#permalink]

### Show Tags

09 Oct 2014, 01:47
Hi Bunuel, could u elaborate the explanation for this one? As soon as I saw that "100x is an integer" , figures like .99, .45, .01 come to mind and thus 100x always has a zero hundredth digit.

example: if x=.abcd
100x is an integer then 100x= ab.cd
for ab.cd to be an integer, cd has to be zero. therefore, hundredth place of x is a zero integer.

_________________

'I read somewhere... how important it is in life not necessarily to be strong, but to feel strong... to measure yourself at least once.'

Math Expert
Joined: 02 Sep 2009
Posts: 48067
If x^2 < x and x is written as a terminating decimal,does x  [#permalink]

### Show Tags

09 Oct 2014, 02:34
shreyagmat wrote:
Hi Bunuel, could u elaborate the explanation for this one? As soon as I saw that "100x is an integer" , figures like .99, .45, .01 come to mind and thus 100x always has a zero hundredth digit.

example: if x=.abcd
100x is an integer then 100x= ab.cd
for ab.cd to be an integer, cd has to be zero. therefore, hundredth place of x is a zero integer.

How is hundredths digit of 0.99, 0.45, or 0.01 zeo?
_________________
Intern
Joined: 06 Nov 2013
Posts: 31
Re: If x^2 < x and x is written as a terminating decimal,does x  [#permalink]

### Show Tags

09 Oct 2014, 03:08
say x is .45
then statement says that 100x is an integer ( of the form xx.0)
if thats true then x cant be .455 or .555, it has to be something like .45 or .10 ( since .45*100 = 45)

I dont even know where im wrong.
_________________

'I read somewhere... how important it is in life not necessarily to be strong, but to feel strong... to measure yourself at least once.'

Math Expert
Joined: 02 Sep 2009
Posts: 48067
Re: If x^2 < x and x is written as a terminating decimal,does x  [#permalink]

### Show Tags

09 Oct 2014, 03:11
shreyagmat wrote:
say x is .45
then statement says that 100x is an integer ( of the form xx.0)
if thats true then x cant be .455 or .555, it has to be something like .45 or .10 ( since .45*100 = 45)

I dont even know where im wrong.

x CANNOT be 0.1 because (1) say that 10x is NOT an integer and if x=0.1, then 10x=1=integer. Anyway, what's your question?
_________________
Intern
Joined: 06 Nov 2013
Posts: 31
Re: If x^2 < x and x is written as a terminating decimal,does x  [#permalink]

### Show Tags

09 Oct 2014, 04:08
I just realized the mistake i was making.
i was counting a unit digit after decimal point and thought that B is sufficient. But now i realized its not the case.

Here is what i understand now:
.abc . question : is b zero or nonzero?

statement 1: a.b is not integer.
x could be :: .001 or .01
b can be zero or non zero if c is non-zero (.011 , .001) ; but if c is zero then b has to be non zero in order for 10x to not be an integer
Insuff
statement 2: c is zero

(1+2)
when c is zero , b is non zero

Is my logic correct this time?
_________________

'I read somewhere... how important it is in life not necessarily to be strong, but to feel strong... to measure yourself at least once.'

Current Student
Joined: 23 May 2013
Posts: 189
Location: United States
Concentration: Technology, Healthcare
Schools: Stanford '19 (M)
GMAT 1: 760 Q49 V45
GPA: 3.5
If x^2 < x and x is written as a terminating decimal,does x  [#permalink]

### Show Tags

09 Oct 2014, 10:12
WoundedTiger wrote:
If $$x^{2} < x$$ and x is written as a terminating decimal, does x have a nonzero hundredths digit?

(1) 10x is not an integer.

(2) 100x is an integer.

Here's how I did it:

I represented x as x = .abc (I didn't go further because the question didn't ask for more than tens/hundredths digits).

1) 10x is NOT an integer. This means that a.bc is NOT an integer. Therefore, b and c cannot BOTH be zero; otherwise 10x would be an integer. Not sufficient.

2) 100x IS an integer. This means that ab.c is an integer, and therefore that c = 0. This just gives us x = .ab0 - no information about b. Not sufficient.

Together though, we know that c = 0. However, we also know that b and c cannot BOTH be zero. Therefore, b has to be nonzero.

Manager
Joined: 05 Jun 2014
Posts: 63
GMAT 1: 630 Q42 V35
Re: If x^2 < x and x is written as a terminating decimal,does x  [#permalink]

### Show Tags

15 Oct 2014, 09:43
Bunuel plz explain where am i going wrong, if I select two numbers i.e 0.105 and 0.125.
Both when multiplied by 10 become 10.5 and 12.5 (non - integers)
both when multiplied by 100 become integers 105 and 125.
But in one the hundreth digit and 0 and the other one its 2..What am i missing??? Thanks in advance !
Math Expert
Joined: 02 Sep 2009
Posts: 48067
Re: If x^2 < x and x is written as a terminating decimal,does x  [#permalink]

### Show Tags

15 Oct 2014, 09:58
Bunuel plz explain where am i going wrong, if I select two numbers i.e 0.105 and 0.125.
Both when multiplied by 10 become 10.5 and 12.5 (non - integers)
both when multiplied by 100 become integers 105 and 125.
But in one the hundreth digit and 0 and the other one its 2..What am i missing??? Thanks in advance !

Check the red parts.

10x = 1.05 and 1.25, receptively.
100x = 10.5 and 12.5, receptively.
_________________
Retired Moderator
Joined: 05 Jul 2006
Posts: 1731
Re: If x^2 < x and x is written as a terminating decimal,does x  [#permalink]

### Show Tags

28 Dec 2016, 03:47
WoundedTiger wrote:
If $$x^{2} < x$$ and x is written as a terminating decimal, does x have a nonzero hundredths digit?

(1) 10x is not an integer.

(2) 100x is an integer.

x is a +ve fraction , in decimal form ... 0.abcd... , is b not 0

from 1

a.bcd... is not integer ... b or c or d could be any digit , i.e b = 0 but c is not or b a no zero digit and c,d = 0 ... insuff

from 2

ab.cd.. = ab thus c,d...etc = 0 ... no idea about b itself .. insuff

both

the decimal representation of x is in the form 0.ab and a.b is not integer thus b aint zero ... suff

C
Non-Human User
Joined: 09 Sep 2013
Posts: 7770
Re: If x^2 < x and x is written as a terminating decimal,does x  [#permalink]

### Show Tags

29 Jan 2018, 13:19
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^2 < x and x is written as a terminating decimal,does x &nbs [#permalink] 29 Jan 2018, 13:19
Display posts from previous: Sort by

# Events & Promotions

 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®.