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12 Days of Christmas GMAT Competition 2025 - Day 1: A painter mixes

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bhanu29

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15 Dec 2025, 19:07

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Bunuel

Weighted average question

the gloss percentage in combined mixture would be ( MG + NH ) / (M + N)

Statement 1 alone is insufficient as we have no idea about M,N AD/BCE
Statement 2 alone is insufficient as we have no idea about G,H AD/BCE

Let G = 7k H= 5k
Let M = 3l N = 4l

Now combining statement 1 and 2

(7k.3l+5k.4l)/(3l+4l) = 41kl/7l = 41k/7

Without knowing k or one of the actual amounts we cannot determine gloss % in resulting mixture.

For example

If G = 7% and H = 5% (k=1), then Result = 41/7 ≈ 5.86%
If G = 14% and H = 10% (k=2), then Result = 82/7 ≈ 11.71%
If G = 70% and H = 50% (k=10), then Result = 410/7 ≈ 58.57%
AD/BCE

Correct Answer E

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A: G% M liters
B: H% N liters

weighted average = (G*M + H*N)/(M+N)

(1)
G/H = 7/5

Insufficient

(2)
M/N = 3/4

Insufficient

(1) + (2)
G=1.4H
M=0.75N

(G*M + H*N)/(M+N) = (1.05HN + HN)/(1.75N) = 2.05/1.75 * H

It is neccesary to know H.
Insufficient

IMO E

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Batch A has G% and M liters
Batch B has H% and N liters

gloss finish percentage of the mixture is (GxM + HxN)/(M+N)

(1)
G=7a
H=5a

Condition insufficient

(2)
M=3b
N=4b

Condition insufficient

(1)+(2)

(GxM + HxN)/(M+N) = (21ab + 20ab)/7b = 41ab/7b = 41a/7 -> a is unknown

Conditions insufficient

Answer E

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15 Dec 2025, 20:46

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G% and M liters combines with H% and N liters so the finish percentage is (GM+HN)/(M+N)

(1)
G=7x and H=5x

Condition (1) is insufficient

(2)
M=3y and N=4y

Condition (2) is insufficient

(1)+(2)
(GM+HN)/(M+N)=(21xy+20xy)/7y=(41/7)*x

we need to know x

Condition (1) and (2) are insufficient

The answer is E

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15 Dec 2025, 20:47

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Bunuel

Gloss Finish Concentration (A:B) = G:H
Quantity (A:B) = M:N
Using Weighted Average: (G*M + H*N)/M+N
A) G:H = 7:5
(7*M + 5*N)/ M+N - no way forward, hence Option A & D eliminated.
B) M:N = 3:4
(G*3 + H*4) / 7 - no way forward, hence Option B eliminated.
Combining both:
(7*3 + 5*4)/7 = 5.85 - therefore, OPTION C.

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15 Dec 2025, 20:54

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G--------AVG-------H
AVG Divides in ratio N:M
(1) G:H given
Avg requires actual value of G & H and ratio of weights
INSUFFICIENT
(2) M:N given
But we don't know value of G and H
INSUFFICIENT
(1) & (2)
We still don't have actual value of G & H
INSUFFICIENT

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15 Dec 2025, 21:08

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Two batches mixture (G% and M liters with H% and N liters)

Calculate (G% * M + H% * N)/(M + N)

(1)
G%/H% = 7/5
Clearly insufficient

(2)
M/N = 3/4

Clearly insufficient

(1) and (2)

(G% * M + H% * N)/(M + N) = ((7/5)*H% * (3/4)*N + H% * N)/(7/4 * N) = 41/35 * H%

It is neccesary to know H%

Insufficient

The correct answer is E

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We have a system of two equations, where t stands for total volume and x stands for the final concentration we're looking for:

$m + n = t$

$m*g + n*h = t*x $

Therefore, $x = \frac{mg + nh }{ t} = \frac{mg + nh }{ m + n}$
In order to find this ratio, we need to figure out the above proportion.

(1) Say g = 7k and h = 5k
Then, $x = \frac{k(7m+5n) }{ m+n}$, which is clearly insufficient.

(2) Say m = 3y and n = 4y
Then, $x = \frac{y(3g + 4h) }{ 3y + 4y} = \frac{3g+4h }{ 7}$, which is insfficient as well.

