At a museum, all visitors in a certain tour group were either students

Question

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.

Bunuel · Accepted Answer

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.

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thisisakr · Answer

- 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

Adit_ · Answer

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  is inferred from 1st statement itself.
INSUFFICIENT.

Answer:  Option E

BongBideshini · Answer

Rented 
 Not Rented 
 Total 
 
  Students 
 a 
 12 
 a+12 
 
  Teachers 
 24 
 b 
 24+b 
 
  Total 
 a+24 
 12+b

Statement (1) 
a = 2b
Table becomes:
    
 Rented 
 Not Rented 
 
  Students 
 2b 
 12 
 
  Teachers 
 24 
 b

Need teachers = 24 + b
But b is unknown.
 Not sufficient.

Statement (2) 
Total rented was twice the total not rented.
Rented total = a + 24
Not rented total = 12 + b
So:
a + 24 = 2(12 + b)
a + 24 = 24 + 2b
a = 2b
Same equation as Statement (1)
 Not sufficient.

Ans E.  Statements (1) and (2) together are not sufficient.

At a museum, all visitors in a certain tour group were either students

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GMAT Data Sufficiency (DS) Questions

At a museum, all visitors in a certain tour group were either students

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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