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

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goal is to find if R > 62.5 %

stm1 means P+R <= 45% so in a max case, R can not exceed 45
stm2 means P+M >40% so in a max case, R can not exceed 60

ans D

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Let R, P and M stand for the probability that the participant is in the Reception group, Planning group or Materials group respectively.

The question is basically asking us is R > 0.625?

St 1 -
Not in Materials group means he is in either Reception or Planning group
Thus, P or R < 0.45
in "or" situation, we add the probabilities, hence R has to be < 0.45
St 1 - sufficient

St 2 -
Not in Reading group means he is in either Planning or Material group
Thus, P or M > 0.4
therefore R < 0.6
St 2 - sufficient

Ans - D

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Answer is option B

Let’s take each statement

Statement 1 only tells the probability for materials group. It only tells less than a certain percentage and does not help in determining the actual probability

Statement 2 is alone sufficient. 5/8 means 62.5%. . If participants not in reception are more than 40% then the probability that the participants are more than 5/8 is definitely not possible.

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Statement 1 gives us combined probability of participants in reception and planning is 9/50 which is less than 5/8 hence we get answer .
statement 2 gives us the probability of participants in reception to be 2/ 5 which is less than 5/8 hence we get out answer. \
Both statements alone are sufficient.

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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Question if R/Total > 5/8 (0.62)

(1) Not M/ total < 0.45 This means that P+R/Total < 0.45 - Thus surely, R < 0.45<0.6
Hence, sufficient.

(2) P+M/Total > 0.4 Now, P+M can be 0.42, this means R can be 1-0.42= 0.58 < 0.62
R is always going to be < 0.6
Hence, sufficient

Thus, Ans D

Bunuel

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P, R, M
Q asking if R/Total > 5/8 or if R/Total > 62.5%

Stmt 1: P+R % is <45% so P alone cannot be > 62.5% - SUFF
Stmt 2: P+M % is > 40%. Even if it is exactly 40%, R cannot be > 60%, so cannot be > 61.5% - SUFF

D)

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There are three groups, denoted as A, R, and M.

The size of each group isn't given.

We're asked to find whether the prob of selecting 1 from these groups is R > 5/8 (or 62.5%)

Consider
1. P(not in M) < 45%: means that P(in A and R) < 45%.
- Then, it couldn't be possible that P(R) will greater than 62.5%.
- We can conclude from here
- This is enough.

2. P(not in R) > 40%: means that P(in R) ≤ 40%
- Then, again, P(R) won't greater than 62.5%
- This is enough

Taken together, choice D where either one is sufficient.

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Not given much info but asked if P_selection_grp > 5/8 => 62.5%
So if we get the info on P_reception grp for participation or non participation we can answer the above

S2 => checking S2 as it takes about reception grp - says non participant probability > 40% => participants < 60% - sufficient
S1 => materials grp < 45 % now 43 is also less than and 10 is also less than plus we don't know anout planning grp so not sufficient

Ans - B S2 alone is sufficient

Bunuel

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Let the variables be P, R & M
To find: R > 0.625

1) not M < 0.45
P + R < 0.45
Therefore, R < 0.625
Sufficient

2) not R > 0.40
R < 0.60
Sufficient

Hence, D

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P(R)+P(P)+p(M)=1
Question asked, whether P(M)>5/8? ,i.e., P(M)>0.625?
It is an yes or no question. Did not ask the exact probability.

Considering Statement 1 alone,

1-P(M)<0.45
.: P(P) + P(R) <0.45,
.: P(R)<0.45 (Since probability values can not be negative)
.: P(R)<0.625
.: Statement 1 alone is sufficient.
.: We can eliminate option B,C & E. Left with optionA & D.

Considering Statement 2 alone,

1-P(R)>0.4
.: 0.6>P(R)
.: P(R)<0.625
.: Statement 2 alone is sufficient.

.: D is correct answer. Both statement alone is sufficient.

Bunuel

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Each participant is assigned to exactly one of the 3 groups - planning, reception or materials.
We have to figure whether the probability of picking someone from the reception is greater than 5/8.

Statement 1 - It suggests that the probability of the selected participant being not in the material group is less than 45%. Therefore, implementing the complement rule, the probability that the selected participant will be from the material's group will be greater than 55%. If that is the case, it is not possible to have a probability of greater than 5/8 (62.5%) for the selected participant to be from reception group. Sufficient.

Statement 2 - It states that the probability of the selected participant not being from the reception group is greater than 40%. Therefore, the probability of the selected participant to be from the reception group would be a maximum of 59.99999% or less than 60%. So we clearly know that it can't be greater than 62.5% or 5/8. Hence, sufficient.

Since each of the statements is sufficient to answer the question, the answer is D.

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Each participant is assigned to exactly one group of three, which means there will be no overlap between groups.
Let us reframe 5/8 in decimals, i.e., 0.625.
We have to determine if p(Reception)>0.625 or not.

(1) p(not Materals)=p(Planning or Reception)=p(Planning)+p(Reception)<0.45
This means p(Reception) cannot be greater than 0.625. Sufficient.

(2) p(not Reception)=p(Planning or Materials)>0.4
This means p(Reception)<0.6. Sufficient.

