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C
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Difficulty:
65%
(hard)
Question Stats:
66% (01:51) correct
34%
(01:36)
wrong
based on 187
sessions
History
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Time
Result
Not Attempted Yet
At a customer support center, 7 agents worked a particular evening shift. Exactly 28 customer tickets were assigned during the shift to the agents, and each ticket was assigned to exactly one agent. Did each agent receive at least 1 ticket assignment?
(1) Each agent was assigned a different number of tickets.
(2) The agent who was assigned the most tickets was assigned 7 tickets.
I31-14
(1) Each agent was assigned a different number of tickets.
(2) The agent who was assigned the most tickets was assigned 7 tickets.
I31-14
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GMAT Club Official Explanation:
At a customer support center, 7 agents worked a particular evening shift. Exactly 28 customer tickets were assigned during the shift to the agents, and each ticket was assigned to exactly one agent. Did each agent receive at least 1 ticket assignment?
(1) Each agent was assigned a different number of tickets.
If the agents received different numbers of tickets, one possible distribution is {0, 1, 2, 3, 4, 5, 13}, which sums to 28 and has all counts distinct. In this case, one agent received 0 tickets. Another valid distribution is {1, 2, 3, 4, 5, 6, 7}. In this case, all agents received at least 1 ticket. Not sufficient.
(2) The agent who was assigned the most tickets was assigned 7 tickets.
We know the maximum is 7, but we do not know the remaining distribution of the 21 other tickets. It is possible that all other agents received at least 1 ticket (for example, {7, 5, 4, 4, 4, 2, 2}), and it is also possible that one agent received 0 tickets (for example, {7, 6, 6, 4, 3, 2, 0}). Not sufficient.
(1)+(2):
From (2), the highest ticket count is 7.
From (1), all 7 ticket counts must be different.
If we assume that 0 tickets is allowed, the largest total we could form using seven distinct nonnegative integers with a maximum of 7 is:
{7, 6, 5, 4, 3, 2, 0}
This sums to 27, which is less than the required total of 28. Therefore, 0 cannot be one of the ticket counts. So the only possible set of seven distinct ticket counts with maximum 7 that sums to 28 is:
{7, 6, 5, 4, 3, 2, 1}
In this distribution, every agent receives at least 1 ticket. Sufficient.
Answer: C.
General Discussion
Archit3110
23 Dec 2025, 09:41
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At a customer support center, 7 agents worked a particular evening shift. Exactly 28 customer tickets were assigned during the shift to the agents, and each ticket was assigned to exactly one agent. Did each agent receive at least 1 ticket assignment?
(1) Each agent was assigned a different number of tickets.
(2) The agent who was assigned the most tickets was assigned 7 tickets.
total agents are 7
tickets are 28
did each agent receive at least 1 ticket
#1
Each agent was assigned a different number of tickets
it could 0, 2,3,4,5,1,13
or
1,2,3,4,5,6,7
insufficient
#2
agent with most tickets was 7 tickets
case 1 ;
1,2,3,4,5,6,7
case 2 :
0,3,3,4,5,6,7
insufficient
from 1 &2
we can say
all agents got at least 1 ticket
1,2,3,4,5,6,7
sufficient
OPTION C
(1) Each agent was assigned a different number of tickets.
(2) The agent who was assigned the most tickets was assigned 7 tickets.
total agents are 7
tickets are 28
did each agent receive at least 1 ticket
#1
Each agent was assigned a different number of tickets
it could 0, 2,3,4,5,1,13
or
1,2,3,4,5,6,7
insufficient
#2
agent with most tickets was 7 tickets
case 1 ;
1,2,3,4,5,6,7
case 2 :
0,3,3,4,5,6,7
insufficient
from 1 &2
we can say
all agents got at least 1 ticket
1,2,3,4,5,6,7
sufficient
OPTION C
