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# If p ≤ q ≤ r ≤ s, is p ≥ 30 ?

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Intern
Joined: 16 Mar 2017
Posts: 13
If p ≤ q ≤ r ≤ s, is p ≥ 30 ? [#permalink]

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19 Sep 2017, 07:28
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Question Stats:

72% (01:43) correct 28% (01:48) wrong based on 67 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
Senior Manager
Joined: 02 Jul 2017
Posts: 289
GMAT 1: 730 Q50 V38
Re: If p ≤ q ≤ r ≤ s, is p ≥ 30 ? [#permalink]

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19 Sep 2017, 07:49
1
KUDOS
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

Intern
Joined: 22 Jun 2017
Posts: 9
Re: If p ≤ q ≤ r ≤ s, is p ≥ 30 ? [#permalink]

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29 Dec 2017, 03:30
Something wrong here !
P can be equal to 30 but can not be greater than 30... Inconclusive ... Ans should be E

Posted from my mobile device
Math Expert
Joined: 02 Aug 2009
Posts: 5713
If p ≤ q ≤ r ≤ s, is p ≥ 30 ? [#permalink]

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29 Dec 2017, 06:19
1
KUDOS
Expert's post
amitpassionate wrote:
Something wrong here !
P can be equal to 30 but can not be greater than 30... Inconclusive ... Ans should be E

Posted from my mobile device

NO....
The minimum value of P is 30, so P has to be greater than or equal to 30..

Quote:
If p ≤ q ≤ r ≤ s, is p ≥ 30 ?

(1) p + q + r + s = 150
(2) 4p ≥ 3s

(1) p + q + r + s = 150
all 4 can have various combination possible..
35+35+40+40=150....p>30
25+35+40+50=150...p<30
insuff..

(2) 4p ≥ 3s
p could be 20, 30,50,..
insuff

combined..
take least value of p as $$\frac{3s}{4}$$ AND all other three are equal..
so $$\frac{3s}{4}+s+s+s=150......\frac{15s}{4}=150...s=40$$
so $$p = \frac{3s}{4}=\frac{3*40}{4}=30$$
so least value of p is 30, hence p ≥ 30
suff

C
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If p ≤ q ≤ r ≤ s, is p ≥ 30 ?   [#permalink] 29 Dec 2017, 06:19
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