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B = original weight of base liquid
F = weight of fragrance oil
G = weight of gel stabilizer
T = original total weight

We know, T = B + F + G

After increasing the base liquid by 1/3:

New base liquid = (4/3)B

New total = T + B/3

We need to find B/T

Statement 1
Before the increase: F/T = 1/5

After the increase: F/(T + B/3) = 1/6

Since F = T/5 -----> (T/5)/(T + B/3) = 1/6

6(T/5) = T + B/3

6T/5 = T + B/3

6T - 5T = 5B/3

T = 5B/3

3T = 5B

B/T = 3/5

Thus, Statement 1 is sufficient


Statement 2

After the increase -----> (4B/3)/(T + B/3) = 2/3

3(4B/3) = 2(T + B/3)

4B = 2T + 2B/3

12B = 6T + 2B

10B = 6T

5B = 3T

B/T = 3/5

Statement 2 is also sufficient. Both statements alone are sufficient.

Option: D
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A cosmetics lab prepared a liquid formula that consisted of base liquid, fragrance oil, and gel stabilizer. The weight of the base liquid in the formula was increased by 1/3 by adding more base liquid, while the weights of the fragrance oil and gel stabilizer remained unchanged. Before this increase, what was the ratio of the weight of the base liquid to the total weight of the formula?

(1) After the addition of base liquid, the ratio of the weight of fragrance oil to the total weight of the formula decreased from 1/5 to 1/6.

(2) After the addition of base liquid, the ratio of the weight of base liquid to the total weight of the formula became 2/3.



let base liquid be x
fragrance oil be y
gel stabilixer be z
increase in weight of x done by 1/3 , while y,z unchanged.
x become 4/3 and y, z remained same

target before increase ratio of x/ ( x+y+z)

#1
y/ ( x+y+z)
decreased from 1/5 to 1/6 with new base liquid base change
we have
y/ ( x+y+z) = 1/5
y/ ( 4/3 x + y+z ) 1/6

we can solve and determine value of ratio x / ( x+y+z)
sufficient

#2
base liquid after addition became 2/3
4/3 x / ((4/3 x + y+ z ) = 2/3

we can solve and determine value of ratio
x / ( x+y+z ) ; sufficient


OPTION D is correct
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Bunuel
A cosmetics lab prepared a liquid formula that consisted of base liquid, fragrance oil, and gel stabilizer. The weight of the base liquid in the formula was increased by 1/3 by adding more base liquid, while the weights of the fragrance oil and gel stabilizer remained unchanged. Before this increase, what was the ratio of the weight of the base liquid to the total weight of the formula?

(1) After the addition of base liquid, the ratio of the weight of fragrance oil to the total weight of the formula decreased from 1/5 to 1/6.

(2) After the addition of base liquid, the ratio of the weight of base liquid to the total weight of the formula became 2/3.


 


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Both are sufficient together but not alone. from statement 1 we can get total amount and from statement 2 the initial amount.
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Bunuel
A cosmetics lab prepared a liquid formula that consisted of base liquid, fragrance oil, and gel stabilizer. The weight of the base liquid in the formula was increased by 1/3 by adding more base liquid, while the weights of the fragrance oil and gel stabilizer remained unchanged. Before this increase, what was the ratio of the weight of the base liquid to the total weight of the formula?

(1) After the addition of base liquid, the ratio of the weight of fragrance oil to the total weight of the formula decreased from 1/5 to 1/6.

(2) After the addition of base liquid, the ratio of the weight of base liquid to the total weight of the formula became 2/3.


 


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Question:

B / (F+B+G) = ?

1)

F/(F+B+G) = 1/5 -- 1

F/(F + 4B/3 + G) = 1/6 -- 1

Solving 1, we get -

5F = F +B +G

4F = B + G

From (2)

3F/3F+4B+3G = 1/6

18F = 3F + 4B + 3G

15F = 4B + 3G
16F = 4B + 4G -- From 1

F = G

Similarly we can find the relationship between F and B.

Statement 1 is sufficient

2) 4B/3 / 4B/3 + G + F = 2/3

4B / 4B+3F+3G = 2/3

12B = 8B + 6F + 6G

B = 6/4(F+G)

B/(F+G) = 6/4 = 2/3

This is sufficient to find the relationship required.

