GMAT Club Around The World!!! The ratio of flour to sugar to baking so

Initial Ratio = x:y:z
New Ratio

Soda:Sugar = 3z:y
Floor:Sugar = x:2y

New ratio = x:2y:6z
Total weight = mx + 2my + 6mz

We are given, 2my=x grams. So m=x/2y

Weight of flour = mx = x*x/2y = (x^2)/2y

IMO Option A

IMO A

F:S:B = x:y:z
new numbers : \(x_{new}, y_{new}, z_{new}\)
\(y_{new} = x;\ find\ x_{new}=??? \)

\(\frac{z}{y} = k_{1}\)
\(\frac{z_{new}}{y_{new}} = 3k_{1}\) -----equation 1

\(\frac{x}{y} = k_{2}\)
\(\frac{x_{new}}{y_{new}} = \frac{1}{2} k_{2}\) ---equation 2

\(y_{new} = x\)
from equation2
\(\frac{x_{new}}{y_{new}} = \frac{1}{2} * \frac{x}{y}\)

\(\frac{x_{new}}{x} = \frac{1}{2} * \frac{x}{y}\)

\(x_{new} = \frac{x^2}{2y}\)

Correct Answer A

The ratio of flour to sugar to baking soda in a recipe is x:y:z. A cook accidentally triples the ratio of baking soda to sugar and halves the ratio of flour to sugar. If the altered recipe will have x total grams of sugar, which of the following expresses the grams of flour it will contain?

Flour(F): Sugar(S): Baking Soda (B) ---> x:y:z

Say total is P
F =xP
S=yP
B=zP
New Ratio
F =xP/2
S=yP = x gram ---> P=x/y
B=3zP

F =x^2/(2y)

Given,
Type----- Flour-----Sugar----Banking Soda
Initial-----x--------y----------z
Finally----x-------2*y-------6*z

Further, 2*y*k= x then, k= x/(2y)
So, Flour= x*k = x*x/(2y) = x^2/(2*y)

I think A.

Ratio of Flour to Sugar to Baking Soda in a recipe = x:y:z
As per the above ratio amount of flour will be x*n, amount of sugar will be y*n, amount of baking soda will be z*n where n is the ratio multiplier to calculate the actual amount

Cook accidentally triples the ratio of baking soda to sugar, so the new ratio will be:
Baking soda:Sugar = 3(z*n/y*n)
Cook accidentally halves the ratio of flour to sugar, so the new ratio will be:
Flour:Sugar = 1/2(x*n/y*n)
So the combined ratio of Baking Soda to Sugar to Flour in this new combination will be:
6z*n : 2y*n : x*n
Now we know altered recipe has x grams of sugar so
2y*n = x
n = x/2y
Now that we have the value of multiplier we can calculate the value flour amount
Flour amount = x*n = x*x/2y = x^2/2y

So the answer will be A

With variables in the question stem that are repeated in the answer choices, we have an opportunity to Plug In.
Let's make x = 1, y = 2, and z = 3.
The chef makes some boo boos. He halves x...ah, we'd end up with a fraction...not a huge fan...maybe quickly switch numbers (I put this here because this is exactly what I did when solving. If it's early in the solving process and you realize you can easily switch numbers to give yourself something you like better, go for it!).
Let's make x = 2, y = 1, and z = 3.
The chef makes some boo boos. He halves the flour and triples the baking soda, so the ratio of the altered recipe is 1:1:9.
The altered recipe has x grams of sugar, so 2 grams of sugar. That means we have 2:2:18, so it has 2 grams of flour.
Let's check the answer choices.

A. x^2/(2y) = 4/2 = 2 Keep it.

B. 2y/x^2 = 2/4 Wrong.

C. xz/y = 6/1 Wrong.

D. yz/(3x) 3/6 Wrong.

E. yz/(4x) 3/8 Wrong.

Answer choice A.

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