GMAT Club World Cup 2022 (DAY 1): Mbappé has two types of sneakers

My answer is (A).

(1)Only
No suitcase has more red sneakers than the first one.
And
In each suitcase, Red sneakers + Blue sneakers remains the same.

We can thus infer that there are more blue sneakers in second, third... suitcase than in the first suitcase.

An extreme case is there are no blue sneakers in the first suitcase, in which case the first suitcase contains 0% of his blue sneakers.

Another extreme case is there are 100,000 blue sneakers in the first suitcase. Still, there will be more sneakers in second and ensuing suitcases.

Now, the first suitcase has 27% of all his red sneakers, and No suitcase has more red sneakers than the first one.
At very minimum, we need three more suitcases to put 100% of his red sneakers. For example, 26% for the second and third suitcase, and the remaining 21% in the fourth suitcase.
In this case, the first suitcase still have less than 25% of total blue sneakers. It can be very close to 25% (think about the extreme case in which there are 100,000 blue sneakers in the first suitcase), but it is always below 25% of the total blue sneakers.

It is possible there are more than four suit cases. The percentage of blue sneakers in the first suitcase will be lower.

Sufficient as the answer is "Yes" to the posed question.

(2) Only
Evidently insufficient.

Mbappé has two types of sneakers: red and blue. When packing for the World Cup, he puts equal number of sneakers in each of his suitcases. The first suitcase has 27% of all his red sneakers. Does the first suitcase have less than 25% of his blue sneakers ?


(1) No suitcase has more red sneakers than the first one.
insufficient, we don't know the total number of suitcase

(2) The first suitcase has between 23% and 27% of his blue sneakers.
insufficient, we still don't know the total number of suitcase

together we still don't know yet so E

Mbappé has two types of sneakers: red and blue. When packing for the World Cup, he puts equal number of sneakers in each of his suitcases. The first suitcase has 27% of all his red sneakers. Does the first suitcase have less than 25% of his blue sneakers ?


(1) No suitcase has more red sneakers than the first one.
SO R2<27%
no info about blue
INSUFFICIENT

(2) The first suitcase has between 23% and 27% of his blue sneakers.
23<B1<27
insufficient again
1+2

if 23
let's say R1+b1= 50
then R2 at max =26
B=24
if R2=1
then B2=49

IMO E

solving using 2x2 matrix

--- R----B--- total
1--- ---- ---- 50
2--- --- -----50
t--- ---- ---- 100
given

--- R----B--- total
1--- 27---- y---- 50
2--- 0--- -----50
t--- 27---73 ---- 100

The first suitcase has 27% of all his red sneakers ; by all we mean that what all he has with him available
need to determine y/73 <.25 or say is y<18.25
#1
(1) No suitcase has more red sneakers than the first one.

--- R----B--- total
1--- 27---- y---- 50
2--- 0--- -----50
t--- 27---73 ---- 100
insufficient

#2
The first suitcase has between 23% and 27% of his blue sneakers.

--- R----B--- total
1--- 27---- y---- 50
2--- --- -----50
t--- --- ---- 100
we have y = .23 to .27 or total blue , not all information available
from 1 &2

--- R----B--- total
1--- 27---- y---- 50
2--- 0--- -----50
t--- 27---73 ---- 100

.23*73<=y<=.27*73
16.79<=y<=19.71
we get yes and no to target
insufficient

OPTION E

1) No information about blue sneakers hence insufficient
2) This range may or may not fulfil the condition required by the question hence insufficient. It could be 23% or 27%. Insufficient

Since the second statement gives a range even with both statements together the information is insufficient.

IMHO Option E

Mbappé has two types of sneakers: red and blue. When packing for the World Cup, he puts equal number of sneakers in each of his suitcases. The first suitcase has 27% of all his red sneakers. Does the first suitcase have less than 25% of his blue sneakers ?


Here we are speaking in terms of percentage. Hence we need to make more observation than calculation.

Note : The first suitcase has 27% of all his red sneakers [ and NOT 27% sneakers is in his suitcase].


(1) No suitcase has more red sneakers than the first one.


With this info we can not say that the first suitcase have less than 25% of his blue sneakers. Insufficient !

(2) The first suitcase has between 23% and 27% of his blue sneakers.

