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

Question

(1)  1 < p < q < 5 < r < 18

(2)  p + q + r < 18

Kinshook · Accepted Answer

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

hiranmay · Answer

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

(1) \(1 < p < q < 5 < r < 18\)

(2) \(p + q + r < 18\)

This question was provided by e-GMAT
for the Game of Timers Competition

Show Answer

Official Answer

B

ruchik · Answer

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

nick1816 · Answer

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

santoshkhatri · Answer

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

freedom128 · Answer

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)

XLmafia21 · Answer

Ok, so when I assume that the original set given in the question is in ascending order, the question is solvable. But, the question does not state as such. How do I know I have to consider them in ascending order or am I missing something?
 Bunuel 
TIA

Bunuel · Answer

There is no indication that the numbers are given in any specific order. Assuming they are in ascending order would be an unsupported assumption and is not allowed.

Even if you assume the numbers are in ascending order, r could still be 16 or 17, leading to different possible ranges.

So the assumption would not even fix the uncertainty.

Also, pure algebraic questions are no longer a part of the  DS syllabus  of the GMAT.

DS questions in GMAT Focus encompass various types of word problems, such as:

Word Problems 
 Work Problems 
 Distance Problems 
 Mixture Problems 
 Percent and Interest Problems 
 Overlapping Sets Problems 
 Statistics Problems 
 Combination and Probability Problems

While these questions may involve or necessitate knowledge of algebra, arithmetic, inequalities, etc., they will always be presented in the form of word problems. You won’t encounter pure "algebra" questions like, "Is x > y?" or "A positive integer n has two prime factors..."

Check  GMAT Syllabus for Focus Edition

You can also visit the  Data Sufficiency forum  and filter questions by  OG 2024-2025, GMAT Prep (Focus), and Data Insights Review 2024-2025 sources  to see the types of questions currently tested on the GMAT.

So, you can ignore this question.

Hope it helps.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards