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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, 06:28
4
00:00

Difficulty:

45% (medium)

Question Stats:

67% (02:28) correct 33% (02:09) wrong based on 71 sessions

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If p ≤ q ≤ r ≤ s, is p ≥ 30 ?

(1) p + q + r + s = 150
(2) 4p ≥ 3s
Current Student
Joined: 02 Jul 2017
Posts: 293
Concentration: Entrepreneurship, Technology
GMAT 1: 730 Q50 V38
Re: If p ≤ q ≤ r ≤ s, is p ≥ 30 ?  [#permalink]

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19 Sep 2017, 06:49
1
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: 16
Location: India
GMAT 1: 670 Q48 V34
GPA: 4
Re: If p ≤ q ≤ r ≤ s, is p ≥ 30 ?  [#permalink]

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29 Dec 2017, 02:30
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: 7206
If p ≤ q ≤ r ≤ s, is p ≥ 30 ?  [#permalink]

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29 Dec 2017, 05:19
1
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
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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If p ≤ q ≤ r ≤ s, is p ≥ 30 ? &nbs [#permalink] 29 Dec 2017, 05:19
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