Option D
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call weight of base liquid, fragrance oil and gel stabilizer respectively be x,y,z
we are finding x/(x+y+z)
the new total weight is (4x/3)+y+z

1. we know: y/x+y+z=1/5 -> let y be 1 for easier calculation -> 1/x+1+z = 1/5 0> x+z =4
we also know: y/[(4x/3)+y+z]=1/6 -> let y be 1 for easy -> (4x/3)+z=5
solving this we have x=3,y=1,z=1 -> can calculate the initial ratio

2. we have: (4x/3)/[(4x/3)+y+z]=2/3 -> solving we have (2x/3)=y+z
plug y+z into the needed to find ratio we have: x/(x+y+z)=x/(x+2x/3) = 3/5

each statement alone is efficient -> choose D
Bunuel
A cosmetics lab prepared a liquid formula that consisted of base liquid, fragrance oil, and gel stabilizer. The weight of the base liquid in the formula was increased by 1/3 by adding more base liquid, while the weights of the fragrance oil and gel stabilizer remained unchanged. Before this increase, what was the ratio of the weight of the base liquid to the total weight of the formula?

(1) After the addition of base liquid, the ratio of the weight of fragrance oil to the total weight of the formula decreased from 1/5 to 1/6.

(2) After the addition of base liquid, the ratio of the weight of base liquid to the total weight of the formula became 2/3.


 


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Let Base liquid be B, Fragrance oil be F and Gel stabilizer be G. So, \(B+F+G=1\)
Therefore,\(B = 1-(F+G)\)
We need to know both F and G to know B.
(1) if true, then two formulas are formed \(B=1-(\frac{1}{5}+G)->B=\frac{4}{5}-G->G=\frac{4}{5} - B\) and another formulate after the change in the amount of B.
which doesn't tell us the absolute size of B before or after the change. Insufficient

(2) If it became 2/3, then before it was less by 1/3 and can be calculated. Sufficient
So, (B) Statement (2) alone is sufficient, but statement one alone is insufficient.

Final answer (B)

Bunuel
A cosmetics lab prepared a liquid formula that consisted of base liquid, fragrance oil, and gel stabilizer. The weight of the base liquid in the formula was increased by 1/3 by adding more base liquid, while the weights of the fragrance oil and gel stabilizer remained unchanged. Before this increase, what was the ratio of the weight of the base liquid to the total weight of the formula?

(1) After the addition of base liquid, the ratio of the weight of fragrance oil to the total weight of the formula decreased from 1/5 to 1/6.

(2) After the addition of base liquid, the ratio of the weight of base liquid to the total weight of the formula became 2/3.


 


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Let the original weights be :
Base = B, Others = O
We need B/(B+O)
After the increase, base becomes 4B/3

1) Fragrance ratio changes from 1/5 to 1/6
Since the fragrance amt. is unchanged, New total/Old total = (1/5) / (1/6) = 6/5
But increasing the base by 1/3 also gives : New total = Old Total + B/3
So, Old total + B/3 = (6/5) * Old total
-> B/3 = Old Total/5
-> B/Old Total = 3/5
Sufficient

2) After the increase, (4B/3) / (old Total + B/3) = 2/3
-> 4B = 2 (Old total + B/3)
-> 12B = 6 Old Total + 2B
-> 10B = 6 Old Total
-> B/Old Total = 3/5
Sufficient

Ans : D
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In this question, let the three initial weight before adding anything to base Liquid be
Base Liquid(B) = B
Fragrance oil = F
And Gel Stabilizer = G
And let the initial total wt. be T

As the wt. of F and G are constant initially and finally we could say there combined wt. is W

We need to find initial ratio of B/T

and After adding 1/3 of B to B we would get final wt. of B = 4/3 B

Now let us check each statement alone:

S1:
Initial IS = F/(B+W) = 1/5; B + W = 5F

Final IS = F/(4b/3 + W) = 1/6; We would get 4B/3 + X = 6F

On subtracting both we get: B/3 = F or 3F = B

If we substitute it to initial equation we will get W = 2F

Now we have everything in terms of F; we could easily find B/B+W = 3F/3F+2F = 3/5
Hence sufficient

