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

It is currently 18 Jan 2019, 22:20

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 January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar
  • Free GMAT Strategy Webinar

     January 19, 2019

     January 19, 2019

     07:00 AM PST

     09:00 AM PST

    Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.
  • FREE Quant Workshop by e-GMAT!

     January 20, 2019

     January 20, 2019

     07:00 AM PST

     07:00 AM PST

    Get personalized insights on how to achieve your Target Quant Score.

If x is an integer greater than 1, is y divisible by x ?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
Manager
Manager
avatar
B
Joined: 29 Nov 2018
Posts: 52
Location: India
Concentration: Entrepreneurship, General Management
GPA: 3.99
WE: Engineering (Computer Hardware)
If x is an integer greater than 1, is y divisible by x ?  [#permalink]

Show Tags

New post 18 Dec 2018, 20:25
1
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

60% (02:13) correct 40% (03:19) wrong based on 5 sessions

HideShow timer Statistics

If x is an integer greater than 1, is y divisible by x?

(1) y is divisible by x−1
(2) y=x!+x−1

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
Both statements (1) and (2) TOGETHER are sufficient to answer the question asked; but NEITHER statement ALONE is sufficient
EACH statement ALONE is sufficient to answer the question asked
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed
Manager
Manager
avatar
B
Joined: 29 Nov 2018
Posts: 52
Location: India
Concentration: Entrepreneurship, General Management
GPA: 3.99
WE: Engineering (Computer Hardware)
Re: If x is an integer greater than 1, is y divisible by x ?  [#permalink]

Show Tags

New post 18 Dec 2018, 20:33
OA from Veritas:

This problem rewards students who remember that all multiples of the integer x will be x units apart. Statement (1) gives that y is divisible by x−1. This can be proven insufficient with a quick number picking thought experiment. If x=4 is it possible to have a number that is divisible by both x=4 and x−1=3? If you multiply 3 and 4 together to get 12, the answer is yes, there are an infinite number of ways to have a value of y that is divisible by both x and x−1.

Conversely, there are also an infinite number of integers that are divisible by x−1 that aren't divisible by x. In the case of x−1=3, 6, 9, and 21 are all divisible by 3 but aren't divisible by 4. Since this means you can get both a "yes" and a "no" based on the information given in statement (1), statement (1) is insufficient. Eliminate (A) and (D).

Statement (2) gives that y=x!+x−1. This may seem to give information similar to what is given in statement (1), but it is much more sufficient.

Remember that x! can be written as "(x)(x−1)(x−2)(x−3).....(2)(1)".

This means that for any given value for x where x is an integer greater than 1, that x! must be divisible by x−1 as well as x.

If you add x−1 to x!, you get a number that is divisible by x−1 but that cannot be divisible by x. To understand this, it helps to pick numbers.

If x=4, then x!=(4)(3)(2)=24. If you add x−1=3 to that, you get 27, which is still divisible by 3 but that isn't divisible by 4.

This is because multiples of the same number are evenly spaced - all multiples of 4 will be 4 apart, all multiples of 3 will be 3 apart, etc. So for whatever number you pick for x, if you add x−1 you will always get a number that is 1 less than a multiple of x, which means that y can never be divisible by x.

This means that statement (2) gives you a consistent "no" and is sufficient. Answer choice (B) is correct.
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 52285
Re: If x is an integer greater than 1, is y divisible by x ?  [#permalink]

Show Tags

New post 18 Dec 2018, 21:02
ruchik wrote:
If x is an integer greater than 1, is y divisible by x?

(1) y is divisible by x−1
(2) y=x!+x−1

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
Both statements (1) and (2) TOGETHER are sufficient to answer the question asked; but NEITHER statement ALONE is sufficient
EACH statement ALONE is sufficient to answer the question asked
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed


Discussed here: https://gmatclub.com/forum/if-x-is-an-i ... 72152.html

THE TOPIC IS LOCKED AND ARCHIVED.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

GMAT Club Bot
Re: If x is an integer greater than 1, is y divisible by x ? &nbs [#permalink] 18 Dec 2018, 21:02
Display posts from previous: Sort by

If x is an integer greater than 1, is y divisible by x ?

  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®.