GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

It is currently 04 Apr 2020, 01:50

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

What is range of the six positive integers: 1, p, 12, q, 15, r?

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

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 62499
What is range of the six positive integers: 1, p, 12, q, 15, r?  [#permalink]

Show Tags

New post 08 Jul 2019, 07:00
1
13
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

45% (01:24) correct 55% (01:37) wrong based on 342 sessions

HideShow timer Statistics

Most Helpful Community Reply
CEO
CEO
User avatar
V
Joined: 03 Jun 2019
Posts: 2502
Location: India
GMAT 1: 690 Q50 V34
WE: Engineering (Transportation)
Premium Member Reviews Badge CAT Tests
Re: What is range of the six positive integers: 1, p, 12, q, 15, r?  [#permalink]

Show Tags

New post 08 Jul 2019, 07:17
3
What is range of the six positive integers: 1, p, 12, q, 15, r?


(1) 1<p<q<5<r<18
r can take values larger than 15, i.e. 16 or 17 which may increase the range. NOT SUFFICIENT.

(2) p+q+r<18
p, q & r are positive integers.
Let us take p & q minimum i.e. p=1 & q=1 to make r as large as possible.
1+1+r<18
=>r<16
r can be maximum 15 and cannot be less than 1.
Therefore, range of 6 integers = 15-1 = 14
SUFFICIENT

Statement 2 alone is SUFFICIENT.


IMO B
General Discussion
Senior Manager
Senior Manager
User avatar
D
Joined: 12 Dec 2015
Posts: 490
Re: What is range of the six positive integers: 1, p, 12, q, 15, r?  [#permalink]

Show Tags

New post 08 Jul 2019, 07:10
3
1
What is range of the six positive integers: 1, p, 12, q, 15, r?


(1) 1<p<q<5<r<18: if r = 15, the range= 15-1=14, but if r = 16, range = 16-1=15, range can't be determined exactly

(2) p+q+r<18 --> correct: case-1: if r = 15, p+q < 3 => p=q=1, case-2: if r=16, p+q < 2 not possible because p & q are positive integer so p+q should be >= 2. So r should be <=15, range = 15-1=14

Answer: B
Manager
Manager
avatar
P
Joined: 29 Nov 2018
Posts: 135
Location: India
Concentration: Entrepreneurship, General Management
GPA: 3.99
WE: Engineering (Computer Hardware)
What is range of the six positive integers: 1, p, 12, q, 15, r?  [#permalink]

Show Tags

New post Updated on: 10 Jul 2019, 19:30
1
1
Option 1:
1<p<q<5<r<181<p<q<5<r<18

r can be greater than 15 or less than 15. if 5<r<15 then the range is 14. If 15<r<18 then range is more than 15.
Insufficient

Option 2: p+q+r<18
If p=q=1 then r<16. since r is a positive integer r can be 15 or less. Hence range will be 14.
If one of p or q is not equal to 1. r being a positive integer will be less than 15. Here too the range will be 14
Sufficient

Ans : B

Originally posted by ruchik on 08 Jul 2019, 07:10.
Last edited by ruchik on 10 Jul 2019, 19:30, edited 1 time in total.
DS Forum Moderator
User avatar
V
Joined: 19 Oct 2018
Posts: 1449
Location: India
Premium Member
Re: What is range of the six positive integers: 1, p, 12, q, 15, r?  [#permalink]

Show Tags

New post 08 Jul 2019, 07:14
1
Statement 1-
r can be any integer from 6 to 17(inclusive)
p can be 2 or 3
q can be 3 or 4

Hence
i) if r is less than or equal to 15, range of 6 number is 15-1=14
ii) if r is 16, range of 6 numbers is 16-1=15
iii) if r is 17, range of 6 numbers is 17-1=16

Insufficient

Statement 2
p+q+r<18
maximum value p, q or r can take is 17-1-1=15
Hence the greatest possible integer among 6 number is 15
Range of 6 numbers= 15-1=14
Sufficient.

IMO B
Intern
Intern
avatar
B
Joined: 30 Aug 2018
Posts: 13
Re: What is range of the six positive integers: 1, p, 12, q, 15, r?  [#permalink]

Show Tags

New post 08 Jul 2019, 22:03
2
okey there are 6 integers 1,p,12,q,15,r.and we have to know the range.
To find the range of any term we have to know the Largest and and the smallest term in the sets.
1) 1<p<q<5<r<18
Notice that all p, q,r are integers.
p and q lies between 1 and 5 means p and q can be {2,3,4} and r is between 5 and 18 means r lowest term can be 6 and largest term of r can be 17.
Now if we arrange our orginal set in asscending order then we can write it as
1,p,q,r,12,15 -------> Here i assumed p=2,q=3 r=7
Since from this we get largest term=15 and lowest term=1 we get rannge=L-S=15-1=14.
1,q,r,12,15,17------> Here i assumed q=2, r=4,r=17
then the largest term=17,lowest =1 then range=17-1=16
AD eliminated.

2) p+q+r<18
if p=1, q=1 r=15 then range after assending order is 15-1=14.
if p=5, q=6, r=7 then again by assecending order range is 15-1=14 again.

So ans =B
Director
Director
avatar
V
Joined: 30 Sep 2017
Posts: 786
GMAT 1: 720 Q49 V40
GPA: 3.8
Premium Member Reviews Badge
What is range of the six positive integers: 1, p, 12, q, 15, r?  [#permalink]

Show Tags

New post 08 Jul 2019, 23:26
1
What is range of the six positive integers: 1, p, 12, q, 15, r?

(1) 1<p<q<5<r<18
- If p,q, and r are positive integers, then the minimum value of p and q are 2 and 3, respectively.
- r has a range between 6 and 17, inclusive.
- The minimum value of the six positive integers is certainly 1, but the maximum value can be 15,16, and 17.
(1) is NOT SUFFICIENT, because the range can be 14,15, or 16

(2) p+q+r<18
- If p and q are 1 each, then the maximum value of r is 15.
- If p and q are 1 and 2, respectively, then the maximum value of r is 14.
Thus, for any combination of p,q, and r, both minimum and maximum values of the six positive integers are always 1 and 15, respectively.
(2) is SUFFICIENT, because the range is 14

ANSWER IS (B)
GMAT Club Bot
What is range of the six positive integers: 1, p, 12, q, 15, r?   [#permalink] 08 Jul 2019, 23:26
Display posts from previous: Sort by

What is range of the six positive integers: 1, p, 12, q, 15, r?

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





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