S2: In this it said: [4B/3] / [(4B/3) + W] = 2/3
to get relation of two variables(B and W) we would solve and it would be W = 2B/3

Now we have W in terms of B, put it in the ratio we need to find; B/B+W = B/[B+(2B/3)] and the ratio would come out to be 3/5
SUFFICIENT

The correct answer would be D
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Bunuel
A cosmetics lab prepared a liquid formula that consisted of base liquid, fragrance oil, and gel stabilizer. The weight of the base liquid in the formula was increased by 1/3 by adding more base liquid, while the weights of the fragrance oil and gel stabilizer remained unchanged. Before this increase, what was the ratio of the weight of the base liquid to the total weight of the formula?

(1) After the addition of base liquid, the ratio of the weight of fragrance oil to the total weight of the formula decreased from 1/5 to 1/6.

(2) After the addition of base liquid, the ratio of the weight of base liquid to the total weight of the formula became 2/3.


 


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1) Before:

Fragrance / T = 1/5

After:

Fragrance / New Total = 1/6

Since the fragrance amount didn't change:

T/5 = New Total/6

So: New Total = 6T/5

The increase in total weight comes only from the added base liquid:

T + B/3 = 6T/5
B/3 = T/5
B/T = 3/5

Sufficient.

2) (4B/3) / (T + B/3) = 2/3

4B = 2(T + B/3)

2B = T + B/3

6B = 3T + B

5B = 3T

B/T = 3/5 Sufficient.

Option D
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D. Each statement alone is sufficient

Question stem tells us:

The previous weights of the liquid are- a, b, c

I am assuming total weight to be 30 (by looking at the question and statements, I understood two things: 1. As we have to get the ratio of a with total quantity, the absolute total quantity does not matter 2. I assume total weight to be something that can be easily divided by 5, 6 and 3)

After increasing the weights become- 4a/3, b, c and total weight is 30 + a/3

Now, we have to find out the ratio of previous base liquid to total weight, which is: a/30

Statement 1: b/30 is 1/5 and b/(30+a/3) is 1/6

So, we can find out b and then we can find out a, which will give us our previous ratio for a/30

Statement 2: New ratio for base liquid/total is given: a/(30+a/3) = 2/3

We can get a from this and hence the previous ratio

So, each statement alone can give us the answer
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have to find

L/L+M

Statement 1 tells us ratio decreased

f = 1/5 x (L+M)

when we solve and compare we get L/L+M as 3/5

Statement 2 similarly tells us us how much it increased, which means we will get the ans

We can solve to confirm

Both Statements are sufficient: D
Bunuel
A cosmetics lab prepared a liquid formula that consisted of base liquid, fragrance oil, and gel stabilizer. The weight of the base liquid in the formula was increased by 1/3 by adding more base liquid, while the weights of the fragrance oil and gel stabilizer remained unchanged. Before this increase, what was the ratio of the weight of the base liquid to the total weight of the formula?

(1) After the addition of base liquid, the ratio of the weight of fragrance oil to the total weight of the formula decreased from 1/5 to 1/6.

(2) After the addition of base liquid, the ratio of the weight of base liquid to the total weight of the formula became 2/3.


 


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Let B and T be the original base and total weight
We need to find B/T
After adding base liquid
base becomes 4/3B
total becomes T+1/3B

Statement I
ratio changes from 1/5 to 1/6
Originally F= T/5
After addition, (T/5)/(T+1/3B) = 1/6
6T=5T+5/3B

sO, B/T = 3/5
sufficient

Statement II
After addition,

(4/3B)/(T+1/3B) = 2/3
4B = 2T + 2/3B
5B=3T
B/T=3/5
Sufficient

Hence D is the answer

Bunuel
A cosmetics lab prepared a liquid formula that consisted of base liquid, fragrance oil, and gel stabilizer. The weight of the base liquid in the formula was increased by 1/3 by adding more base liquid, while the weights of the fragrance oil and gel stabilizer remained unchanged. Before this increase, what was the ratio of the weight of the base liquid to the total weight of the formula?

(1) After the addition of base liquid, the ratio of the weight of fragrance oil to the total weight of the formula decreased from 1/5 to 1/6.

