12 Days of Christmas GMAT Competition 2025 - Day 6: "Sweetness" is

linnet

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22 Dec 2025, 13:14

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So we ca get 3 salads from the fruits: Mango + Apple, Mango + Lemon, Apple + Lemon
Also Mango>Apple> Lemon
Does the salad has Mango?
Statement 1 Salad<Apple
Aloe is not sufficient
Statement 2 Salad>Apples +Lemon
The fruit salad has either Mango +Apple or Mango +Lemon
Statement 2 Alone is sufficient

Answer: Statement 2 alone is sufficient but Statement 1 alone is not

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22 Dec 2025, 13:16

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Bunuel

the question deals with averages - the avg of two objects with values a & b lies between a & b inclusive
avg= x a +y b /(x+y), where x & y are quantity of both objects
let sweetness of
mango=3
apple =2 l
lemon=1
stmnt A - any a containing apple and mango will have sweetness between-2 to 3(inclusive)
but since here it says the sweetness is below the sweetness of apple,the the salad must not contain mango
sufficient
stmntB- fruit salad sweeter that fruit salad made with equal parts of apple and lemon
avg sweetness of this salad of apple and lemon= 2+1/3= 1
Now any salad that contains mango and apple can have avg sweetness greater than this or any salad having greater percentage of apple than lemon can have sweetness greater than this
insufficient

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22 Dec 2025, 13:27

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sweetness defined as qty. of sugar to the qty. of salad by weight.
M's are sweeter then A's and A's are sweeter than L's.
equal weights of exactly two of these fruits are used in the salad.
are M's in the salad??
1. salad is less sweet than A's clearly signifies that ,salad contains equal weights of A's and L's.
so no M's ---sufficient
2. salad is sweeter than the salad formed using equal weights of A's and L's ,only possible if it contains M's ----sufficient
so D

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22 Dec 2025, 13:36

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Solution:

1. Apples are sweeter than Lemons.

2. Mangoes are sweeter than Apples.

Thus, the sweetest fruit salad must contain Mangoes.

1. Fruit salad is less sweet than apples. This means it contains only lemons. Hence, no apples. Sufficient

2. Fruit salad is sweeter than a fruit salad made using equal weights of apples and lemons and no other ingredients. If the fruit salad is sweeter than the fruit salad that contains only apples and lemons, that means it contains apples. Hence, Sufficient

Hence, Option D

Bunuel

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22 Dec 2025, 14:15

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Bunuel

------- L -------- A -------------M

1)

a) One possiblity is that L and M are very close to A, such that the sum (L+M) is less than 2A

---------------- L + M -------- 2A

In this case, the fruit salad contains mango.

Other possiblility could be L + A is less than 2A

In the first case, the fruit salad contains mangoes, and in the second case it doesn't. Hence I alone is Not sufficient.

2) ------------------ (A + L) ------------ << sweetness of FS Lies here >>

The only way this is possible if the fruit salad contains mangoes.

Hence, Statment 2 is sufficent.

Option B

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22 Dec 2025, 14:26

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Sweetness : Mango (M)> Apple (A) > Lemons (L)

(1) fruit salad < A means that fruit salad consists of (A+L) OR (M+L) ---- Not Sufficient
(2) Fruit salad > (A+L) fruit salad means it can be (M+A) or (M+L) ---- Sufficient as in both scenario it contains Mango

So Answer is B

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22 Dec 2025, 15:36

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AD BCE

The prompt tells us that:
Mangos are sweeter > Apples
Apples are sweeter > Lemons

This means that Mangos are sweeter than all, and lemons are the least.

Statement 1: If the fruit salad is less sweet than Apples, then it can't contain Mangos. Sufficient

Statement 2: If the Salad is sweeter than a sald made of equal parts of Apples and Lemons, it must contain Mangos. Sufficient.

D

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22 Dec 2025, 15:45

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1. Read twice and simplify it

2. The data states

M > A > L

FS = 2 fruits only

Question: FS=M+A and/or FS=M+L?

3. Answer choice

(1) FS < A

meaning FS=A+L or FS=M+L (we don't know Mango+Lemon more or less sweet than apple)

so, insufficient

(2) FS > A+L

meaning FS=M+A or FS=M+L -> both possibility include mango

so, sufficient

The answer is B

Bunuel

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22 Dec 2025, 17:22

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Answer a

1) only apple / lemon is less sweet therefore no mango SUFFICIENT

2) either mango and apple or mango and lemon could be sweeter than apples and lemons dont know which INSUFFICIENT

Bunuel

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22 Dec 2025, 20:32

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Option B, statement 2 alone is sufficient
Stat 1: it is given that salad is less sweet than apple, that means at it can contain apple and lemon and mango and lemon also.
Stat 2: to be sweeter than apple + lemon, it should contain mango.

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22 Dec 2025, 22:25

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"Sweetness" is defined as sugar content per unit of weight. At a fruit stand, mangoes are sweeter than apples, and apples are sweeter than lemons. A fruit salad is made using equal weights of exactly two of these fruits and no other ingredients. Does the fruit salad contain mango?

(1) The fruit salad is less sweet than apples.

(2) The fruit salad is sweeter than a fruit salad made using equal weights of apples and lemons and no other ingredients.

Sweetness ---> Mangoes > Apples > Lemons

AD -> when the salad is less sweet than apples possible combinations are Apple & Lemons or Mangoes and Lemons ------ Insufficient.

B ----> Sweetness of Salad > Apples and Lemons ---- possible salads for equal weight are Mangoes + Lemons or Mangoes + Apples. ---In both cases Salad Contains Mango.---Sufficient. B answer.

