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

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

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08 Jul 2019, 07:00
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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

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Re: What is range of the six positive integers: 1, p, 12, q, 15, r?  [#permalink]

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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
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Re: What is range of the six positive integers: 1, p, 12, q, 15, r?  [#permalink]

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08 Jul 2019, 07:10
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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

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

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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.
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Re: What is range of the six positive integers: 1, p, 12, q, 15, r?  [#permalink]

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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
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Re: What is range of the six positive integers: 1, p, 12, q, 15, r?  [#permalink]

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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

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

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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

What is range of the six positive integers: 1, p, 12, q, 15, r?   [#permalink] 08 Jul 2019, 23:26
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# What is range of the six positive integers: 1, p, 12, q, 15, r?

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