(D)

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Bunuel

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The questions asks whether P(R), which equals, R/(P+R+M) > 5/8

Statement 1 tells us that the probability of selecting either a planning or reception participant is less than 45%. Thus, P(R) cannot be greater than 45%, which is less than 5/8. Sufficient.
Statement 2 tell us that the probability the participant is in the reception group is less than 60%. Thus, P(R) is less than 5/8. Sufficient.

Answer is D.

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Let r be the probability that a participant is in the reception group
We need to determine whether

r>5/8=0.625

Statement 1:

Let m be the probability of the materials group
then 1-m<0.45
m>0.55

since p+r=1-m<0.45

We know that r<0.45, which is certainly less than 0.625

Statement (1) alone is sufficient

Statement 2

1-r>0.4
r<0.6

r<0.6<0.625

Statement (2)alone is sufficient

each statemnent alone is sufficient to caluclate the answer

Bunuel

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Bunuel

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My answer is D. P(reception) > 5/8? 5/8 = 62.5%

Statement 1) P(Not materials) < 45%
=> P(reception) + P(planning) < 45% (because these two are non mutually exclusive, we dont have to worry about subtracting overlaps).
=> P(reception) is NOT > 5/8 (because P(planning) is between 0 and 1, and the sum of them is <45%, meaning P(reception) is individually already less than 45% and 5/8 as a result)
S1 is Sufficient

Statement 2) P(Not reception) > 40%
=> 1 - P(reception) > 40%
=> P(reception) < 60% and < 5/8. Sufficient

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08 Jul 2026, 22:35

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there are three groups.
planning, reception, and materials.

each is assigned to exactly one on three.
find : P(participant is in reception group) > 5/8 ( or > 62.5%)

S-1
P (not in material group) <45/100
that means the person is in either other two group. and if that probability is less than 45%, then person in alone reception group cant be greater than 62.5%

sufficient.

S-2
P(not in reception group ) > 2/5
that means probability of person in either of other two group is > 40% and person in reception group is less than 40%.

so if the Probability of person is in reception group is less than 40%, its sufficient to ans the que.

each statement alone is sufficient.

Choice D

Bunuel

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There are 3 groups and each group contains a specific number of pople.
The question asks whether the probability of number of people in the Reception group is more than 5/ 8 = 62.5% or not. It implies that if members in Reception group is greater than 62.5%, all other groups combined will have 100-62.5 = 37.5% members. Moreover, if the Reception group is combined with any other group total probability will be more than 62.5%.

Statement 1 : The probability that the selected participants is not in the materials group is less than 45%. It means that other two groups' (Planning and reception) probability is <45%. Which is not true. It should be more than 62.5%. Hence, we can say that probability that selected participant is in the reception group is not greater than 5/8.

Statement 2 : The probability that the selected participant is not in the reception group is greater than 40%. As per this statement other two groups (Planning and material) is having greater than 40% probability. If this is the case than Reception group can not have 5/8 (i.e. 62.5% probability). Hence, we can conclude that the probability of selected participant is in the reception group is not greater than 5/8.

Bunuel

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5/8 = 62.5%. Therefore the question can be rephrased to: Is P(Reception) > 62.5%?

Now lets look at the statements
Statement 1: P(Not Materials Group) < 45% => P(Planning or Reception) < 45%. Therefore P(Reception) cannot be > 62.5%. This is a definitive NO answer
Statement 2: P(Not Reception Group) > 40% => P(Reception) < 60%. Therefore P(Reception) cannot be > 62.5%. This is definitive NO answer

Both statements gives us a definitive answer. Therefore the correct option is D

Bunuel

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We have three groups, planning (P), reception (R), and materials (M). Their probabilities add up to 1:

P + R + M = 1
The question asks: Is Re greater than 5/8 (which is 0.625)?

Statement (1): P(not materials) is less than 45%.
If someone is not in materials, they must be in either planning or reception. This statement tells us:
P + R < 0.45

Since P is a probability, it is at least 0. This means R must be even smaller than the combined total:
R < 0.45

And 0.45 is well below 0.625. So we can confidently say: R is not greater than 5/8. That’s a clear, definite answer: "No."
So Statement (1) is sufficient.

Statement (2): P(not reception) is greater than 40%.
If someone is not in reception, they are in planning or materials. This tells us:
1 - R > 0.40

Rearranging that:
R < 0.60

Once again, 0.60 is comfortably below 0.625. So we also get a clean, definite "No". Re is not greater than 5/8.
Therefore, Statement (2) is also sufficient on its own.

Putting it together:
Both statements, completely independently, allow us to answer the question with certainty (the answer being "No" in both cases). Since each one stands alone without needing the other, the answer is:
D — Each statement alone is sufficient.

The trap here is that both statements feel incomplete because they give inequalities instead of exact numbers, but that's all you need. The question is a yes/no question, not a "find the value" question. Once you can rule out R > 5/8 with certainty, you're finished, even if you don’t know R's exact value.

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Statement 1) Tells us directly that the probability that particpant is not in the materials group is less than 45%

Therefore ans is no
Same with statement 2

Therefore each statement gives us ans. D

Bunuel

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