With this info we can not say that the first suitcase have less than 25% of his blue sneakers. Insufficient !


But if we combine both:


We know that the quantity of sneakers are same in both bags. And the first one has more red sneakers. Then definitely we can comment about whether the first suitcase have less than 25% of his blue sneakers. IMO Option C !!

Given: Mbappé has two types of sneakers: red and blue. When packing for the World Cup, he puts equal number of sneakers in each of his suitcases. The first suitcase has 27% of all his red sneakers.

Let the total number of Red and Blue sneakers be r & b respectively
The first suitcase has red sneakers = 27%*r = .27r

Asked: Does the first suitcase have less than 25% of his blue sneakers ?

(1) No suitcase has more red sneakers than the first one.
No suitcase has more than .27r red sneakers,
Every suitcase has more blue sneakers than the first suitcase.
Case 1: .27r + .26b = .26r + .27b
Case 2: .27r + .23b = .23r + .27b
NOT SUFFICIENT

(2) The first suitcase has between 23% and 27% of his blue sneakers.
Case 1: .27r + .26b = .26r + .27b
Case 2: .27r + .24b = .24r + .27b
NOT SUFFICIENT

(1) + (2)
(1) No suitcase has more red sneakers than the first one.
(2) The first suitcase has between 23% and 27% of his blue sneakers.
Case 1: .27r + .26b = .26r + .27b
Case 2: .27r + .24b = .24r + .27b
NOT SUFFICIENT

IMO E

The answer is D. OE is already posted. Edited for correct answer.

Lets assume that Mbappé has 100 numbers of blue and 100 numbers of red sneakers.

Given

1) He puts equal number of sneakers in each of his suitcases.
2) The first suitcase has 27% of all his red sneakers in the first suitcase.

Statement 1

As No suitcase has more red sneakers than the first one, we need minimum of 4 suitcases.

We want to keep the number of sneakers in each suitcase same, the surplus from one will compensate the other color.

As we already have 27% of red sneakers in suitcase 1, the percentage of blue sneakers has to be less than 25% to maintain the constant.

Hence I is sufficient.

Statement 2

We know that each suitcase has equal number of sneakers. To keep the number constant we need less than 25% in suitcase 1.

Hence D

Usually with percent questions, its a good practice to start with 100 as a base value to test your options, now we can test out other options as well to eliminate and check other possibilities
So, let Blue Sneakers = 100 and Red Sneakers = 100, so total sneakers = 200

(1) No suitcase has more red sneakers than the first one.

1st suitcase: Number of red sneakers = 27
Total sneakers = 200 and there is the condition that all suitcases have equal number of sneakers
So each suitcase needs to have sneakers equal to a factor of 200 which is greater than 27 (number of red sneakers in this case). Possible options = 40/50/100
Blue sneakers = 13/23/73

Now in first 2 options, percent of blue sneakers are less than 25 percent
Let us examine the last option, if blue sneakers in suitcase 1 are 73, that means total sneakers in suitcase 1 are 100 and suitcase 2 will also need 100 sneakers to make the 200 because each suitcase has equal number of sneakers BUT IN THIS CASE NUMBER OF RED SNEAKERS IN SUITCASE 1 WILL BE LESS THAN IN SUITCASE 2, so this options cannot be right

13/23 are the only 2 options for number of blue sneakers and percent wise 13/23 which are both less than 25

Since it involves percentages, we can use any set of numbers even with red more than blue or blue more than red, answer shall be the same in all

SUFFICIENT

(2) The first suitcase has between 23% and 27% of his blue sneakers.

We already examined in statement 1 that percent of blue sneakers to satisfy the condition of each suitcase having equal number of sneakers has to be 13/23 and this statement says its between 23 and 27 so 23 is the only option that applies. Less than 25 percent

SUFFICIENT

Answer - D

we don't know how many suitcases Mbappe will take with him ! We need to know that

From the 1st statement, (1) No suitcase has more red sneakers than the first one.
The first one contains 27% of all the reds ones, let's say that all the reds are in the number of 100 and blues in the number of 100 (just to facilitate),
we know that the first suitcase has 27 red sneakers, so the remaining suitcases have 73.
we should find the number of suitcases that leads to a number of red sneakers that is under 27.

