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

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Ak20047

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I solved this question using the alligation method(cross weighted avg diagram method). the answer came out to be C- both statements are necssary.

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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Given the variables given, we are supposed to find (GM+NH)/100(M+N)

(1) Given G= 7x and H =5x. We also need to know M and N. Not sufficient

(2) Given M = 3y and N =4y. We also need to know G and H. Not sufficient.

Combining both statements, (21xy +20xy)/100*7y. We still need to know the value of x to solve the equation. Not sufficient.

Therefore, Option E

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15 Dec 2025, 10:38

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There is a shortcut to solve the weightable average which is by cross multiplication

X...............Y
.......Z........
Y-Z.......Z-X
Ratio 1......Ratio 2

Z is the average after mixing both the mixture. Subtracting X from Z and Z from Y gives the ratio and hence both combined will give answer

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15 Dec 2025, 10:40

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It is basically weighted average concept.
So what we need is
(G% of M + H% of N) * 100 / M + N
= (G*M + H*N) / M + N

If we observe here, for M and N, even if we get the ratio of them, it still works, as the multiplier gets cancelled from both the numerator and the denominator.
But we would need the actual values for G and H (since we can't cancel off their multiplier).

To clearly see,
= (7k * 3a + 5k * 4a) / 7a
= 41k / 7
So option E, both won't help us, as we would still need the multiplier for the G and H ratio given.

Bunuel

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Bunuel

The gloss finish percentage of the final mixture, by volume is given by:
[GM + HN][/ M+N]
where,
G%= gloss concentration of Batch A
H%= gloss concentration of Batch B
M= Litres of Batch A
N= Litres of Batch B

To determine a numerical percentage, we would require both:
- the ratio of G and H
- the ratio of M and N

Statement 1- This tells us the relative concentrations, but gives no info about the volumes M and N.

Statement 2- This tells us the relative volumes, but gives no information about the concentrations G and H.

Statements together:
Let G= 7k, H=5k
Let M= 3x, N= 4x

Then, Mixture= (7k*3x + 5k*4x)/ (3x + 4x) =41k/7 which is a unique value. Thus answer will be C.

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15 Dec 2025, 10:55

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Gloss finish percentage by volume: needs atleast some kind of base data parameter in units apart from ratios. SO, E is the Answer choice

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Gloss Finish % by volume for Batch A is G%. So if M litres are used from Batch A in mixture then concentration of gloss finish will be GM/100 litres. Similarly Gloss Finish % by volume for Batch B is H %. So , if N litres are used from Batch B in mixture then concentration of gloss finish will be HN/100 litres. so Gloss finish % in mixture will be (GM/100 + HN/100) / (M+N) . Now taking statement A , G/H = 7/5 , it's not sufficient since M and N values are not known and either of specific G and H value is not known. Similarly taking statement B , M/N = 3/4 , it's not sufficient since G and H values are not known. Even if we take combination of both statements , either of specific G or H value is not known. So the correct answer is E.

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Nice and tricky...we gotta find ......the new gloss finish by percentage in new mixture......
Paint 1 - G%
Paint 2 - H%

We would have to know the values of G and H ...and the ratio of M and N......How ?
( GM + HN )/ M + N will give us .........

Statement 1. G:H is 7:5 We know only ratios of G and H..they could be 7% 5% or 14% 10% The resultant percentage will always be a value between G and H..depending on the ratio they are mixed....This is insufficient....

Statement 2: M:N is 3:4...But we dont know G and H value

Combine...We still know only ratio between G and H not the value...values is crucial....So E answer

Algebrically when combined...... G:H be = 7a : 5a ...M:N be = 3x : 4x.....( G X M + H X N ) / M + N = (7a*3x + 5a*4x )/ 3x + 4x = 41ax/7x....41a/7....Still a is unknown ...E is answer

Bunuel

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Question is asking for the weighted average of the solutions

Statement 1

Ratio of G to H is 7 to 5

Actual percentages could be (7% and 5%) or (70% and 50%). So this information is clearly insufficient.

Statement 2

Ratio of M to N is 3 to 4

While the weights ratio are given, we have no idea about actual solution percentages. So this information is insufficient.

Combining 1 & 2
We have weights but we don't have concrete values of actual percentages,
for ex
\(1:1\) of 7% and 5% is 6%
\(1:1\) of 70% and 50% is 60%

So together also the information is insufficient

Ans: E

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The equation we get is [(G/100)M+(H/100)N]/(M+N).

If we have the ratios of G and H and M and N, we will still be left with variables since ratios are not exact numbers. So, the answer is E

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A. Statement 1 is sufficient

Bunuel

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We have to identify % gloss finish by volume for resulting mixture which is
= [G*M+H*N]/[M+N]

(1) G:H = 7:5
(2) M:N = 3:4

Both individually is clearly not enough as the above value cannot be calculated by them.
and even if, we consider them together.

G = 7x, H = 5x
M = 3y, N = 4y

=[7x*3y+5x*4y]/[3y+4y]
=[21xy+20xy]/7y
= 40xy/7y
= 40x/7

x is still unknown.
Hence the required value cannot be computed by considering (1) and (2) together too.

