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A researcher combined x ounces of a saline solution that contained 20

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Bunuel
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A researcher combined x ounces of a saline solution that contained 20 [#permalink] A researcher combined x ounces of a saline solution that contained 20   26 Apr 2023, 01:30
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60% (01:28) correct 40% (01:31) wrong based on 86 sessions
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A researcher combined x ounces of a saline solution that contained 20 percent saline, by volume, with y ounces of a saline solution that contained 5 percent saline, by volume, to produce z ounces of a saline solution that was 12 percent saline, by volume. What is the value of x?

(1) y = 16
(2) z = 30


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D
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Re: A researcher combined x ounces of a saline solution that contained 20 [#permalink] A researcher combined x ounces of a saline solution that contained 20   26 Apr 2023, 03:20
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The answer is D.

Even before you go towards each of the prompts you need to find the ratio of mixtures. Through the alligation method you can find the ratio of the two mixtures - X:Y = 7/8. Now remember that these are just the ratios and not the actual amount of quantity. all you need is either the total quantity of the mixture of just the value of Y.

Statement one gives you the value of Y - super. sufficient.

Statement two gives you the value of X+Y - Super. Sufficient.
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Re: A researcher combined x ounces of a saline solution that contained 20 [#permalink] A researcher combined x ounces of a saline solution that contained 20   04 May 2023, 09:26
Can we solve it with the density concept?

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Re: A researcher combined x ounces of a saline solution that contained 20 [#permalink] A researcher combined x ounces of a saline solution that contained 20   04 May 2023, 10:11
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Bunuel
A researcher combined x ounces of a saline solution that contained 20 percent saline, by volume, with y ounces of a saline solution that contained 5 percent saline, by volume, to produce z ounces of a saline solution that was 12 percent saline, by volume. What is the value of x?

(1) y = 16
(2) z = 30
Solution:
Pre Analysis:
  • From the given information, we can apply aligation method
Attachment:
saline.png
saline.png [ 7.83 KiB | Viewed 1583 times ]
  • We can write \(\frac{x}{y}=\frac{7}{8}\) and \(x+y=z\)
  • We are asked the value of \(x\)

Statement 1: y = 16
  • From this we can easily get the value of x using \(\frac{x}{y}=\frac{7}{8}\)
  • Thus, statement 1 alone is sufficient and we can eliminate options B, C and E

Statement 2: z = 30
  • We can assume \(x=7a\) and \(y=8a\)
  • We know \(x+y=z⇒7a+8a=30⇒a=2\) or \(x=7a=14\)
  • Thus, statement 2 alone is also sufficient

Hence the right answer is Option D
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Re: A researcher combined x ounces of a saline solution that contained 20 [#permalink]
04 May 2023, 10:11
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Bunuel
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