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GMAT Club World Cup 2026 (Day 3): A community center is organizing a

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JohnByro

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09 Jul 2026, 05:41

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imo D
Since in 1 its given that p(m')<0.45 so P+R<0.45 so r cannot be greater than 5/8=0.625 sufficient
in 2 P(r')>0.4 p+m>0.4 p+m+r=1 so 1-r>0.4 r<0.6 sufficient that its <0.625

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09 Jul 2026, 05:42

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Each participant is assigned to exactly one group and we are to find the probability of a randomly selected participant is in reception group greater that 5/8 i.e 62.5%
Now,
statement 1 - P (not in material group) < 45%
So if not material group then either planning or reception or both is less than 45%
So probability > 62.5% No --> Sufficient

statement 2 - P (not in reception group) > 40%
So in reception group would be <= 40% so again No --> Sufficient

Option D

Bunuel

A community center is organizing a weekend workshop. Each participant is assigned to exactly one of three groups: planning, reception, or materials. If one participant is selected at random from all the participants, is the probability that the selected participant is in the reception group greater than 5/8?

(1) The probability that the selected participant is not in the materials group is less than 45%.

(2) The probability that the selected participant is not in the reception group is greater than 40%.

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09 Jul 2026, 05:45

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P = planning
R = reception
M = materials

p(R) > 5/8 = 62.5% ?

p(P) + p(R) + p(M) = 100%

(1)
p(not M) = p(P) + p(R) < 45%

If p(P) + p(R) < 45% then p(R) < 45% and p(R) is not greater than 62.5%.
The answer is no.

Sufficient

(2)
p(not R) = p(P) + p(M) > 40%

As p(P) + p(R) + p(M) = 100% then p(R) < 60% that is not greater than 62.5%.
The answer is no.

Sufficient

IMO D

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09 Jul 2026, 05:46

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P(R)>5/8 which is we want to know if P(R)>.625

1. P(NOT M) = P(P OR R) =1-P(M) =1-M/T< .45 that gives M/T>0.55 If P(m) is greater than .55 then no way is the probability of R greater than .625 . Ans is NO but S-1 IS SUFFICIENT

2. P(NOT R)>0.40 That means P(R)<0.60 again it cannot be greater than .625 therefore Ans is NO and S2 IS SUFFICIENT

ANS IS D

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Bunuel

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Note: A really good question to understand, as I've seen tougher/higher level question being based similarly

Understanding the question:

Each participant is assigned to exactly one of the three groups
One participant is selected at random from ALL

Ask:
The probability that the selected participant is from the reception group is >5/8

Solving:
P(Reception) > 5/8 or 62.5%

Statement 1:
The probability that a selected participant is not in the materials group is less than 45%

Therefore, the probability that a selected participant is in the materials group is (100-45)% more than 55%
Now, understand that the probability of the other 2 groups combined is 45%
Even if all but 1 of them are in the reception group, the max probability can be 44.9999%, still way less than the asked
Therefore, statement 1 is sufficient

Statement 2:
The probability that a selected participant is not in the reception group is greater than 40%
Similarly, the counterargument will be that the probability that a selected participant is in the reception group is less than 60%

This makes Statement 2 sufficient to answer as well.

Therefore Option D

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09 Jul 2026, 05:59

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planning
reception
materials

probability(reception) > 5/8 = 62.5% ?

(1)
probability(not in materials) = probability(planning) + probability(reception) < 45%

All are positive numbers so probability(reception) < 45% and probability(reception) is not greater than 62.5%.

Condition (1) is sufficient

(2)
probability(not in reception) > 40%

probability(not in reception) + probability(reception) = 100%

probability(reception) < 60% and probability(reception) is not greater than 62.5%.

Condition (2) is sufficient

The answer is D

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09 Jul 2026, 06:06

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Assign Variables : p r m

Stem :
Is r/(p +r +m) > 5/8 ; Simplify

Is r/ (p+m) >5/3

S1

(p+r) / (p+r+m) <45/100; simplify

m/(p+r) > 9/11
NS

S2

(p+m)/ (p+r+m)>40/100; simplify

r/(p+m)<3/2

Sufficient

Answer : B

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P = probability of Planning
M = Probability of Materials
R = Probability of Reception

Since exactly 1 group and the probability can't be greater than 1
So, P + R + M = 1
Need to validate: R > 5/8 = 0.625?
Option1: P + R < 0.45
Since P >= 0
Therefore, R < 0.45
But, 0.45 < 0.625 ; R is less than 5/8
So, Option 1 is sufficient.

Option2: P + M > 0.40
R = 1 - (P + M )
Therfore, R< 0.60
again, 0.6 < 0.625; R is less than 5/8
So, Option 2 is sufficient.

Hence, both are sufficient independently.

Answer D is Correct.

