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

 It is currently 14 Oct 2019, 02:29 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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  If n is a positive integer, how many of the ten digits from

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

Hide Tags

Intern  Joined: 08 Feb 2014
Posts: 1
If n is a positive integer, how many of the ten digits from  [#permalink]

Show Tags

4
1
36 00:00

Difficulty:   65% (hard)

Question Stats: 59% (01:37) correct 41% (01:52) wrong based on 969 sessions

HideShow timer Statistics

If n is a positive integer, how many of the ten digits from 0 through 9 could be the units digits of n^3 ?

A. Three
B. Four
C. Six
D. Nine
E. Ten

Can anyone help me with this question? Thanks!
Math Expert V
Joined: 02 Sep 2009
Posts: 58288
Re: If n is a positive integer, how many of the ten digits from  [#permalink]

Show Tags

8
7
Qoofi wrote:
Any one with a better solution for this?

If n is a positive integer, how many of the ten digits from 0 through 9 could be the units digits of n^3 ?

A. Three
B. Four
C. Six
D. Nine
E. Ten

The question is fairly straightforward, it basically asks: which digits can be the units digit of a perfect cube.

Can it be 0? Yes, 10^3=1,000.
Can it be 1? Yes, 1^3=1.
Can it be 2? Yes, 8^3=512.
Can it be 3? Yes, 7^3=343.
Can it be 4? Yes, 4^3=64.
Can it be 5? Yes, 5^3=125.
Can it be 6? Yes, 6^3=...6.
Can it be 7? Yes, 3^3=27.
Can it be 8? Yes, 2^3=8.
Can it be 9? Yes, 9^3=...9.

_________________
SVP  Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1751
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: If n is a positive integer, how many of the ten digits from  [#permalink]

Show Tags

8
3
For a number to be a cube, any digit from 0 to 9 may be in the units place,

however for a number to be a square, there are only six possibilities in units place which are

0, 1, 4, 5, 6, 9
_________________
Kindly press "+1 Kudos" to appreciate General Discussion
Intern  B
Status: Going the extra mile
Joined: 08 Feb 2014
Posts: 14
Location: Netherlands
Concentration: Strategy, International Business
GMAT 1: 470 Q37 V18 GMAT 2: 570 Q36 V32 GMAT 3: 560 Q37 V30 GMAT 4: 610 Q41 V34 Re: If n is a positive integer, how many of the ten digits from  [#permalink]

Show Tags

2
Im also not completely sure about this one. But if you simply plug in values for ''n'' from 0 tot 9.
This will show you that units digit can be 0,1,2,3,4,5,6,7,8,9 = 10.
0^3=0 , 1^3=1 , 2^3=8 , 3^3=27, 4^3=64, 5^3=125, 6^3=216, 7^3=343, 8^3=512, 9^3=729

These possibilities keep repeating themselves.
_________________
Structural persistence is the key to succes .
Party hard, study harder.

Still bashing, will continue to do so , although it's important to chill aswell ; )
STUDY+CHILL=VICTORY

Originally posted by CarloCjm on 08 Feb 2014, 12:43.
Last edited by CarloCjm on 09 Feb 2014, 03:15, edited 1 time in total.
Manager  Joined: 11 Jan 2014
Posts: 86
Concentration: Finance, Statistics
GMAT Date: 03-04-2014
GPA: 3.77
WE: Analyst (Retail Banking)
Re: If n is a positive integer, how many of the ten digits from  [#permalink]

Show Tags

I did it exactly like carlocjm explained, in around 2 minutes. Keep in mind that you don't have to go through the whole multiplication process, just get the units digits and stop, since that's what we're concerned about. Also, for some numbers, you actually don't have to do manual stuff (5^3 is by heart 125, for example).