Hence, the answer is (E)

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We need the final gloss finish percent of the mixture. For that we would need atleast the initial percentages, i.e. G% & H% as the final percent would be between these. Neither of the option gives that, both gives just ratios. Ans E

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Gloss from A = (G/100)*M
Gloss from B = (H/100)*N

Final conc. = (GM+HN)/(M+N)

1. G=7x, H=5x
Conc = x(7M+5N)/(M+N)..
Not sufficient

2. M=3y, N=4y ...
(3M+4N)/7...Not sufficient

Together,
21x+20x / 7 = 41x/7
Not Sufficient

Ans E

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OK first we evaluate the question

Ratio of quantity of batch A and B along with their concentrations will tell us the concentration of the resulting mixture.
So far, we have no values. Silly alphabets only. There's not much more we can infer from the question.

1. This gives me the ratio of the concentrations. But the ratio could mean that the concentration is 3.5% to 2.5%, 21% to 15%
Or even as high as 98% to 70% . Very important to realize this here and now, because not only does this rule out statement A but also indicates that this might be heading towards option E.

2. statement 2 gives me the ratio in which the two solutions are mixed. While this information is useful and does give me half the information I need it does not tell me the other half. Without knowing the concentrations we don't know anything about the mixture, concentration.

If you don't make the inference that the first statement gives you a ratio of the concentration rather than the concentrations itself, you might mark C, but since it only gives us a ratio and no specific concentration, the answer goes
both statements together are insufficient

Bunuel

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Bunuel

To get the gloss finish percentage we need the volume or at least the ratio of each bath and concentration of each of each bath by volume or ratio.
Looking at the statements provided none of the same is sufficient by itself but when combined the two statement provide us with all the information that we need hence C

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Bunuel

The painter mixes two batches of paint to create a custom colour.

Let the two batches are Batch A, and Batch B respectively. Let their volumes be M and N litres respectively.

We are mixing G% of M belonging to Batch A and H% of N belonging to Batch B.

Resulting mixture volume = ?

Statement 1:

The ratio of G to H is 7:5

Let the ratio G. : H = 7x : 5x

7x % of M is mixed with 5x % of N .

Without knowing M and N. Insufficient

Statement 2:

The ratio of M to N is 3 to 4.

Let the ratio of M : N = 3k : 4K

G% (3k) is mixed with H%(4k) .

Without knowing G and H. Insufficient

Combining both statements 1 and 2, we get

= (MG% + NH% )/(M+N)

= [7x% (3K) + 5x%(4k)] /(3k+4k)

= (21xk+20xk) / (7k)

= 41x/7

x can take any values. Hence, Insufficient

Option E

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Given

Batch	Gloss finish by volume in percentage	Solution in liters
A	G/100	M
B	H/100	N

We have find the gloss finish percentage by volume in final mixture ?

Total volume = M +N

Gloss in Batch A = (G/100)*M
Gloss in Batch B = (H/100)*N

gloss percentage in final mixture = (((G/100)*M + (H/100)*N)/(M+N) ) * 100 = GM+ HN / (M+N) ------->Equation 1

Now lets consider the statement 1 - Ratio og G and H is 7: 5, so G/H = 7/5 => G = (7/5)*H

when substituted G value in Equation 1, we get value as = ((7/5)*HM+ HN)/(M+N)

Therefore statement 1 is not sufficient

Now lets consider the statement 2 - Ratio of M and N = 3/4, so M/N = 3/4 => M = (3/4)*N

when we substitute M value in equation 1 , we get value as = (G* (3/4)N) +HN /((3/4)*N+N)

There statement 2 is also not sufficient

Now, lets try to consider both statement 1 and statement 2, whee G = (7/5)*H and M =(3/4)*N

on substituting both in equation 1 , will result as following = ((21/20)HN+ HN )/((3/4)N+N) = (41/20)*H/ (7/4)

Therefore , statement 1 and statement 2 are not sufficient

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Gloss finish % = G/100*M+H/100*N /M+N

GM/100+HN/100 /M+N

We need the values of G,H,M and N

St1: G/H = 7k/5k. We don't know the values of M and N. Not sufficient

St2: M/N = 3x/4x. We don't know the value of G and H. Not sufficient

Combined, 7k*3x+5k*4x/7x = 21kx+20kx/7x = 41kx/7x = 41k/7
We don't know what is the value of K. Both statements together is also not sufficient.

Option (E)

Bunuel

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So, From the given,
Amount of gloss finish in Batch-A: Quantity X Gloss finish concentration= M X (G/100)
Similarly, Amount of gloss finish in Batch-B: N X (H/100)

Assume that, Gloss finish percentage of the resulting mixture: x
Volume of resulting mixture: (M + N)
Amount of gloss finish in the mixture: (M+N) X (x/100)

therefore, M X (G/100) + N X (H/100) = (M+N) X (x/100)

So, If (1) is only consider, the above equation become: (7M/5) + N = (M+N) X (x/H) ==> Not sufficient

If (2) is only consider, the above equation become: 3G + H = 7x ==> Not sufficient

If (1) & (2) are both consider, the above equation become: 26H/35 = x, Since we don't the value of H, again ==> Not suffient

Hence, Answer E

Bunuel