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22 Dec 2025, 23:04

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Bunuel

Sweetness of Mango/ unit weight: M
Sweetness of Apple/ unit weight: A
Sweetness of Lemon/ unit weight: L

Now we have that M>A and A>L.
In mixtures, when we mix the two quantities, the mixture will have a value between the two quantities.

Fruit Salad made using equal weights of exactly two of these fruits.
Fruit Salad contain Mango?

1. Fruit Salad less sweet than apples.
We don't know the sweetness of lemons. The mixture of mangoes and lemons can give a fruit salad less sweet than apples as well. Since we don't know the numbers we cannot determine.
NOT SUFFICIENT.

2. The fruit salad is sweeter than the fruit salad made using equal weights of apples and lemons and no other ingredients.
We know that the mixture of apples and lemons is less sweeter than apples. Mangoes are sweeter than apples. This implies that the salad will contain mangoes in order to make it sweeter than the mixture of lemons and apples.
SUFFICIENT.

ANSWER: B

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22 Dec 2025, 23:32

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Let's denote sweetness of each fruits as M, A, L => given: M > A > L & the resulting fruit salad is either M+A/2 or A+L/2 or M+L/2
ask? does the fruit salad (with 2 fruits) contain Mango -> Y/N?

A -> the combo is less sweet than Apple -> a combination of A and L or M and L could give resulting sweetness b/w them and it can vary based on amount of sweetness.
with A and L -> Mango not there
with L and M -> Mango is present hence no clear answer.
B -> sweeter than (A + L)/2 -> in either case mango is must -> hence Yes -> is sufficient.

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22 Dec 2025, 23:44

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m > a > l

possible combinations:
(m,a)
(a, l)
(m,l)

Statement 1:

two possibilities:
1. (a, l) -> less sweet than apple since it is average of a and l
2. (m,l) -> possible to have value less than apple (assuming apple is not exactly at the midpoint of m and l)

insufficient

Statement 2:

greater than (a,l), then it should either use (m, a) or (m, l)
(m,l) assuming that a is not midpoint of m or l.

So in both cases, m is present.

sufficient

ans : option B

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23 Dec 2025, 00:41

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The key to this question is to note that the fruit salad is made using equal weights of exactly two of the fruits.

Imagine on a number line, L, then A, then M, where each represents the sweetness of the corresponding fruit.
Since we are taking only two of these and in equal quantities, the overall sweetness of the salad could be any of the three points: (L+A)/2, (L+M)/2, or (A+M)/2.
Now, why these points? This is a weighted averages problem, the weights being the quantities of the fruits, and since both are taken in equal quantities, both will have equal weights. And when weights are equal, the average lies right at the midpoint.

(1) Now two possibilies for this given case, since the salad is less sweet than apples, it could be either the salad contains only lemon and apples (L < (L+A)/2 < A), or it could contain lemon and mangoes (L < (L+M)/2 < M, and since we don't know the distance between L, A and M, the midpoint could lie left of A or righ of A). So not sufficient.

(2) Since the fruit salad is sweeter than the salad made using A and L, for sure, mangoes should be included.
Why? If mangoes weren't taken, then only apples and lemons would be taken in equal quantities, and our fruit salad would have the same sweetness as the salad given here. Since it is sweeter, then either mangoes and lemon are taken, or mangoes and apples are taken. Sufficient.

Option B.

Bunuel

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23 Dec 2025, 01:14

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Bunuel

Given :

Sweetness per gram : Mango > Apple > Lemon

Each salad made up of exactly two of these fruits in equal amount

Question :

Does the fruit salad contain mango ?

Statement 1 : Fruit salad sweetness < Apple sugar sweetness

Mango + Lemon Mixture < Apple ( possible)

Apple + Lemon Mixture < Apple ( possible)

So we don't know if it definitely contains Mango or not ----- Not sufficient

Statement 2 : Actual Fruit salad > Apple + Lemon Sweetness

Apple + Mango > Apple + Lemon ( Possible)

Mango + Lemon > Apple + Lemon ( Possible)

So Mango is there in it in every case ----- Sufficient

Our Answer is B

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23 Dec 2025, 01:15

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We know that the salad must contain two different fruits, so the only combinations possible are A+L or A+M or M+L. Also, the sweetness levels are $M>A>L$

(1) Just apples would be as sweet as A+A; so, to make it less sweet, we could easily go A+L. However, we don't know how proportionately the sweetness differs - which means that potentially we can have M+L be more sour than A+A, in case that the sweetness differences are M-A<A-L, meaning that limes are more sour than mangoes are sweeter. Insufficient, since we have two options.

(2) If we're 'sweeter' than A+L, then we have to go M+A or M+L - and although we have two options, both must contain mango. Sufficient.

Therefore, the answer is B.

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23 Dec 2025, 01:24

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Sugar Content be

Mango = M
Apple = A
Lemon = L

M > A > L

Since the fruit salad is made from equal weights the sugar contents would be following

M and A sweet content = (M+A)/2 -- (a)
M and L sweet content = (M+L)/2 -- (b)
A and L sweet content = (A+L)/2 -- (c)

From this we can definitely say that
1. M+A salad is sweeter than A+L salad
2. M+A salad is sweeter than M+L salad
3. M+L salad is sweeter than A+L salad

So, A+L salad is the least sweet salad

1. The fruit salad is less sweet than apples
Here we have 2 possibilities, either M+L or A+L salad
Since both are possible, we cannot be sure.
Insufficient

2. The fruit salad is sweeter than a fruit salad made using equal weights of Apples and Lemons
This refers to the A+L salad. We already know that A+L is the least sweet salad hence the other salad must definitely contain Mangoes.
Sufficient

Option B

Bunuel