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A chemist mixed Solution P and Solution Q to make 40 liters of a blend. Is the blend more than 30 percent acid?
(1) Solution P is 20 percent acid and Solution Q is 50 percent acid, and the blend contains 24 liters of Solution P.
(2) The blend contains 16 liters of Solution Q.
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Correct answer
A
The blend's acid fraction is total acid divided by 40 liters; we ask whether that exceeds 0.30 (i.e. Whether the acid exceeds 12 liters).
Statement (1): 24 liters of P (so 40 − 24 = 16 liters of Q), with P at 20 percent and Q at 50 percent. Acid = 0.20 × 24 + 0.50 × 16 = 4.8 + 8 = 12.8 liters; fraction = 12.8 over 40 = 0.32, which is more than 0.30, a determinate yes. Sufficient.
Statement (2): 16 liters of Q (so 24 liters of P) tells us the split but gives no concentrations for P or Q, so the acid amount is unknown, if both are weak the blend could be under 30 percent, if both strong it could be over. Not sufficient.
This is the percent-of-base / weighted-average structure: the key move is to compute the acid as an absolute amount from each component (concentration times volume) and divide by the fixed 40-liter total, rather than averaging the two percentages directly.
The "(2) gives the volume split, so it must help" reflex (missing-the-base, a split without concentrations cannot fix the acid amount). And the denominator-static lure: a careless solver may average 20 and 50 to 35 percent and pick a yes from (1) without weighting by the unequal volumes (the 24/16 split pulls it down to 32 percent). (1) alone settles; (2) alone does not; key A.
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