NEW HERE? LEARN MORE
closeclose
Last visit was: 26 Apr 2024, 19:50 It is currently 26 Apr 2024, 19:50
Decision Tracker
My Rewards
New posts
New comers' posts

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

A positive integer X; divided by 7 has a remainder 2. Which of the fol

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Sajjad1994
GRE Forum Moderator
Joined: 02 Nov 2016
Posts: 13961
Own Kudos [?]: 32951 [1]
Given Kudos: 5780
GPA: 3.62
Send PM
CAT Tests Forum Quiz Mode
A positive integer X; divided by 7 has a remainder 2. Which of the fol [#permalink] New post   28 Oct 2020, 02:06
1
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

5% (low)

Question Stats:

98% (01:14) correct 2% (03:59) wrong based on 45 sessions
Hide Show timer Statistics
A positive integer X, divided by 7 has a remainder 2. Which of the following must be true?

I. X is odd
II. X cannot be a prime number
III. (X + 5) divided by 7 has remainder 0.

(A) I only

(B) I and II only

(C) III only

(D) I and III only

(E) I, II and III
ShowHide Answer
Official Answer
C
User avatar
L
CrackverbalGMAT
GMAT Club Legend
GMAT Club Legend
Joined: 03 Oct 2013
Affiliations: CrackVerbal
Posts: 4946
Own Kudos [?]: 7629 [0]
Given Kudos: 215
Location: India
Send PM
Re: A positive integer X; divided by 7 has a remainder 2. Which of the fol [#permalink] New post   28 Oct 2020, 04:17
Top Contributor
Sajjad1994 wrote:
A positive integer X, divided by 7 has a remainder 2. Which of the following must be true?

I. X is odd
II. X cannot be a prime number
III. (X + 5) divided by 7 has remainder 0.

(A) I only

(B) I and II only

(C) III only

(D) I and III only

(E) I, II and III



Taking values and solving will help

Statement I: Not True. 16 divided by 7 gives a remainder of 2. 16 is even.

Statement II: Not True. 2 divided by 7 gives a remainder of 2. 2 is prime.

Statement III: Always true True. Since the remainder is 2, adding 5 will get us to a number which is a multiple of 7.



Option C

Arun Kumar
avatar
Frodo0808
Intern
Intern
Joined: 22 Aug 2020
Posts: 1
Own Kudos [?]: 3 [0]
Given Kudos: 3
Send PM
Re: A positive integer X; divided by 7 has a remainder 2. Which of the fol [#permalink] New post   28 Oct 2020, 06:15
We can represent X as 7n+2. The important word here is "must" so if there exists a number for which the statement is false we can eliminate that option.

1) 2 is even. 7n will be even for all even values of n. Option 1 eliminated.
2) We can test for a few values of n=1,2,3 etc. For n=3 X=23 (Prime). Option 2 eliminated
3) X+5=7n+7 which will always be divisible by 7. Hence option 3 must be true.

Answer is C.
User avatar
L
Abhishek009
Board of Directors
Joined: 11 Jun 2011
Status:QA & VA Forum Moderator
Posts: 6072
Own Kudos [?]: 4690 [0]
Given Kudos: 463
Location: India
GPA: 3.5
WE:Business Development (Commercial Banking)
Send PM
GMAT ToolKit User
Re: A positive integer X; divided by 7 has a remainder 2. Which of the fol [#permalink] New post   28 Oct 2020, 07:16
Sajjad1994 wrote:
A positive integer X, divided by 7 has a remainder 2. Which of the following must be true?

I. X is odd
II. X cannot be a prime number
III. (X + 5) divided by 7 has remainder 0.

(A) I only

(B) I and II only

(C) III only

(D) I and III only

(E) I, II and III

Least possible value of x is 2

I. x can be even
II. x can be a prime number
III. \(\frac{(x+5)}{7}\) = remiander 0, Hence answer must be (C)
GMAT Club Bot
gmatclubot
Re: A positive integer X; divided by 7 has a remainder 2. Which of the fol [#permalink]
28 Oct 2020, 07:16
Moderators:
Bunuel
Math Expert
92948 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions