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# If p ≤ q ≤ r ≤ s, is p ≥ 30 ?

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Intern
Joined: 16 Mar 2017
Posts: 13

Kudos [?]: 11 [0], given: 15

If p ≤ q ≤ r ≤ s, is p ≥ 30 ? [#permalink]

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19 Sep 2017, 06:28
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Difficulty:

65% (hard)

Question Stats:

58% (01:53) correct 42% (02:19) wrong based on 24 sessions

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If p ≤ q ≤ r ≤ s, is p ≥ 30 ?
1) p+q+r+s = 150
2) 4p ≥ 3s
[Reveal] Spoiler: OA

Kudos [?]: 11 [0], given: 15

Senior Manager
Joined: 02 Jul 2017
Posts: 281

Kudos [?]: 108 [0], given: 66

GMAT 1: 730 Q50 V38
Re: If p ≤ q ≤ r ≤ s, is p ≥ 30 ? [#permalink]

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19 Sep 2017, 06:49
Given : p ≤ q ≤ r ≤ s
Find if p ≥ 30 ?

1) p+q+r+s = 150
Here value of numbers can be anything like p,q,r,s = 0,0,0,150 or p can have negative value as well as lower limit is not provided .
Insufficient

2) 4p ≥ 3s
Minimum value will be when q=r=s (as s is the largest number in given series) and 4p=3s => s= 4/3p
But no other data given. so p and s can take any value.
Insufficient

(1)+(2)
p+q+r+s =150 and 4p ≥ 3s
=> p and q and r cant be equal to 0.
Minimum value will be when q=r=s (as s is the largest number in given series) and 4p=3s => s= 4/3p
p+q+r+s = 150
=> p+3* 4/3 *p =150 => 5p =150
=> p= 30 => p $$\geq{30}$$
Sufficient

Kudos [?]: 108 [0], given: 66

Re: If p ≤ q ≤ r ≤ s, is p ≥ 30 ?   [#permalink] 19 Sep 2017, 06:49
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