(2) After the addition of base liquid, the ratio of the weight of base liquid to the total weight of the formula became 2/3.


 


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D. each statement alone is sufficient
Let base = b, total before = T. Base becomes b+b/3=4b/3, new total=T+b/3. We want b/T.
Statement (1) fragrance oil weight f is unchanged. f/T=1/5 and f(T+b/3)=1/6
So T = 5f and T+b/3=6f, giving b/3=f, so b=3f=3(T/5). Then b/T=3/5. Sufficient
Statement (2) new base/new total=(4b/3)/(T+b/3)=2/3
Cross multiply=>b/T=3/5. Sufficient.
Each alone works


Bunuel
A cosmetics lab prepared a liquid formula that consisted of base liquid, fragrance oil, and gel stabilizer. The weight of the base liquid in the formula was increased by 1/3 by adding more base liquid, while the weights of the fragrance oil and gel stabilizer remained unchanged. Before this increase, what was the ratio of the weight of the base liquid to the total weight of the formula?

(1) After the addition of base liquid, the ratio of the weight of fragrance oil to the total weight of the formula decreased from 1/5 to 1/6.

(2) After the addition of base liquid, the ratio of the weight of base liquid to the total weight of the formula became 2/3.


 


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base liquid = b, fragrance =f, gel = g
Reqd. b / b+f+g = ??

1. given: f/(b+f+g)=1/5....b+g=4f
f/(4b/3 + f +g ) = 1/6
18f=4b+3f+3g
15f=4b+3g
15f=3b+3g+b
15f=3(b+g)+b
15f=12f+b
b=3f

Reqd = 3f /5f =3/5 ....Sufficient

2. (4b/3) /(4b/3 + f + g) = 2/3
12b =8b+6f+6g
b= 3 (f+g) / 2

Reqd b/(b+ 2b/3) = 3/5 ... Sufficient

Each alone Sufficient

Ans D
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T=TOTAL WEIGHT, X=LIQUID BASE WEIGHT, Y=Oil weight, Z=GEL WEIGHT
Y/T=1/5

statement 1 gives us:-
(1/5T)/ (4/3 X+Y+Z)= 1/6

Not sufficient alone.

Statement 2 gives us:-
X/ 4/3 X+Y+Z = 2/3

Not sufficient alone.

But substituting value of T from statement 1 in statement 2 we can get the required ratio.
Bunuel
A cosmetics lab prepared a liquid formula that consisted of base liquid, fragrance oil, and gel stabilizer. The weight of the base liquid in the formula was increased by 1/3 by adding more base liquid, while the weights of the fragrance oil and gel stabilizer remained unchanged. Before this increase, what was the ratio of the weight of the base liquid to the total weight of the formula?

(1) After the addition of base liquid, the ratio of the weight of fragrance oil to the total weight of the formula decreased from 1/5 to 1/6.

(2) After the addition of base liquid, the ratio of the weight of base liquid to the total weight of the formula became 2/3.


 


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TotalBefore = base + fragance + gel
TotalAfter = base + fragance + gel + base/3 = TotalBefore + base/3 (1)

find base/TotalBefore

(1)
F/TotalBefore = 1/5
F/TotalAfter = 1/6

TotalBefore/5 = TotalAfter/6

TotalAfter = (6/5)*TotalBefore

Substituting in (1):
(6/5)*TotalBefore = TotalBefore + base/3
(1/5)*TotalBefore = base/3
base = (3/5)*TotalBefore
base/TotalBefore = 3/5

Condition sufficient

(2)
(base + base/3)/TotalAfter = (4/3)*base/TotalAfter = 2/3
TotalAfter = 2*base

Substituting in (1):
2*base = TotalBefore + base/3
5*base = 3*TotalBefore
base/TotalBefore = 3/5

Condition sufficient

Answer D
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Total weight of formula= B+F+G
After adding 1/3 base , new base = B+(1/3)B =(4/3)B
New total = (4/3)B +F+G

1) F/total = 1/5 to F/new total=1/6
F= (1/5)Total. &. F=(1/6)New total
T/5 =T+(B/3)/6
B/T = 3/5
It is sufficient

2) (4B/3)/new total= 2/3
B/T = 6/10=3/5
It is sufficient

D. Each statement alone is sufficient to answer
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