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The ratio, by weight, of the four ingredients A, B, C, and D of a cert [#permalink]
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23 Apr 2015, 03:59
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The ratio, by weight, of the four ingredients A, B, C, and D of a cert [#permalink]
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23 Apr 2015, 14:30
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Lets say our thing has the weight X(4+7+8+12) = 31*X. When we change mixture our weight changes to X(4 + 7 + 2 + 12*Y) =13*X+12*X*Y We also know that 7*X = 0,2(13*X+12*X*Y). Need to find Y. Reduce that last equation by X and lets just solve it for Y: Y = (7  0,2*13)/2,4 = 44/24 = 11/6 So the original ratio was 4/12 = 1/3 The new ratio is 1*6/(3*11) = 2/11 The resulting percentages are: (1/32/11)/(1/3) = 1  6/11 = 5/11 = 0,454 ~ 45%
Answer ends up being "D"



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Re: The ratio, by weight, of the four ingredients A, B, C, and D of a cert [#permalink]
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23 Apr 2015, 21:20
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I guess answer is B . original ratio A:B:C:D = 4:7:8:12 in ratio , A:C is quardapled , and A:B is constant Hence , New ratio = 16:B:32:D since ,A:B is constant , Find B from above two equations , which comes as 28 so new ratio =16:28:32:D Now it is told that B constitutes , 20% of new mixture . 28=20/100 (new mixture) so New mixtre quantity = 140 so 16:28:32:D =140 Hence D=64 hence ratio of A:D in new mixture= 16:64=25% In old mixture = 4:12=33.33% Change = (33.3325)/33.33 = 8.33/33.33 which is approximately 25%
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Re: The ratio, by weight, of the four ingredients A, B, C, and D of a cert [#permalink]
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23 Apr 2015, 22:45
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Bunuel wrote: The ratio, by weight, of the four ingredients A, B, C, and D of a certain mixture is 4:7:8:12. The mixture will be changed so that the ratio of A to C is quadrupled and the ratio of A to D is decreased. The ratio of A to B will be held constant. If B will constitute 20% of the weight of the new mixture, by approximately what percent will the ratio of A to D be decreased?
A. 15% B. 25% C. 35% D. 45% E. 55%
Kudos for a correct solution. Start with what you know so that use of variables is minimized. A:B:C:D = 4:7:8:12 B is 20% of the weight of new mixture so 7 parts is 20% of the weight. This means total weight of the new mixture is 35 parts. Ratio of A:B remains constant so 4:7. Ratio of A:C (4:8) is quadrupled (4*4:8 = 2:1). Since A is 4 parts, C must be 2 parts. 4:7:2:D Total must add up to 35 parts. So D must be 35  (4 + 7 + 2) = 22 parts. A:D ratio has changed from 4:12 (1/3) to 4:22 (2/11). This is a decrease of (1/3  2/11)/(1/3) * 100 = 45% approx
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The ratio, by weight, of the four ingredients A, B, C, and D of a cert [#permalink]
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24 Apr 2015, 02:30
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Bunuel wrote: The ratio, by weight, of the four ingredients A, B, C, and D of a certain mixture is 4:7:8:12. The mixture will be changed so that the ratio of A to C is quadrupled and the ratio of A to D is decreased. The ratio of A to B will be held constant. If B will constitute 20% of the weight of the new mixture, by approximately what percent will the ratio of A to D be decreased?
