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# If p + q = 400 and p < q, is (p + q) < (r + s) ? (1) p + r + s = 600

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Math Expert
Joined: 02 Sep 2009
Posts: 60647
If p + q = 400 and p < q, is (p + q) < (r + s) ? (1) p + r + s = 600  [#permalink]

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04 Nov 2019, 02:45
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Difficulty:

45% (medium)

Question Stats:

63% (02:17) correct 37% (01:59) wrong based on 41 sessions

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If $$p + q = 400$$ and $$p < q$$, is $$(p + q) < (r + s)$$ ?

(1) $$p + r + s = 600$$

(2) $$q + r > 400$$

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Joined: 25 Jul 2018
Posts: 482
Re: If p + q = 400 and p < q, is (p + q) < (r + s) ? (1) p + r + s = 600  [#permalink]

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04 Nov 2019, 03:01
p+q = 400
p < q

(—> q= 400– p
p < 400 —p
2p < 400
p < 200)

Is (p+q) < (r+s)?
—> r+s > 400 ???

(Statement1): p+r+s = 600
—> p cannot be 200. It is less than 200. (p< 200)
—> r+s > 400
Sufficient

(Statement2)
q+ r> 400
—> No info about what r and s are
Insuffient

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Intern
Joined: 14 Apr 2019
Posts: 1
Re: If p + q = 400 and p < q, is (p + q) < (r + s) ? (1) p + r + s = 600  [#permalink]

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04 Nov 2019, 03:12
Given - p+q = 400

Assume, p = q, then p=q= 200

but given that p < q, therefore, p < 200

Statement 1 : p + r + s = 600

if p = 200, then r + s = 400. Thus, as p < 200, r + s > 400

therefore, p+q < r+s

A is sufficient

statement 2: there is no information about s.
Therefore Ans is A.
Re: If p + q = 400 and p < q, is (p + q) < (r + s) ? (1) p + r + s = 600   [#permalink] 04 Nov 2019, 03:12
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