I'd say (E), too. Waiting for other solutions.
Manager  B
Joined: 18 Dec 2012
Posts: 94
Location: India
Concentration: General Management, Strategy
GMAT 1: 660 Q49 V32 GMAT 2: 530 Q37 V25 GPA: 3.32
WE: Manufacturing and Production (Manufacturing)
Re: If n is a positive integer, how many of the ten digits from  [#permalink]

Show Tags

Any one with a better solution for this?
_________________
I'm telling this because you don't get it. You think you get it which is not the same as actually getting it. Get it?
Intern  Joined: 30 Mar 2014
Posts: 4
Re: If n is a positive integer, how many of the ten digits from  [#permalink]

Show Tags

I'm confused. I got D) 9, because I read "n is a positive integer" and immediately wrote down on my paper n>0. So I did not consider 0^3.

I thought zero was not positive or or negative. Can someone confirm??
Math Expert V
Joined: 02 Sep 2009
Posts: 58288
Re: If n is a positive integer, how many of the ten digits from  [#permalink]

Show Tags

1
macey15 wrote:
I'm confused. I got D) 9, because I read "n is a positive integer" and immediately wrote down on my paper n>0. So I did not consider 0^3.

I thought zero was not positive or or negative. Can someone confirm??

Yes, zero is neither positive nor negative.

But 0 still can be the units digit of a perfect cube, consider 10^3=1,000.
_________________
Intern  Joined: 30 Mar 2014
Posts: 4
Re: If n is a positive integer, how many of the ten digits from  [#permalink]

Show Tags

Bunuel wrote:
macey15 wrote:
I'm confused. I got D) 9, because I read "n is a positive integer" and immediately wrote down on my paper n>0. So I did not consider 0^3.

I thought zero was not positive or or negative. Can someone confirm??

Yes, zero is neither positive nor negative.

But 0 still can be the units digit of a perfect cube, consider 10^3=1,000.

Of course!! For some reason I got stuck on n = 1-9, which looking back, the problem definitely does NOT say. Thanks!
Intern  Joined: 20 Sep 2015
Posts: 8
Re: If n is a positive integer, how many of the ten digits from  [#permalink]

Show Tags

CarloCjm wrote:
Im also not completely sure about this one. But if you simply plug in values for ''n'' from 0 tot 9.
This will show you that units digit can be 0,1,2,3,4,5,6,7,8,9 = 10.
0^3=0 , 1^3=1 , 2^3=8 , 3^3=27, 4^3=64, 5^3=125, 6^3=216, 7^3=343, 8^3=512, 9^3=729

These possibilities keep repeating themselves.

You got to the right conclusion, but be careful: the question states n has to be a POSITIVE integer, therefore 0 is excluded. The 0 units digit comes from 10^3
Current Student D
Joined: 12 Aug 2015
Posts: 2574
Schools: Boston U '20 (M)
GRE 1: Q169 V154 Re: If n is a positive integer, how many of the ten digits from  [#permalink]

Show Tags

Outstanding Question.
Here we need to get the units digit of n^3
Consider the unit digit of n being 0,1,2...
0=> 0
1=> 1
2=>8
3=>7
4=>4
5=>5
6=>6
7=>3
8=>2
9=>9

Hence all ten digits are possible.

Hence E
_________________
Manager  B
Joined: 26 Mar 2017
Posts: 107
Re: If n is a positive integer, how many of the ten digits from  [#permalink]

Show Tags

ok im not the only one who didn't read thoroughly _________________
I hate long and complicated explanations!
Intern  B
Joined: 26 Jun 2015
Posts: 37
Location: India
Concentration: Entrepreneurship, General Management
WE: Engineering (Energy and Utilities)
Re: If n is a positive integer, how many of the ten digits from  [#permalink]

Show Tags

I am expecting a quicker way than below..
The question is fairly straightforward, it basically asks: which digits can be the units digit of a perfect cube.

Can it be 0? Yes, 10^3=1,000.
Can it be 1? Yes, 1^3=1.
Can it be 2? Yes, 8^3=512.
Can it be 3? Yes, 7^3=343.
Can it be 4? Yes, 4^3=64.
Can it be 5? Yes, 5^3=125.
Can it be 6? Yes, 6^3=...6.
Can it be 7? Yes, 3^3=27.
Can it be 8? Yes, 2^3=8.
Can it be 9? Yes, 9^3=...9.
Manager  B
Joined: 26 Mar 2017
Posts: 107
If n is a positive integer, how many of the ten digits from  [#permalink]

Show Tags

hotcool030 wrote:
I am expecting a quicker way than below..
The question is fairly straightforward, it basically asks: which digits can be the units digit of a perfect cube.

