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| Author: | Bunuel [ 08 Apr 2020, 10:42 ] |
| Post subject: | The strength of a salt solution is p% if 100 ml of the solution contai |
The strength of a salt solution is p% if 100 ml of the solution contains p grams of salt. If three salt solutions A, B, C are mixed in the proportion 1 : 2 : 3, then the resulting solution has strength 20%. If instead the proportion is 3 : 2 : 1, then the resulting solution has strength 30%. A fourth solution, D, is produced by mixing B and C in the ratio 2 : 7. What is the ratio of the strength of D to that of A ? A. 3 : 10 B. 1 : 3 C. 2 : 5 D. 1 : 4 E. 1 : 5 Are You Up For the Challenge: 700 Level Questions |
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| Author: | smyarga [ 08 Apr 2020, 11:12 ] |
| Post subject: | Re: The strength of a salt solution is p% if 100 ml of the solution contai |
Let three salt solutions A, B, C have the strengths p%, q%, r% respectively. Using weights from ratio 1:2:3 we will have the equation \(\frac{p}{6}+\frac{2q}{6}+\frac{3r}{6}=20\) or \(p+2q+3r=120\) Using weights from ration 3:2:1 we have the next equation \(\frac{3p}{6}+\frac{2q}{6}+\frac{r}{6}=30\) or \(3p+2q+r=180\) If we subtract first equation from the second one, we obtain: 2p-2r=60 or r=p-30. If we put it in the second equation, we get 3p+2q+p-30=180 or 2q=210-4p or q=105-2p The question is to find the ratio: \((\frac{2q}{9}+\frac{7r}{9}):p=(210-4p+7p-210):9p=3p:9p=1:3\) The correct answer is B. |
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| Author: | Kinshook [ 10 Apr 2020, 09:30 ] |
| Post subject: | Re: The strength of a salt solution is p% if 100 ml of the solution contai |
Bunuel wrote: The strength of a salt solution is p% if 100 ml of the solution contains p grams of salt. If three salt solutions A, B, C are mixed in the proportion 1 : 2 : 3, then the resulting solution has strength 20%. If instead the proportion is 3 : 2 : 1, then the resulting solution has strength 30%. A fourth solution, D, is produced by mixing B and C in the ratio 2 : 7. What is the ratio of the strength of D to that of A ? A. 3 : 10 B. 1 : 3 C. 2 : 5 D. 1 : 4 E. 1 : 5 Are You Up For the Challenge: 700 Level Questions Given: 1. The strength of a salt solution is p% if 100 ml of the solution contains p grams of salt. 2. If three salt solutions A, B, C are mixed in the proportion 1 : 2 : 3, then the resulting solution has strength 20%. 3. If instead the proportion is 3 : 2 : 1, then the resulting solution has strength 30%. 4. A fourth solution, D, is produced by mixing B and C in the ratio 2 : 7. Asked: What is the ratio of the strength of D to that of A ? Let the strength of solutions A, B & C be x%, y% & z% respectively 2. If three salt solutions A, B, C are mixed in the proportion 1 : 2 : 3, then the resulting solution has strength 20%. (x + 2y + 3z) / 6 = 20 x + 2y + 3z = 120 (1) 3. If instead the proportion is 3 : 2 : 1, then the resulting solution has strength 30%. 3x + 2y + z = 180 (2) (1) + (2) 4x + 4y + 4z = 300 x + y + z = 75 (3) 2*(3) - (1) x - z = 30 x = z + 30 z = x - 30 (5) y = 75 - x - z = 75 - x - (x-30) = 105 - 2x (6) 4. A fourth solution, D, is produced by mixing B and C in the ratio 2 : 7. Strength of D = (2y +7z)/9 The ratio of the strength of D to that of A = (2y + 7z)/9x = {2(105 -2x) +7(x-30)} / 9x = (210 - 4x + 7x - 210 )/9x = 3x/9x = 1/3 IMO B |
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| Author: | bumpbot [ 19 Jan 2023, 03:40 ] |
| Post subject: | Re: The strength of a salt solution is p% if 100 ml of the solution contai |
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. |
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