tricky ratio

buoyant wrote:The ratio of flour to water to sugar in a recipe is 7:4:1. The ratio in a new recipe calls for a doubling of the ratio of flour to water from the original recipe and a halving of the ratio of flour to sugar.If the new recipe calls for 8 cups of water, how much sugar is required?

a)4 cups
b)6 cups
c)8 cups
d)12 cups
e)16 cups

[spoiler]OA:C[/spoiler]

While somehow the wording of the question is a little confusing, once one has decided what the wording means, getting the answer is pretty straightforward.

Start with flour 7 water 4 sugar 1.

Double the flour to water. The easiest way to do this is change from 7 flour:4 water to 14 flour:4 water.

Flour to sugar was 7:1. Now needs to be half of that, which is 7:2. Easiest way to do this is just leave the flour at 14 and increase the sugar. So to get 7:2 ratio with 14 flour therefore need 4 Sugar.

So the new ratio is 14:4:4.

Water and sugar are equal. So with 8 cups of water, need 8 cups of sugar.

Choose C.

buoyant wrote:The ratio of flour to water to sugar in a recipe is 7:4:1. The ratio in a new recipe calls for a doubling of the ratio of flour to water from the original recipe and a halving of the ratio of flour to sugar.If the new recipe calls for 8 cups of water, how much sugar is required?

a)4 cups
b)6 cups
c)8 cups
d)12 cups
e)16 cups

[spoiler]OA:C[/spoiler]

While somehow the wording of the question is a little confusing, once one has decided what the wording means, getting the answer is pretty straightforward.

Start with flour 7 water 4 sugar 1.

Double the flour to water. The easiest way to do this is change from 7 flour:4 water to 14 flour:4 water.

what i did here is that i multiplied 2 in both numerator and denominator, resulting in 14:8 . that is the reason i did not get to the answer.

Flour to sugar was 7:1. Now needs to be half of that, which is 7:2. Easiest way to do this is just leave the flour at 14 and increase the sugar. So to get 7:2 ratio with 14 flour therefore need 4 Sugar.

Again i did the same mistake of taking half of both 7 and 2 , as if i am finding a common multiple.but i was supposed to double and halve the whole ratio respectively and therefore multiply by 2 or take half of the whole ratio in above two cases.


So the new ratio is 14:4:4.

Water and sugar are equal. So with 8 cups of water, need 8 cups of sugar.

Choose C

Buoyant, your analysis is interesting.

Possibly even more interesting is what this entire discussion illustrates, which is that GMAT quant is at least as much about logic as it is about math.

Surely wasn't any complex math and weren't any arcane concepts on this question, and one can still get smoked by it.

Marty Murray wrote:Buoyant, your analysis is interesting.

Possibly even more interesting is what this entire discussion illustrates, which is that GMAT quant is at least as much about logic as it is about math.

Surely wasn't any complex math and weren't any arcane concepts on this question, and one can still get smoked by it.

well said!

Steps:

Flour: Water: Sugar
7: 4: 1

Need to double Flour: Water ~> 7:4 becomes 14:4
Need to halve Flour: Sugar ~> 7:1 becomes 7:2 or 14:4 for simplicity for integration with the above ratio

New ratio:
Flour: Water: Sugar
14:4:4

Cups of sugar = cups of water

Answer = 8 cups

As a few people have already explained, you want to break this ratio into pieces.

Flour : Water = 7 : 4

To DOUBLE this, multiply it by 2/1. This gives us 7/4 * 2/1, or 7/2. So the NEW ratio of F:W = 7:2.

Flour : Sugar = 7 : 1

To HALVE this, multiply it by 1/2. This gives us 7/1 * 1/2, or 7/2. So the NEW ratio of F:S = 7:2.

Since F = 7 in both ratios, we can combine the two ratios, giving us F:W:S = 7:2:2.

We have the SAME amount of water and sugar, so if we have 8 cups of water, we must have 8 cups of sugar.