let's say we have 2 other suitcases (on top of the 1st one) then 73/2 = 35,6 which is impossible, since no suitcase has more than the 1st one in terms of red sneakers,

If we have 3 other suitcases (on top of the 1st one) then 73/3 = 24x3 +1, which is a possible case, So let's consider this case (other cases of more than 4 global suitcases are possible)
4 suitcases in total, with the first one with 27 red sneakers. since we have a total of 200 ( 100 red and 100 blue) then, each suitcase should have 50 sneakers.
So the first one must have 23 blue sneakers, so yes it is under 25, the 1st one is sufficient,

the 2nd statement, says that (2) The first suitcase has between 23% and 27% of his blue sneakers.
cannot lead to an information about the number of suitcases, IMO not sufficient, Answer is A

(1) No suitcase has more red sneakers than the first one.

(2) The first suitcase has between 23% and 27% of his blue sneakers.


1)Suppose there are 100 red sneakers. Then in the first suitcase it is 27.
Rest of the suitcases have 20 18 16 12 7 respectively.
Now if we consider that total number of sneakers in each suitcase is 30 .
In that case number of blue sneakers in each of them are 3 10 12 14 18 23
So the percentage of blue sneaker in the first suitcase is always less than 25%
2)No information about number of red sneakers .Insufficient.

So the answer is A

Let number of boxes = n
Let total red sneakers = R
Let total blue sneakers = B
Let number of red sneaker in i th box = ri (i.e. r1, r2, r3 etc.)
Let number of blue sneaker in i th box = bi (i.e. b1, b2, b3 etc.)

Given r1=0.27R
Given each suitcase has same number of total sneakers. r1+b1=r2+b2=r3+b3=r4+b4=... (a)
Question: Is b1 < 0.25 B ?

S1:
'No suitcase has more red sneakers than the first one.'

r1 >= r2 >= r3 >=r4 ... etc. ... (b)

Here note that n >=4. Also since we have to answer the question Is b1 < 0.25B ? let's try to make b1 maximum. This can be achieved when n=4, b1=b2=b3=0.27R and b4=0.19R ... (c) [Total must be 0.27+0.27+0.27+0.19=1]

From (a) and (b)
b1 <= b2 <=b3 <=b4 ... (d)

Combining all 4 equations we get b1=b2=b3 and b4 > b1: in order to maintain equal number of sneakers in each suitcase
Thus b1/(b1+b2+b3+b4)=b1/(3b1+b4) < 25% (Because b4 > b1).

So statement alone is SUFFICIENT.

S2::
'The first suitcase has between 23% and 27% of his blue sneakers.'

This is INSUFFICIENT as b1 can vary anything between 23 and 27 percent.

So ANS is A

Mbappé has two types of sneakers: red and blue. When packing for the World Cup, he puts equal number of sneakers in each of his suitcases. The first suitcase has 27% of all his red sneakers. Does the first suitcase have less than 25% of his blue sneakers ?


(1) No suitcase has more red sneakers than the first one.

(2) The first suitcase has between 23% and 27% of his blue sneakers.

Answer - C

Statement 1 - Not given anything about Blue sneakers
Statement 2 - Not given anything about Red sneakers

On combining we get info about both , blue and red sneakers

Answer: A

Mbappé has two types of sneakers: red and blue. When packing for the World Cup, he puts equal number of sneakers in each of his suitcases. The first suitcase has 27% of all his red sneakers. Does the first suitcase have less than 25% of his blue sneakers ?

(1) No suitcase has more red sneakers than the first one.
=> there will be minimum 4 suitcases with first suitcase having maximum 27% of red sneakers.
Since, all suitcases have equal number of sneakers => more percentage of blue sneakers will be available in rest of the suitcases compared to 1st
And, since we already know there will be minimum 4 suitcases, the first suitcase will have less than 25% of blue sneakers.
Statement 1 alone is sufficient.

(2) The first suitcase has between 23% and 27% of his blue sneakers.
No. of suitcases is unknown. It could be any no. > 2.
Since the no. of sneakers in each suitcase is equal, it can easily be arranged to have 24% blue sneakers or 26% blue sneakers in first case with remaining in other cases.
Insufficient.

Ans:C

(1) No suitcase has more red sneakers than the first one.

(2) The first suitcase has between 23% and 27% of his blue sneakers.