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

It is currently 15 Feb 2019, 19:23

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 February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar
  • $450 Tuition Credit & Official CAT Packs FREE

     February 15, 2019

     February 15, 2019

     10:00 PM EST

     11:00 PM PST

    EMPOWERgmat is giving away the complete Official GMAT Exam Pack collection worth $100 with the 3 Month Pack ($299)
  • Free GMAT practice

     February 15, 2019

     February 15, 2019

     10:00 PM EST

     11:00 PM PST

    Instead of wasting 3 months solving 5,000+ random GMAT questions, focus on just the 1,500 you need.

If 1 ≤ n ≤ 100, and n + 7/2 is a multiple of 4 but not a multiple of 3

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

Hide Tags

 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 52905
If 1 ≤ n ≤ 100, and n + 7/2 is a multiple of 4 but not a multiple of 3  [#permalink]

Show Tags

New post 05 Feb 2019, 03:51
1
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

45% (02:31) correct 55% (02:11) wrong based on 22 sessions

HideShow timer Statistics

If 1 ≤ n ≤ 100, and \(\frac{n + 7}{2}\) is a multiple of 4 but not a multiple of 3, then which of the following could be true?

I. n is prime
II. n is a multiple of 3
III. n is a multiple of 4

A. I only
B. II only
C. III only
D. I and II only
E. I, II and III

_________________

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

SVP
SVP
User avatar
G
Joined: 18 Aug 2017
Posts: 1770
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
GMAT ToolKit User Premium Member CAT Tests
If 1 ≤ n ≤ 100, and n + 7/2 is a multiple of 4 but not a multiple of 3  [#permalink]

Show Tags

New post Updated on: 05 Feb 2019, 05:18
1
Bunuel wrote:
If 1 ≤ n ≤ 100, and \(\frac{n + 7}{2}\) is a multiple of 4 but not a multiple of 3, then which of the following could be true?

I. n is prime
II. n is a multiple of 3
III. n is a multiple of 4

A. I only
B. II only
C. III only
D. I and II only
E. I, II and III



1 ≤ n ≤ 100, and \(\frac{n + 7}{2}\) is a multiple of 4
for this relation to be valid
n has to be odd no.

so option 3 are ruled out
n= is prime is correct and n is a multiple of 3 is correct
IMO D is correct.
_________________

If you liked my solution then please give Kudos. Kudos encourage active discussions.


Originally posted by Archit3110 on 05 Feb 2019, 04:24.
Last edited by Archit3110 on 05 Feb 2019, 05:18, edited 1 time in total.
Intern
Intern
avatar
B
Joined: 21 May 2018
Posts: 5
CAT Tests
Re: If 1 ≤ n ≤ 100, and n + 7/2 is a multiple of 4 but not a multiple of 3  [#permalink]

Show Tags

New post 05 Feb 2019, 05:12
Question has asked for COULD BE TRUE scenario.

For the expression to be divisible by 2, n value should be ODD
This rules out 3rd option.

Let's try to plug n=9
so, 9+7/2=8

Let's try to plug n=13
so, 13+7/2 =10

Above 2 scenarios explain that n can be multiple of 3 or prime number. Hence, the answer is D
_________________

Please appreciate with Kudos!

Intern
Intern
avatar
B
Joined: 25 Feb 2018
Posts: 8
Location: Japan
Concentration: Strategy, International Business
GMAT 1: 540 Q47 V18
GPA: 3.57
CAT Tests
Re: If 1 ≤ n ≤ 100, and n + 7/2 is a multiple of 4 but not a multiple of 3  [#permalink]

Show Tags

New post 05 Feb 2019, 18:44
Given n+7/2 = 4x
so n+7=8x
Meaning that n+7 is some numbers which can be divided by 8.
then N could be an odd number.
III. is out.

Try check other numbers.
From 8, 16, 24,32 ,40, 48, 56, 64, 72, 80, 88, 96, 104
cut off the numbers which are divided by 3.
We will have N+7 as 8, 16,32,40,56,64,80,88,104

We will have N as 1,9,25,33,49,57,73,81,97

9 could be divided by 3
and
73 is a prime number.

So D is the answer.
Manager
Manager
User avatar
P
Joined: 28 Jul 2016
Posts: 240
Location: India
Concentration: Finance, Human Resources
GPA: 3.97
If 1 ≤ n ≤ 100, and n + 7/2 is a multiple of 4 but not a multiple of 3  [#permalink]

Show Tags

New post 05 Feb 2019, 21:02
given n+7/2 is a multiple of 4
thus \(4k =\frac{n+7}{2}\)
hence n is of form 8k-7
now this expression will never be divisible 4. .... statement III out
k can take any number for which n will be prime such as k =3 = 24-7 =17.
Hence statement I is possible.
8k-7 can be re-written as\(8k-4-3= 4(2k-1) -3\)
this is divisible by 3 for k = 2,
Hence statement II is possible.


Thus only I and II statements are possible.
Thus option D
_________________

Please give Kudos. Kudos encourage active discussions and help the community grow

GMAT Club Bot
If 1 ≤ n ≤ 100, and n + 7/2 is a multiple of 4 but not a multiple of 3   [#permalink] 05 Feb 2019, 21:02
Display posts from previous: Sort by

If 1 ≤ n ≤ 100, and n + 7/2 is a multiple of 4 but not a multiple of 3

  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®.