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

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New post 25 Nov 2019, 02:57
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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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Re: If p ≤ q ≤ r ≤ s, is p ≥ 30 ? (1) p + q + r + s = 150 (2) 4p ≥ 3s  [#permalink]

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New post 25 Nov 2019, 05:56
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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) \(4p ≥ 3s\)
Nothing is given about values


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

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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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