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07 Jun 2026, 14:45
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C
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Difficulty:
65%
(hard)
Question Stats:
66% (02:36) correct
34%
(02:23)
wrong
based on 100
sessions
History
Date
Time
Result
Not Attempted Yet
At a professional conference, two optional events were offered: a product demo and a networking breakfast. If 70% of the attendees registered for the product demo and 25% of the attendees registered for both events, how many attendees registered for neither event?
(1) 30 attendees registered for the networking breakfast but not for the product demo.
(2) 150 attendees did not register for the networking breakfast.
(A) Statement 1 alone is sufficient, but statement 2 alone is not.
(B) Statement 2 alone is sufficient, but statement 1 alone is not.
(C) Both statements together are sufficient, but neither alone is sufficient.
(D) Each statement alone is sufficient.
(E) Neither statement is sufficient, even when combined.
(1) 30 attendees registered for the networking breakfast but not for the product demo.
(2) 150 attendees did not register for the networking breakfast.
(A) Statement 1 alone is sufficient, but statement 2 alone is not.
(B) Statement 2 alone is sufficient, but statement 1 alone is not.
(C) Both statements together are sufficient, but neither alone is sufficient.
(D) Each statement alone is sufficient.
(E) Neither statement is sufficient, even when combined.
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M47-187
12 Jun 2026, 01:30
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GMAT Club Official Solution:
At a professional conference, two optional events were offered: a product demo and a networking breakfast. If 70% of the attendees registered for the product demo and 25% of the attendees registered for both events, how many attendees registered for neither event?
{Total} = {Demo only} + {Breakfast only} + {Both} + {Neither}
Also:
{Demo} = {Demo only} + {Both}
So:
{Demo only} = {Demo} - {Both} = 0.70 * {Total} - 0.25 * {Total} = 0.45 * {Total}
The question asks for {Neither}.
(1) 30 attendees registered for the networking breakfast but not for the product demo.
So:
{Breakfast only} = 30
Using the total formula:
{Total} = {Demo only} + {Breakfast only} + {Both} + {Neither}
{Total} = 0.45 * {Total} + 30 + 0.25 * {Total} + {Neither}
{Neither} = 0.30 * {Total} - 30
But {Total} is not known.
Not sufficient.
(2) 150 attendees did not register for the networking breakfast.
Those attendees are in {Demo only} and {Neither}. So:
{Demo only} + {Neither} = 150
0.45 * {Total} + {Neither} = 150
But {Total} is not known.
Not sufficient.
(1)+(2) From statement (1):
{Neither} = 0.30 * {Total} - 30
From statement (2):
0.45 * {Total} + {Neither} = 150
Substitute:
0.45 * {Total} + 0.30 * {Total} - 30 = 150
0.75 * {Total} = 180
{Total} = 240
Therefore:
{Neither} = 0.30 * 240 - 30 = 72 - 30 = 42
Sufficient.
Answer: C.
At a professional conference, two optional events were offered: a product demo and a networking breakfast. If 70% of the attendees registered for the product demo and 25% of the attendees registered for both events, how many attendees registered for neither event?
{Total} = {Demo only} + {Breakfast only} + {Both} + {Neither}
Also:
{Demo} = {Demo only} + {Both}
So:
{Demo only} = {Demo} - {Both} = 0.70 * {Total} - 0.25 * {Total} = 0.45 * {Total}
The question asks for {Neither}.
(1) 30 attendees registered for the networking breakfast but not for the product demo.
So:
{Breakfast only} = 30
Using the total formula:
{Total} = {Demo only} + {Breakfast only} + {Both} + {Neither}
{Total} = 0.45 * {Total} + 30 + 0.25 * {Total} + {Neither}
{Neither} = 0.30 * {Total} - 30
But {Total} is not known.
Not sufficient.
(2) 150 attendees did not register for the networking breakfast.
Those attendees are in {Demo only} and {Neither}. So:
{Demo only} + {Neither} = 150
0.45 * {Total} + {Neither} = 150
But {Total} is not known.
Not sufficient.
(1)+(2) From statement (1):
{Neither} = 0.30 * {Total} - 30
From statement (2):
0.45 * {Total} + {Neither} = 150
Substitute:
0.45 * {Total} + 0.30 * {Total} - 30 = 150
0.75 * {Total} = 180
{Total} = 240
Therefore:
{Neither} = 0.30 * 240 - 30 = 72 - 30 = 42
Sufficient.
Answer: C.
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