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09 Jul 2026, 06:19

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Let Planning, Reception and Materials be PRM
(1) says not in M, so its P+R < 45%
(2) says not in R, therefore P+M > 40%

If we try to manipulate the equations, we don't get a definite range for R,
so I assume we cannot determine it from the above two statements.

My answer is E.

Bunuel

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09 Jul 2026, 06:28

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IMO : B
let the no. of people in Planning = P
Reception count = R
Material = M
Now total no of people = P+R+M
we need to find/ check if R/P+R+M >5/8
now taking option 1 :
P+R/P+R+M >9/20
which will give nothing more that M/P+R+M <11/20
we cant conclude anything about R prob
now option 2:
P+M/P+R+M >2/5 therefore R/P+R+M <3/5
on comparing 3/5 with 5/8 we can see that 5/8 is greater and since prob of R is already less that 3/5 then it will definately be less than 5/8. hence B

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09 Jul 2026, 06:39

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Let R, P, M be the number of participants assigned to reception, planning, materials respectively.

To determine if P(R) > 5/8 which is 62.5%

Analysing statements
I
P(P) + P(R) < 45%
Therefore P(R) < 45%
So P(R) < 62.5%
The answer is a definite no.
Statement I is sufficient

II
1 - P(R) > 40%
P(R) < 60%
So, 60% < 62.5%
This is also definite.
So statement II is sufficient

Answer is D

Bunuel

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09 Jul 2026, 06:40

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1. Not materials<45
reception+planning<45
reception < 45<5/8 or 62.5

Hence Definite No.
Statement is sufficient

2. Not Reception > 40
reception<60
and 60<62.5
Hence Definite No.
Statement is suffiecient

Answer D

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09 Jul 2026, 06:40

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We know that,
There are 3 groups -> planning, reception and materials
Each participant is assigned to exactly one of the 3 groups
So, let,
Probability of participant in planning group = P
Probability of participant in reception group = R
Probability of participant in materials group = M

=> P + R + M = 1

We need to know if Probability of being in reception group is greater than 5/8
Lets have a look at the given statements

Statement 1 -> Probability that selected participant is not in material group is less than 45%

=> P + R < 0.45

Since P has to be greater than 0 and less than 0.45 and same goes for R
We can straight up say that, R is not greater than 0.625

Statement (1) is sufficient

Statement (2) -> Probability that selected participant is not in the reception group is greater than 40%

=> P + M > 0.4
=> 1 - R > 0.4
=> R < 0.6

=> R cannot be greater than 0.625

=> Statement(2) is sufficient

=> D. Each statement alone is sufficient

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09 Jul 2026, 07:35

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We need to find P (perception) > 5/8 (which is 0.625 or 62.5%) ?

Statement 1 : P < 45%
if someone is not material they are either in planning or reception. so :
P(planning)+ P (reception) <45%
since P(reception)is just part of the sum, P (reception) must be less than 45% too
is 45%> 5/8 (62.5)
so P(reception) isnt greater than 5/8
Sufficent

Statement 2 : P (not reception) > 40%
if P(not reception) > 40% means : P (reception) < 60%
is 60% > 5/8
so P(not reception) is not greater than 5/8
Sufficent

Answer: D

Bunuel

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09 Jul 2026, 07:50

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Option D is the answer

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IMG_5545.jpeg [ 163.95 KiB | Viewed 121 times ]

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Ans Choice D: As each participant is assigned to 1 of 3 groups, there is no intersection between any 2 groups. Therefore, sum of their probabilities = 1 i.e. P + R + M = 1 where P, R, M denotes their respective probabilities. Ques stem asks if R>5/8=0.625 ??
Stmt 1: 1-M < 0.45 ; P + R < 0.45.
This gives R<0.45<0.625
Sufficient
Stmt2: 1-R > 0.4 ; R<0.6<0.625
Sufficient

Bunuel

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09 Jul 2026, 07:51

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The question asked
is P (R) is > 5/8?
meaning R > 5 and P+M < 3

(1)
P (~M) < 45/100, P (~M) < 9/20
meaning
M > 11 out of 20
P+R < 9 out of 20
meaning

Sufficient. because here M > R (more dominant M than R)

(2)
P (~R) > 40%
Meaning
P(R) < 60% or 60/100 or 3/5
Compare to data P(R) > 5/8
3/5 < 5/8
insuffiecient.

So, answer is A only statement 1) sufficient.

Bunuel

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why cant I see the options?

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Bunuel

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Subliminal01

why cant I see the options?

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This is a data sufficiency question. Options for DS questions are always the same and usually omitted on the site.

The data sufficiency problem consists of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements, plus your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of the word counterclockwise), you must indicate whether—

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
D. EACH statement ALONE is sufficient to answer the question asked.
E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

Hope this helps.