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Russ19
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Solution A contains 8 percent salt by weight, and solution B contains 17 Jan 2020, 05:50
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73% (02:31) correct 27% (02:32) wrong based on 153 sessions

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Solution A contains 8 percent salt by weight, and solution B contains 12.5 percent salt by weight. If 4.5 grams of solution A is mixed with 3 grams of solution B, then what percent of the weight of the resulting solution is salt?

(A) 9.6

(B) 9.8

(C) 10.4

(D) 10.8

(E) 11

Source: GMAT Quantum Math Course
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Solution A contains 8 percent salt by weight, and solution B contains 17 Jan 2020, 06:02
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Since we're using more of A than of B, the answer will be closer to 8% than to 12.5%, so that alone lets you guess between the first two answer choices very quickly. To solve exactly, since we're mixing the two parts in a 4.5 to 3, or a 3 to 2 ratio, then 3/5 of the mixture is A and 2/5 of the mixture is B. So the resulting concentration is (3/5)(8%) + (2/5)(12.5%) = (24 + 25)/5 = 9.8%. Or you can use alligation (a number line) if you know that technique -- that's how I would solve this, but a solution using that method would be hard to follow if you're unfamiliar with it.
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Solution A contains 8 percent salt by weight, and solution B contains 17 Jan 2020, 11:04
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sjuniv32
Solution A contains 8 percent salt by weight, and solution B contains 12.5 percent salt by weight. If 4.5 grams of solution A is mixed with 3 grams of solution B, then what percent of the weight of the resulting solution is salt?

(A) 9.6

(B) 9.8

(C) 10.4

(D) 10.8

(E) 11

Source: GMAT Quantum Math Course
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\(\frac{8}{100}*4.5 + \frac{12.5}{100}*3\)

\(= 0.36 + 0.375\)

\(= 0.735\)

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what percent of the weight of the resulting solution is salt?
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\(= \frac{0.735}{(4.5 + 3.0)}*100\)

\(= 9.80\), Answer must be (B)
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Solution A contains 8 percent salt by weight, and solution B contains 09 Apr 2025, 19:07
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IanStewart
Since we're using more of A than of B, the answer will be closer to 8% than to 12.5%, so that alone lets you guess between the first two answer choices very quickly. To solve exactly, since we're mixing the two parts in a 4.5 to 3, or a 3 to 2 ratio, then 3/5 of the mixture is A and 2/5 of the mixture is B. So the resulting concentration is (3/5)(8%) + (2/5)(12.5%) = (24 + 25)/5 = 9.8%. Or you can use alligation (a number line) if you know that technique -- that's how I would solve this, but a solution using that method would be hard to follow if you're unfamiliar with it.
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Can you please show how can we solve it using the alligation method? I tried but I'm getting the wrong answer.
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Solution A contains 8 percent salt by weight, and solution B contains 10 Apr 2025, 11:48
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Budhaditya_Saha
IanStewart
Since we're using more of A than of B, the answer will be closer to 8% than to 12.5%, so that alone lets you guess between the first two answer choices very quickly. To solve exactly, since we're mixing the two parts in a 4.5 to 3, or a 3 to 2 ratio, then 3/5 of the mixture is A and 2/5 of the mixture is B. So the resulting concentration is (3/5)(8%) + (2/5)(12.5%) = (24 + 25)/5 = 9.8%. Or you can use alligation (a number line) if you know that technique -- that's how I would solve this, but a solution using that method would be hard to follow if you're unfamiliar with it.
Can you please show how can we solve it using the alligation method? I tried but I'm getting the wrong answer.
IanStewart
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I'll assume you're familiar with the general principles of alligation -- this post will not make much sense to anyone reading who does not know that method. Here, the ratio of A to B is 4.5 to 3, or simplifying, 3 to 2. Group A is larger than group B, so the overall average, which is what we want to find, will be closer to A's average, which is 8%. On a number line, we have a picture like this:

----8%---------x%---------------------12.5%

By alligation principles, because the groups are in a 2 to 3 ratio, the distance between 8 and x above is 2/5 of the entire distance between 8 and 12.5, and the distance between x and 12.5 above is 3/5 of the entire distance between 8 and 12.5. So the distance from 8 to x is (2/5)(4.5) = 1.8, and x = 8 + 1.8 = 9.8
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