There are five sales agents in a certain real estate office. One month Andy sold twice as many properties as Ellen, Bob

BTGmoderatorLU wrote: ↑

Mon Jan 18, 2021 2:57 am

Source: Official Guide

There are five sales agents in a certain real estate office. One month Andy sold twice as many properties as Ellen, Bob sold 3 more than Ellen, Cary sold twice as many as Bob, and Dora sold as many as Bob and Ellen together. Who sold the most properties that month?

A. Andy
B. Bob
C. Cary
D. Dora
E. Ellen

The OA is C

Solution:

We can create the following equations:

A = 2E

B = E + 3

C = 2B

D = B + E

Looking at our equations, Ellen is not the person who sold the most properties because at least Bob sold more than she did. We also see that Dora sold more than Bob, so Bob is not the person who sold the most properties. Since B = E + 3 (so B > E), we see that Dora sold more than Andy (D > B since B + E > E + E). So Andy is not the person who sold the most properties and we are left with Cary and Dora. Since B > E, we see that Cary sold more than Dora (C > D since B + B > B + E). Thus, Cary sold the most properties.

Alternate Solution:

We can create the following equations:

A = 2E

B = E + 3

C = 2B

D = B + E

Let’s substitute B = E + 3 in the last two equations:

C = 2(E + 3) = 2E + 6

D = (E + 3) + E = 2E + 3

Now, we have everything expressed in terms of E; thus it just remains to compare the quantities 2E, E + 3, 2E + 6, 2E + 3 and E. Since E is the number of properties sold by Ellen, it is a positive integer. Thus, the greatest expression among the five possibilities is 2E + 6, which belongs to Cary.

Answer: C