Last Updated on May 9, 2023
GMAT OFFICIAL GUIDE DS
Solution:
We are given that the ratio of the number of teachers to the number of students is the same in School District M and School District P. Let’s define some variables for the number of students and teachers in both districts.
a = number of teachers in school district M
b = number of students in school district M
c= number of teachers in school district P
d = number of students in school district P
Since the ratio of the number of teachers to the number of students is the same in School District M and School District P, we can say:
a/b = c/d
ad = bc
We need to determine the value of b/d. If we isolate b/d in the equation ad = bc we see that b/d = a/c. Thus, if we can determine a value of a/c, we also can determine a value for b/d.
Statement One Alone:
There are 10,000 more students in School District M than there are in School District P.
Using the information from statement one, we can create the following equation:
b = d + 10,000
Substituting d + 10,000 for b in the expression b/d we obtain:
(d + 10,000)/d
Without knowing the value of d, we do not have enough information to determine a value for b/d. Statement one is not sufficient to answer the question. We can eliminate answer choices A and D.
Statement Two Alone:
The ratio of the number of teachers to the number of students in School District M is 1 to 20.
Using the information in statement two we can create the following equation:
a/b = 1/20
20a = b
The information in statement two does not provide enough information to determine a value for b/d. We can eliminate answer choice B.
Statements One and Two Together:
From statements one and two we know that b = d + 10,000 and that 20a = b. However, even with both of these equations we still cannot determine a value for b/d or a/c.
Answer: E
