Teacher to Student ratio

[kobel51]

If the ratio of the number of teachers to the number of students is the same in School District M and School District P, what is the ratio of the number of students in School District M to the number of students in School District P?

1) There are 10,000 more students in School District M than there are in School District P.

2) The ratio of the number of teachers to the number of students in School District M is 1 to 20.

[Patrick_GMATFix]

To get sufficiency, we need the ratio of total student & teacher populations from one district to the next. For instance if we learn that District M has 10 times the population of district P, we'll know that M has 10 times as many students and 10 times as many teachers.

The full solution below is taken from the GMATFix App.



-Patrick

[Bill@VeritasPrep]

If the ratio of the number of teachers to the number of students is the same in School District M and School District P, what is the ratio of the number of students in School District M to the number of students in School District P?

1) There are 10,000 more students in School District M than there are in School District P.

2) The ratio of the number of teachers to the number of students in School District M is 1 to 20.

From the stem: TM/SM = TP/SP, and we need SM/SP

1) SM = SP + 10,000, but that leaves many possibilities. Insufficient.

2) TM/SM = 1/20 (which also equals TP/SP). Still insufficient; TP and SP could be equal, or one or the other could be greater.

Together: Still insufficient. You could have TM= 100, SM = 2,000 and TP=600, SP=12,000, which would give you SM/SP = 2000/12000 = 1/6. You could also have TM=1,000, SM=20,000 and TP=1500, SP = 30,000, giving you SM/SP = 20,000/30,000 = 2/3. Still insufficient.

[GMATGuruNY]

If the ratio of the number of teachers to the number of
students is the same in School District M and School
District P, what is the ratio of the number of students
in School District M to the number of students in
School District P ?

(1) There are 10,000 more students in School
District M than there are in School District P.

(2) The ratio of the number of teachers to the
number of students in School District M is
1 to 20.

Each district has the same teacher-student ratio.
Statement 2 implies that, in each district, the number of teachers is 1/20 of the number of students.
The following cases satisfy BOTH statements.

CASE 1:

_________________P_____________M

Students_______2000________12000

Teachers_______100___________600

Here, the student ratio = 2000:12000 = 1:6.

CASE 2:

__________________P_____________M

Students_______10000________20000

Teachers________500__________1000

Here, the student ratio = 10000:20000 = 1:2.

Since different student ratios are possible, the two statements combined are INSUFFICIENT.

The correct answer is E.

[jeph86]

because the prompt says that the ration for each district are equal, does that mean the ration student to student should be 1:1.

DS is still confusing me!!

[[email protected]]

Hi jeph86,

The ONLY way that a ratio would be 1:1 would be if there were the same NUMBER of teachers and NUMBER of students. That is NOT what prompt states - it states that the two RATIOS (for the two Districts) is the same.

For example, if the ratio is 1:2 in District M, then it is also 1:2 in District P. This does NOT mean that the two Districts have the same numbers of teachers and students, just the same RATIOS.

Using this same example, District M could have 1 teacher and 2 students, while District P could have 100 teachers and 200 students (1:2 and 100:200 are the SAME RATIO) - so the specific NUMBERS involved could vary significantly.

GMAT assassins aren't born, they're made,
Rich

[jeph86]

Hi Rich,

so in order for the information to be sufficient combine, district M and P should have the same ratio which be choice C instead of E?

[Matt@VeritasPrep]

Hi Rich,

so in order for the information to be sufficient combine, district M and P should have the same ratio which be choice C instead of E?

Yup, you've got it!

For instance, suppose our ratio is 3:4, which means we can write it as 3x : 4x. If we add 9 of the first thing and 12 of the second, we'll have (3x + 9) : (4x + 12), or 3(x + 3) : 4(x + 3), so our ratio stays the same!