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

It is currently 13 Dec 2018, 08:02

R1 Admission Decisions:

Stanford Chat (Calls Started)  |  Wharton Chat  (Calls Expected Soon)  |  Fuqua Chat (Calls Expected Soon)


Close

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel
Events & Promotions in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
  • The winning strategy for 700+ on the GMAT

     December 13, 2018

     December 13, 2018

     08:00 AM PST

     09:00 AM PST

    What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL.
  • GMATbuster's Weekly GMAT Quant Quiz, Tomorrow, Saturday at 9 AM PST

     December 14, 2018

     December 14, 2018

     09:00 AM PST

     10:00 AM PST

    10 Questions will be posted on the forum and we will post a reply in this Topic with a link to each question. There are prizes for the winners.

If X is a positive integer, what is the

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

Hide Tags

e-GMAT Representative
User avatar
D
Joined: 04 Jan 2015
Posts: 2303
If X is a positive integer, what is the  [#permalink]

Show Tags

New post Updated on: 13 Aug 2018, 01:18
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

70% (01:43) correct 30% (01:43) wrong based on 150 sessions

HideShow timer Statistics

e-GMAT Question:



If \(X\) is a positive integer, what is the units digit of \(X^a\)?

1) \(X\) when divided by \(10\) gives a remainder of \(2\)
2) \(8^a\) ends with \(6\)

A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D) EACH statement ALONE is sufficient.
E) Statements (1) and (2) TOGETHER are NOT sufficient

This is

Question 5 of The e-GMAT Number Properties Marathon




Go to

Question 6 of the Marathon


_________________








Register for free sessions
Number Properties | Algebra |Quant Workshop

Success Stories
Guillermo's Success Story | Carrie's Success Story

Ace GMAT quant
Articles and Question to reach Q51 | Question of the week

Must Read Articles
Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2 | Remainders-1 | Remainders-2
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line | Inequalities

Practice Questions
Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets



| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com


Originally posted by EgmatQuantExpert on 27 Feb 2018, 09:43.
Last edited by EgmatQuantExpert on 13 Aug 2018, 01:18, edited 2 times in total.
PS Forum Moderator
avatar
D
Joined: 25 Feb 2013
Posts: 1217
Location: India
GPA: 3.82
GMAT ToolKit User Premium Member Reviews Badge
Re: If X is a positive integer, what is the  [#permalink]

Show Tags

New post 27 Feb 2018, 09:59
1
EgmatQuantExpert wrote:

Question:



If \(X\) is a positive integer, what is the units digit of \(X^a\)?

1) \(X\) when divided by \(10\) gives a remainder of \(2\)
2) \(8^a\) ends with \(6\)

A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D) EACH statement ALONE is sufficient.
E) Statements (1) and (2) TOGETHER are NOT sufficient


We need to know the unit's digit of \(x\) & \(a\)

Statement 1: this implies that unit's digit of \(x\) is \(2\). But nothing mentioned about \(a\). Insufficient

Statement 2: this implies that \(a\) is a multiple of \(4\) because unit's digit of \(8^4\) is \(6\). Hence \(a=4k\), where \(k\) is any integer. but nothing mentioned about \(x\). Insufficient

Combining 1 & 2: we know that unit's digit of \(2^4=6\) and \(6\) raised to any power will have unit's digit \(6\). So unit's digit of \(x^a\) will be \(6\). Sufficient

Option C
e-GMAT Representative
User avatar
D
Joined: 04 Jan 2015
Posts: 2303
Re: If X is a positive integer, what is the  [#permalink]

Show Tags

New post 27 Feb 2018, 22:58

Solution:



Step 1: Analyse Statement 1:
\(X\), when divided by \(10\), gives a remainder of \(2\)
    • Per our conceptual understanding, when a number is divided by \(10\), the remainder is equal to the units digit of the number.
      o Here, when X is divided by \(10\), the remainder is \(2\).
      o Hence, \(2\) is the units digit of X.
    • But to calculate the units digit of the expression, \(X^a\), we need more information on the value of a.

Since we do not have that information,
Statement 1 alone is NOT sufficient to answer the question.
Hence, we can eliminate answer choices A and D.
Step 2: Analyse Statement 2:
\(8^a\) ends with \(6\)
    • Per our conceptual understanding, we know that the cyclicity of \(8\) is \(4\) and for \(8^a\) end with \(6\), \(a\) should be of the form :\(4k\). From this, we know the nature of the number \(a\), but we do not have any information about\(X\).

Since we do not know the value of \(X\),
Statement 2 alone is NOT sufficient to answer the question.
Hence, we can eliminate answer choice B.

Step 3: Combine both Statements:
    • From the first statement, we know: The units digit of \(X\) is \(2\)
    • From the second statement we have: a is a multiple of \(4\)
    • We know that a is of form 4k, and we also know\(2^{4k}\) always has a units digit: \(6\).
Thus, we know that the units digit of the expression \(X^a\) is \(6\).
By combining both statements we got a unique answer.
Correct Answer: Option C
_________________








Register for free sessions
Number Properties | Algebra |Quant Workshop

Success Stories
Guillermo's Success Story | Carrie's Success Story

Ace GMAT quant
Articles and Question to reach Q51 | Question of the week

Must Read Articles
Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2 | Remainders-1 | Remainders-2
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line | Inequalities

Practice Questions
Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets



| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

VP
VP
User avatar
V
Status: It's near - I can see.
Joined: 13 Apr 2013
Posts: 1352
Location: India
Concentration: International Business, Operations
GMAT 1: 480 Q38 V22
GPA: 3.01
WE: Engineering (Consulting)
Premium Member Reviews Badge CAT Tests
Re: If X is a positive integer, what is the  [#permalink]

Show Tags

New post 29 Mar 2018, 01:48
EgmatQuantExpert wrote:

e-GMAT Question:



If \(X\) is a positive integer, what is the units digit of \(X^a\)?

1) \(X\) when divided by \(10\) gives a remainder of \(2\)
2) \(8^a\) ends with \(6\)

A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D) EACH statement ALONE is sufficient.
E) Statements (1) and (2) TOGETHER are NOT sufficient


Given: X > 0

Units digit of X^a

St 1: X = 2, 12, 22, and Units digit of X^a can be 2, 4, 8, 6. Insufficient, no information about "a"

St 2: \(8^a\) ends with \(6\) means "a" is a multiple of "4" , but we don't know about "X" Insufficient

Combining we get unit digit of X^a will be "6" as every 4th power of 2 or 12 or 22 will give you units digit "6"

(C)
_________________

"Do not watch clock; Do what it does. KEEP GOING."

GMAT Club Bot
Re: If X is a positive integer, what is the &nbs [#permalink] 29 Mar 2018, 01:48
Display posts from previous: Sort by

If X is a positive integer, what is the

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


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

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®.