Can it be 0? Yes, 10^3=1,000.
Can it be 1? Yes, 1^3=1.
Can it be 2? Yes, 8^3=512.
Can it be 3? Yes, 7^3=343.
Can it be 4? Yes, 4^3=64.
Can it be 5? Yes, 5^3=125.
Can it be 6? Yes, 6^3=...6.
Can it be 7? Yes, 3^3=27.
Can it be 8? Yes, 2^3=8.
Can it be 9? Yes, 9^3=...9.

what do you mean by "I am expecting a quicker way"

Thats a very fast way

you don't have to compute x^3 if that is your questions

For instance: 5^2 = 25 --> 5^3 = 5*5 = xx5
_________________
I hate long and complicated explanations!
Target Test Prep Representative D
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8040
Location: United States (CA)
Re: If n is a positive integer, how many of the ten digits from  [#permalink]

Show Tags

1
1
Pimenton wrote:
If n is a positive integer, how many of the ten digits from 0 through 9 could be the units digits of n^3 ?

A. Three
B. Four
C. Six
D. Nine
E. Ten

To solve, we need to raise each digit of 0 through 9 to the third power to determine how many unique units digits we can produce.

0^3 = 0

1^3 = 1

2^3 = 8

3^3 = 27 (units digit of 7)

4^3 = 64 (units digit of 4)

5^3 = 125 (units digit of 5)

Since after the base of 5 the number starts getting fairly large, we can rely on our knowledge of units digit patterns of a number raised to a power to determine the units digits of the remaining numbers.

6^3 = units digit of 6

We should recall that 6 raised to any whole number exponent will always have a units digit of 6.

7^3 = units digit of 7

We should recall that the repeating pattern for the units digits when the base of 7 is raised to an exponent is 3-9-7-1.

8^3 = units digit of 2

We should recall that the repeating pattern for the units digits when the base of 8 is raised to an exponent is 8-4-2-6.

9^3 = units digit of 9

We should recall that the pattern for the units digits when the base of 9 is raised to an exponent is 9-1.

Thus, there are 10 possible units digits for n^3 for the integers 0 through 9.

_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Intern  Joined: 31 May 2017
Posts: 2
If n is a positive integer, how many of the ten digits from  [#permalink]

Show Tags

Can someone please explain how "how many of the ten digits from 0 through 9 could be the units digits of n^3 ?" translates to "which digits can be the units digit of a perfect cube?"
Math Expert V
Joined: 02 Sep 2009
Posts: 58288
Re: If n is a positive integer, how many of the ten digits from  [#permalink]

Show Tags

sunilrawat wrote:
Can someone please explain how "how many of the ten digits from 0 through 9 could be the units digits of n^3 ?" translates to "which digits can be the units digit of a perfect cube?"

n^3 is a prefect cube, a cube of an integer. The question asks how many values can the units digit of n^3 take.
_________________
Intern  Joined: 09 Oct 2018
Posts: 2
Re: If n is a positive integer, how many of the ten digits from  [#permalink]

Show Tags

Bunuel wrote:
sunilrawat wrote:
Can someone please explain how "how many of the ten digits from 0 through 9 could be the units digits of n^3 ?" translates to "which digits can be the units digit of a perfect cube?"

n^3 is a prefect cube, a cube of an integer. The question asks how many values can the units digit of n^3 take.

hi,
"how many of the ten digits from 0 through 9 could be the units digits of n^3 ?"

what is the meaning of "ten digits from 0 through 9 "
can you please explain this...
My first impression is that it means tenth digit equal to unit digit Re: If n is a positive integer, how many of the ten digits from   [#permalink] 28 Dec 2018, 21:11
Display posts from previous: Sort by

If n is a positive integer, how many of the ten digits from

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

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne  