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

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hritik04

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16 Dec 2025, 05:37

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Bunuel

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.

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This question is related to Mixture and allegation, and the general formula for it is:

Net concentration = M*G + N*H/ M + N

Statement 1: Ratio of G to H is given, therefore G = 7k and H = 5k

Nothing is given for M and N so, it is not sufficient.

Statement 2: Ratio of M to N is given, therefore M = 3t and N = 4t

Nothing is given for G and H so, it is not sufficient.

1+2 ,
Now, putting both value in formula,

Net conc = 3t*7k + 4t*5k / 3t + 4t

= 21k + 20k / 7 = 41k/7

Still k is unknown, therefore both 1+2 is also not sufficient.

Therefore, option E is correct.

meenumaria

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16 Dec 2025, 06:12

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IMO E
We can't ge thte exact answer as we dont know the exact concentration. As both statement given are ratios.So both not sufficient individually as well as together

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16 Dec 2025, 06:41

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Bunuel

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Gloss finish Percentage =x= (0.01GM+0.01HN)/(M+N)

AD ---> G:H given ---> x=0.01G{M+(H/G)N}/(M+N) --Insufficient

B ---> M:N Given ---> still G & H will be required to find %age. --> Insufficient

C---> upon combing both ---> x = 0.01 GM {1+(HN/GM)}/ M(1+N/M) ----> G required for complete solution Hence, answer is E.

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16 Dec 2025, 07:35

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What we know is that, Batch A has gloss finish percentage of G% by volume and B has a gloss finish percentage of H% by volume.
M litres of A is combined with N litres of B and we have to find gloss finish percentage by volume of the mixture.

We are also given 2 statements,
(1) The ratio of G to H is 7 to 5
(2) The ratio of M to N is 3 to 4

We know that,
Mixture % = (MG + NH) / M + N

Statement (1),
The ratio of G to H is 7:5
=> We now know the relative concentration , but not the amount used

Statement (2),
The ratio of M to N is 3:4
=> We now know the relative volumes, but not the concentrations

Combining (1) and (2),
Lets say,
G = 7x , H = 5x
M = 3y , N = 4y
Mixture = (3y * 7x + 4y*5x) / 3y + 4y = 41xy / 7y = 41x / 7

=> The mixture percentage is unknown since we dont know what x is here too

Thus,
E. The two statements together are not sufficient

cann2406

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16 Dec 2025, 07:37

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Through problem statement, we are mixing M liters of Batch A and N liters of Batch B with concentration of G and H respectively.
So through mixture formula, (MG +NH)/(M+N)
we need values for M,N,G&H

Now,
Statement 1: gives only G and H. Not have value for M and N. Not sufficient.
Statement 2: gives only M and N. Not have value for G and H. Not Sufficient.

Now statement 1+2:
We have values for M,N, G & H
So, together its sufficient. C is correct answer

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16 Dec 2025, 07:38

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Given:
Batch A => gloss finish = G%, volume added = M
Batch B => gloss finish = H%, volume added = N

By formula for mixtures:

Final percentage = (M*G+N*H)/100* (M+N)

Statement 1 => G/H = 7/5 => Upon substitution => Value of M, N, G/H not known. Not sufficient.

Statement 2 => M/N = 3/4 => Upon substitution => (M*G + 4/3M*H)/100 (M+4/3M). M gets cancelled by Value of G & H still Unknown.

Both Together => (M*7/5H + 4/3M*H)/100 (M+4/3M). M gets cancelled but H (or conversely G) still remains. Not Sufficient.

Hence both together are not sufficient => E

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16 Dec 2025, 08:17

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Given: Batch A = G% and B = H%
To find =
mixture percentage = (mG+ nH)/ m+n
Statement 1= g:h = 7:4
it gives us a ratio not a fixed value, and can have several possibilities (N.S)
statement 2=
m:n = 3:4
incomplete information (N.S)
Combining boh
(21xy+20xy/(3x+4x)= 41y/7

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Concentration of G% in A and H% in B where, if G = 7, H = 5
Similarly, M and N liters of paint are mixed such that if M = 3, N = 4

G% of high gloss in M liters of paint can be written as M x G/100 OR 3a x 7b/100
And, H% of high gloss in N liters of paint as N x H/100 OR 4a x 5b/100

Both a and b are the variable that would have some value which could not be identified even on using both the statements, so solving further for the final percentage is not relevant. Hence, both statements together are not sufficient to answer the question.

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First we take AD, BCE now So to know the volume of gloss item in the mixture with A and B with M and N respective quantities , I need to know the value of G and H along with M and N with volumes rather than the ratios because while solving Statement 1 it isn't sufficient because of Mixture % = MG +NH/M+N but doesn't solve and same goes with Statement 2 alone . Statement 1 and 2 alone give 41m/7 in which don't know the value of m. So E

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17 Dec 2025, 01:01

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Quote:

BunuelA 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.

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Gloss finish concentrations,
A -> G%
B -> H%

Volumes,
A -> M litre
B -> N litre

Gloss finish percentage of resulting Mixture = $\frac{Total gloss finish percentage }{ Total Volume }$

=$\frac{M * G/100 + N * H/100}{M + N}$

Considering Statement I,

$G/H = 7/5 $---> We cannot substitute this in the equation and find the answer as there are 4 unknowns.

Not Sufficient.

Considering Statement II,

$M/N = 3/4$ ---> Again, we cannot substitute this in the equation and find the answer.

Not Sufficient.

Taking both statements together, we cannot substitute both to get an answer .

Not Sufficient.

Correct option is option E