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# If p ≤ q ≤ r ≤ s, is p ≥ 30 ? (1) p + q + r + s = 150 (2) 4p ≥ 3s

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Joined: 02 Sep 2009
Posts: 60727
If p ≤ q ≤ r ≤ s, is p ≥ 30 ? (1) p + q + r + s = 150 (2) 4p ≥ 3s  [#permalink]

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25 Nov 2019, 02:57
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45% (medium)

Question Stats:

68% (02:48) correct 32% (01:56) wrong based on 30 sessions

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If $$p ≤ q ≤ r ≤ s$$, is $$p ≥ 30$$ ?

(1) $$p + q + r + s = 150$$

(2) $$4p ≥ 3s$$

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Math Expert
Joined: 02 Aug 2009
Posts: 8327
Re: If p ≤ q ≤ r ≤ s, is p ≥ 30 ? (1) p + q + r + s = 150 (2) 4p ≥ 3s  [#permalink]

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25 Nov 2019, 05:56
1
If $$p ≤ q ≤ r ≤ s$$, is $$p ≥ 30$$ ?

(1) $$p + q + r + s = 150$$
Now $$p ≤ q ≤ r ≤ s$$, We can just say that the max value of p will be when all are equal, so $$p ≤ \frac{150}{4}.........p ≤ 37.5$$
So p can be anything when it comes to the least value.. It can be -100, -10, 0 or 37.5

(2) $$4p ≥ 3s$$

Combined..
Let us take the least value of p.
It will be least when $$4p=3s$$, that is $$s=\frac{4p}{3}$$, and rest all are equal to s.
so $$p+\frac{4p}{3}+\frac{4p}{3}+\frac{4p}{3}=150......p+3*\frac{4p}{3}=150....5p=150...p=30$$
So 30≤ p ≤37.5
Suff

C
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Re: If p ≤ q ≤ r ≤ s, is p ≥ 30 ? (1) p + q + r + s = 150 (2) 4p ≥ 3s   [#permalink] 25 Nov 2019, 05:56
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