A. 15% B. 25% C. 35% D. 45% E. 55%
Kudos for a correct solution. Given : The ratio of A to B will be held constant and B is not changed , so 'A' is also not changed. If 'A' is not changed then the only way A:C will be quadrupled is by reducing C , from C to C/4 . A:D is decreased , again 'A' is not changed , so , D is increased. In new mixture B is 20% , so A+C+Dis 80% . Asked : \(\frac{Old_{A:D }  New_{A:D }}{Old_{A:D }}*100\)Solution: A:B:C:D=4:7:8:12 Old : 4x , 7x, 8x, 12x \(Old_{A:D } = \frac{1}{3}\) New : 4x, 7x, 2x, UNKNOWN,Say 'Y' (>12x) we are told that 7x=20%( 4x+7x+2x+y)====>35x=13x+y======>22x=y \(New_{A:D } = \frac{4x}{22x}\) \(\frac{Old_{A:D }  New_{A:D }}{Old_{A:D }}*100\) = 45% Answer C
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Re: The ratio, by weight, of the four ingredients A, B, C, and D of a cert [#permalink]
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27 Apr 2015, 02:25
Bunuel wrote: The ratio, by weight, of the four ingredients A, B, C, and D of a certain mixture is 4:7:8:12. The mixture will be changed so that the ratio of A to C is quadrupled and the ratio of A to D is decreased. The ratio of A to B will be held constant. If B will constitute 20% of the weight of the new mixture, by approximately what percent will the ratio of A to D be decreased?
A. 15% B. 25% C. 35% D. 45% E. 55%
Kudos for a correct solution. First, make a quick table to represent the ratios in the original mixture: A B C D 4 7 8 12 One way forward is to make the A:C change, holding A:B and A:D constant. (We know that A:D decreases, but we don’t know by how much, so for now, pretend that the ratio stays constant.) To quadruple the ratio A:C, we can either multiply A by 4 or divide C by 4. Since we want to leave A:B and A:D constant, it’s more efficient to divide C by 4. So if A:D weren’t changing, the new mixture would have these ratios: A B C D 4 7 2 12 Since A:D decreases, let’s add an unspecified amount to D. (We don’t want to mess with the A side of the ratio, since A is involved in other ratios.) Call that amount x. A B C D 4 7 2 12 + x Now we know that B will constitute 20% of the whole, so the ratio of B to the whole in the final mixture will be 20 to 100, or 1:5. If we look at the table, the ratio of B to the whole is 7 to 25 + x. We can equate these proportions: 1/5 = 7/(25 + x) 25 + x = 35 x = 10 So now we know that the final mixture has these proportions: A B C D 4 7 2 22 The new ratio of A to D is 4:22, or 2:11. As a fraction, this ratio is 2/11. The original ratio of A to D is 4:12, or 1:3. As a fraction, this ratio is 1/3. Finally, we are asked this: if 1/3 is decreased to 2/11, what is the percent decrease? A fast way to compute this number is first to figure out the factor that you multiply 1/3 by to get 2/11. Call that factor y. (1/3)y = 2/11 y = 6/11 So 2/11 is 6/11 of 1/3. As a percent, 6/11 is approximately 55% (as a decimal, 6/11 = 0.5454…). If the new number (2/11) is 55% of the old number (1/3), then the percent decrease is 100% – 55%, or 45%. The correct answer is D.
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Re: The ratio, by weight, of the four ingredients A, B, C, and D of a cert [#permalink]
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29 Jun 2015, 23:02
VeritasPrepKarishma wrote: Bunuel wrote: The ratio, by weight, of the four ingredients A, B, C, and D of a certain mixture is 4:7:8:12. The mixture will be changed so that the ratio of A to C is quadrupled and the ratio of A to D is decreased. The ratio of A to B will be held constant. If B will constitute 20% of the weight of the new mixture, by approximately what percent will the ratio of A to D be decreased?
A. 15% B. 25% C. 35% D. 45% E. 55%
Kudos for a correct solution. Start with what you know so that use of variables is minimized. A:B:C:D = 4:7:8:12 B is 20% of the weight of new mixture so 7 parts is 20% of the weight. This means total weight of the new mixture is 35 parts.Ratio of A:B remains constant so 4:7. Ratio of A:C (4:8) is quadrupled (4*4:8 = 2:1). Since A is 4 parts, C must be 2 parts. 4:7:2:D Total must add up to 35 parts. So D must be 35  (4 + 7 + 2) = 22 parts. A:D ratio has changed from 4:12 (1/3) to 4:22 (2/11). This is a decrease of (1/3  2/11)/(1/3) * 100 = 45% approx You solved the complete Q there itself, awesome. Thanks for updating your solution. Regards, Gaurav



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Re: The ratio, by weight, of the four ingredients A, B, C, and D of a cert [#permalink]
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