(1) + (2) Combining both, we get: $x = \frac{3*7k + 4*5k }{ 7} = \frac{41k}{7}$, which seems like a very good value, but without any numerical constraints it's as unknown as it was before we solved anything, since it's fully dependent on k.

So, the answer is E.

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This question being a mixture problem, we need to determine the percentage of gloss in resulting mixture.
Let us understand this as : M litres of G% solution is mixed with N litres of H% solution. The Gloss quantity in each of this contributing mixtures is as follows:
M*G/100 and N*H/100
The gloss finish concentration in resulting mixture = gloss quantity / overall quantity
= ((MG/100)+(NH/100))/(M+N)
This equation has four variables.

Statement A: 5G = 7H
1 equation, 4 variables - not solvable
Statement B: 4M = 3N
1 equation, 4 variables - not solvable
Combining equations and re-writing
The gloss finish concentration in resulting mixture = ((MG/100)+(4M*5G)/(3*7*100))/(M+(4M/3))
Cancelling M in all terms, the equation becomes ((G/100) + (4*5G)/(3*7*100))/(7/3)
We still do not have value of G.
Hence answer is E

Bunuel

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A painter mixes two batches of paint to create a custom color. Batch A has a gloss finish concentration of G% by volume. Batch B has a gloss finish concentration of H% by volume. The painter combines M liters of Batch A with N liters of Batch B. What is the gloss finish percentage, by volume, of the resulting mixture?

(1) The ratio of G to H is 7 to 5.
(2) The ratio of M to N is 3 to 4.

Batch A has G% gloss
Batch B has h% gloss

M liters of batch A
N liters of batch B

Gloss volume is M*G + N*H / ( M+N)
need to have values of all variables

OPTION # 1 does not have M:N ; insufficient

Option 2 does not have value G :H ; insufficient

OPTION C is correct sufficient

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Answer: E

In order to find out the % by volume of the resulting mixture, we need the values of G%, H%, M and N. After that we can just apply the weighted average/ alligation formula to find out the required %.

(1) gives us the ratio of G to H which is not sufficient.
(2) Ratio of M to N, although required for alligation formula, is not sufficient in itself

(1) & (2) combined give us:
Required %= $(GM + HN)/(M+N) $
Since we still dont know the fixed values of G & H, we cannot derive at a fixed numerical value.
Thus, these 2 statements are insufficent.

Bunuel

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I'm pretty sure I marked this one wrong - but while revising the solution today morning after solving this last evening, I could see where I went wrong, so my explanation will be basis that.

I like to assume numbers for such one, only because variables scare me, and number make the logic simpler for me. I also like to humanize the objects of the question for my own understanding.

A painter mixes two batches of paint to create a customer color. Batch A (Amber) has a gloss concentration of G% by volume. Batch B (Brown) has a gloss percentage of H% by volume. The painter combines M litres of Amber with N litres of Brown.

Now for the statements.

Statement I: The ratio of the gloss concentration in Amber to Brown is 7 to 5. Let's assume this translates to 35% to 20%, to relate things better. For us to find the percentage in the mixture, we still need to know in what quantity were each of the paints mixed. For instance, if we assume 35% for Amber, and 20% for Brown, but if Amber is just a litre, but Brown is four, the resultant ratio will be different than if it is, say, Amber two litres and Brown three. Hence, Statement I is not enough.

Statement II: The ratio of the quantity of Amber paint mixed with Brown paint is 3 to 4. Without the ratio of the volume of gloss concentration, however, we cannot find the gloss concentration for the resultant mixture. For instance, if Amber only has 10% of gloss, versus 80% for Brown, the proportions will be quite different than if both have 50% ratios.

Both together: If we assume 3 litres of Amber is added to 4 Litres of Brown, with Amber having, say, a 7% concentration of gloss and Brown having a 5% concentration, we can define what the resulting ratio is - 5.86%.

But this what I failed to consider:
If we assume 3 litres of Amber is added to 4 litres of Brown, with Amber having, say, a 35% concentration to a 20$ concentration of Brown, we can define the resulting ratio as 26.2%

So, two (and more) answers, hence, E. Clearly, one way to solve this would've been to know the concentration percentage rather than the ratio used.

Bunuel

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Final Gloss percentage depends upon ;
Relative concentrations G and H .
Relative quantities M vs N .

Option 1 : It didn't tell us How much A vs B is used.
Option 2 :Whether A or B has higher gloss concentration ?

