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D
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Difficulty:
95%
(hard)
Question Stats:
38% (02:21) correct
62%
(02:24)
wrong
based on 91
sessions
History
Date
Time
Result
Not Attempted Yet
At a professional training conference, 44 attendees signed up for the data analytics workshop and 31 signed up for the public speaking workshop. Were at least 60 attendees at the conference?
(1) At least 16 attendees signed up for neither workshop.
(2) 1/4 of the attendees signed up for both workshops.
(1) At least 16 attendees signed up for neither workshop.
(2) 1/4 of the attendees signed up for both workshops.
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02 Apr 2026, 02:30
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GMAT Club Official Solution:
At a professional training conference, 44 attendees signed up for the data analytics workshop and 31 signed up for the public speaking workshop. Were at least 60 attendees at the conference?
(1) At least 16 attendees signed up for neither workshop.
{Total} = {data analytics} + {public speaking} - {both} + {neither}
{Total} = 44 + 31 - {both} + {neither}
{Total} = 75 - {both} + {neither}
Since the greatest possible value of {both} is 31, so 75 - {both} is at least 44 and since {neither} is at least 16, we get:
{Total} = 75 - {both} + {neither} ≥ 60
So the total number of attendees must be at least 60.
Sufficient.
(2) 1/4 of the attendees signed up for both workshops.
This gives:
{Total} = {data analytics} + {public speaking} - {both} + {neither}
{Total} = 44 + 31 - {Total}/4 + {neither}
5/4 * {Total} = 75 + {neither}
Multiply by 4/5:
{Total} = 60 + 4/5 * {neither}
Since {neither} cannot be negative, the total number of attendees must be at least 60.
Sufficient.
Answer: D
At a professional training conference, 44 attendees signed up for the data analytics workshop and 31 signed up for the public speaking workshop. Were at least 60 attendees at the conference?
(1) At least 16 attendees signed up for neither workshop.
{Total} = {data analytics} + {public speaking} - {both} + {neither}
{Total} = 44 + 31 - {both} + {neither}
{Total} = 75 - {both} + {neither}
Since the greatest possible value of {both} is 31, so 75 - {both} is at least 44 and since {neither} is at least 16, we get:
{Total} = 75 - {both} + {neither} ≥ 60
So the total number of attendees must be at least 60.
Sufficient.
(2) 1/4 of the attendees signed up for both workshops.
This gives:
{Total} = {data analytics} + {public speaking} - {both} + {neither}
{Total} = 44 + 31 - {Total}/4 + {neither}
5/4 * {Total} = 75 + {neither}
Multiply by 4/5:
{Total} = 60 + 4/5 * {neither}
Since {neither} cannot be negative, the total number of attendees must be at least 60.
Sufficient.
Answer: D
General Discussion
29 Mar 2026, 22:23
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Statement 1:
The minimum number of ppl attending the workshop not including neither is 44.
Now 16 ppl add under neither making 44+16=60. Hence atleast 60.
SUFFICIENT.
Statement 2:
1/4[Total] = Both
Total = 44+31-Both.
[Now it is very important to assume here that neither is not part of it and not to get confused with statement 1. We are treating this statement as a separate statement and seeing if D is an answer.]
Total = 75-Both.
Substituting back:
1/4[75-Both] = Both.
Both = 15.
Thus Total = 75-15 = 60. Atleast 60
SUFFICIENT.
Answer: Option D
The minimum number of ppl attending the workshop not including neither is 44.
Now 16 ppl add under neither making 44+16=60. Hence atleast 60.
SUFFICIENT.
Statement 2:
1/4[Total] = Both
Total = 44+31-Both.
[Now it is very important to assume here that neither is not part of it and not to get confused with statement 1. We are treating this statement as a separate statement and seeing if D is an answer.]
Total = 75-Both.
Substituting back:
1/4[75-Both] = Both.
Both = 15.
Thus Total = 75-15 = 60. Atleast 60
SUFFICIENT.
Answer: Option D
Bunuel
