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27 Apr 2026, 19:00
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
70% (02:03) correct
30%
(02:28)
wrong
based on 79
sessions
History
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Time
Result
Not Attempted Yet
At a museum, all visitors in a certain tour group were either students or teachers. Some visitors rented audio guides, and the rest did not. If 12 students did not rent audio guides, whereas 24 teachers did rent audio guides, how many teachers were in the tour group?
(1) The number of students who rented audio guides was twice the number of teachers who did not rent audio guides.
(2) The total number of visitors in the group who rented audio guides was twice the total number of visitors who did not rent audio guides.
(1) The number of students who rented audio guides was twice the number of teachers who did not rent audio guides.
(2) The total number of visitors in the group who rented audio guides was twice the total number of visitors who did not rent audio guides.
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M47-130
01 May 2026, 01:30
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GMAT Club Official Solution:
At a museum, all visitors in a certain tour group were either students or teachers. Some visitors rented audio guides, and the rest did not. If 12 students did not rent audio guides, whereas 24 teachers did rent audio guides, how many teachers were in the tour group?
Let:
students who rented audio guides = x
teachers who did not rent = y
The question asks for the total number of teachers: 24 + y.
(1) The number of students who rented audio guides was twice the number of teachers who did not rent audio guides.
This implies x = 2
But we still do not know y, so we cannot find 24 + y. Not sufficient.
(2) The total number of visitors in the group who rented audio guides was twice the total number of visitors who did not rent audio guides.
This implies:
x + 24 = 2(12 + y)
x = 2y
This is exactly the same information as in statement (1). So we still cannot find y, and therefore we cannot find the total number of teachers.
Not sufficient.
(1) + (2) Together, the two statements still give only x = 2y. So the total number of teachers, 24 + y, still cannot be determined. Not sufficient.
Answer: E.
GMAT-Club-Forum-2ix8pn64.png [ 9.37 KiB | Viewed 475 times ]
GMAT-Club-Forum-61etxf0r.png [ 9.75 KiB | Viewed 471 times ]
GMAT-Club-Forum-bimx98qp.png [ 11.32 KiB | Viewed 445 times ]
At a museum, all visitors in a certain tour group were either students or teachers. Some visitors rented audio guides, and the rest did not. If 12 students did not rent audio guides, whereas 24 teachers did rent audio guides, how many teachers were in the tour group?
Let:
students who rented audio guides = x
teachers who did not rent = y
The question asks for the total number of teachers: 24 + y.
(1) The number of students who rented audio guides was twice the number of teachers who did not rent audio guides.
This implies x = 2
But we still do not know y, so we cannot find 24 + y. Not sufficient.
(2) The total number of visitors in the group who rented audio guides was twice the total number of visitors who did not rent audio guides.
This implies:
x + 24 = 2(12 + y)
x = 2y
This is exactly the same information as in statement (1). So we still cannot find y, and therefore we cannot find the total number of teachers.
Not sufficient.
(1) + (2) Together, the two statements still give only x = 2y. So the total number of teachers, 24 + y, still cannot be determined. Not sufficient.
Answer: E.
Attachment:
GMAT-Club-Forum-2ix8pn64.png [ 9.37 KiB | Viewed 475 times ]
Attachment:
GMAT-Club-Forum-61etxf0r.png [ 9.75 KiB | Viewed 471 times ]
Attachment:
GMAT-Club-Forum-bimx98qp.png [ 11.32 KiB | Viewed 445 times ]
General Discussion
27 Apr 2026, 23:05
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- Sy = students who rented
- Tn = teachers who did not rent
- Given: 12 students did not rent, 24 teachers rented
- We need to find: 24 + Tn
Statement 1
Sy = 2Tn
Two unknowns, one equation. Not sufficient
Statement 2
(Sy + 24) = 2(12 + Tn)
Sy + 24 = 24 + 2Tn
Sy = 2Tn
Same equation as Statement 1. Not sufficient
Both Together
Both statements give Sy = 2Tn. They are identical, so combining them adds nothing new. Still two unknowns, one equation.
Not sufficient
Answer E
- Tn = teachers who did not rent
- Given: 12 students did not rent, 24 teachers rented
- We need to find: 24 + Tn
Statement 1
Sy = 2Tn
Two unknowns, one equation. Not sufficient
Statement 2
(Sy + 24) = 2(12 + Tn)
Sy + 24 = 24 + 2Tn
Sy = 2Tn
Same equation as Statement 1. Not sufficient
Both Together
Both statements give Sy = 2Tn. They are identical, so combining them adds nothing new. Still two unknowns, one equation.
Not sufficient
Answer E
27 Apr 2026, 23:30
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The contingency matrix will be helpful in this case.
Statement 1:
Once drawn out we see that we don't know the total number of people of any single category or the total.
Hence we cannot find the variable asked and thus find total number of teachers.
INSUFFICIENT.
Statement 2:
Again this is also not enough.
INSUFFICIENT.
Combining thw two:
2nd statement is actually the same as first statement and adds nothing actually.
From 1st statement we get Rent = 24+2x and No Rent = 12+x.
Rent = 2[No Rent] is inferred from 1st statement itself.
INSUFFICIENT.
Answer: Option E
Statement 1:
Once drawn out we see that we don't know the total number of people of any single category or the total.
Hence we cannot find the variable asked and thus find total number of teachers.
INSUFFICIENT.
Statement 2:
Again this is also not enough.
INSUFFICIENT.
Combining thw two:
2nd statement is actually the same as first statement and adds nothing actually.
From 1st statement we get Rent = 24+2x and No Rent = 12+x.
Rent = 2[No Rent] is inferred from 1st statement itself.
INSUFFICIENT.
Answer: Option E
Bunuel