Statement 1 and 2 Together : Both Ratios are known weighted averages are locked .
Assuming ;
A has 7 units of gloss per unit
B has 5 units of gloss per unit
Mix 3 units of A and 4 units of B
Total Gloss = 3x7+4x5 = 41
Total Paint = 3+4 =7
Final Gloss percentage = 41/7 %

If not assumed Values then
Final Gloss % = MG+NH /M+N
3t X 7k +4t X 5k/3t +4t , t and k will be cancelled will give 41/7.

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For using allegation method, M1, M2, M, N1 and N2 are the parameters in use.
We know, M1 is G, M2 is H, N1 is M and N2 is N.
Having fixed values of either M1 or M2 is key (give ratio of N1 and N2).
All four parameters cannot be in the form of ratio.
Statement 1: Gives nothing about N1 and N2. Hence NS.
Statement 2: Gives nothing about M1 and M2, hence NS.
Two together, have different constants in place, we get the answer as 41/7 k where k is a constant.
HENCE E.

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Bunuel

Batch A -> G% Gloss
Batch B -> H% Gloss

Total Gloss in mixture = [(MG/100) + (NH/100)]/(M+N) = 1/100 * [MG + NH]/(M+N) -- (1)

(1) G:H = 7:5
=> G = 7H/5

Using this in eq (1) we get

Gloss in mixture = 1/100 * [MH(7/5) + NH]/(M+N)
= 1/500 * H[7M + 5N]/[M+N]
We cannot get the value of this expression.

Insufficient

(2) M:N = 3:4
=> M = 3N/4
Gloss in mixture = 1/100 * [(3/4)NG + NH]/(3N/4+N)
=> 1/100 * (3NG + 4NH)/(3N + 4N)
=> 1/100 * (3G + 4H)/7 -- eq (2)

Cannot reduce further. Insufficient.

(1) and (2) together we get
Gloss in mixture = 1/100 * (3G + 4H)/7
Now using G = 7H/5 in the above equation we get a value

Gloss in mixture = 1/700 * (21H/5 + 4H) = 1/700 * 41H/5

Even with both statement we cannot find out the value of the equation. Insufficient.

Option E

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Individually not sufficient.

Together, still we need any absolute value of G or H%.

E

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For statement 1 alone, if we consider just the ratios of the gloss finish concentration, we do not have any specific information around the overall volume of the entire mixture. Hence this statement is insufficient, we can eliminate option (A) & by default option (D)

Similarly for statement 2 alone, if we consider the ratios of the volumes alone we do not have any information around the gloss finish concentration based on this statement along. Hence we can also eliminate option (B).

If we combine both statements together, if we assume the ratios to be 7V & 5V based on the volume ratios of G & H. And if we assume the total volume to be T & based on the second statement, the volumes of M & T would be 3T & 4T respectively.

Since we have two variables, here & if we calculate gloss finish as 7V*3T+5V*4T/(3T+4T), we still will be left with the variable T which we do not know. Hence option (C) is also insufficient

Therefore the answer is option (E) none of the two statements together are sufficient

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Correct option is E.

Bunuel

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A painter mixes two batches of paint to create a custom color. Batch A has a gloss finish concentration of G% by volume. Batch B has a gloss finish concentration of H% by volume. The painter combines M liters of Batch A with N liters of Batch B. What is the gloss finish percentage, by volume, of the resulting mixture?
Gloos finish percentage= (MG+NH)/(M+N) =?

(1) The ratio of G to H is 7 to 5.
It only provides the ratio and not the actual values. So it is insufficient to answer the question.
(2) The ratio of M to N is 3 to 4.
It only provides information about how much paint is mixed and not about the gloss mixture. So alone is insufficient.
(1)&(2)
G:H = 7:5 or G=7x & H=5x
M:N=3:4 or M=3y & N=4y
Put in the gloss mixture percentage equation= ((3y)(7x)+(4y)(5x))/(3y+4y) = 41x/7
We still have one unknown x
This is still insufficient to answer the question
E

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(M*G+N*H)/(M+N)

By statement 1- Ratio of G and H given but no info about M and N so not sufficient
Statement 2- Ratio of m and N given but no information on G and H. Not sufficient

By both st. 1 and 2= let G=7X, H=5X. M=3Y, N=4Y

This gives 2 variable in numerator and one in denominator so the variable X can't be eliminated. Hence not sufficient

Bunuel

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