M7MBA wrote: ↑Thu Nov 04, 2021 12:18 pm
A store sells only two types of shirts - branded and non-branded. All the branded shirts are priced at $60 per unit and all the non-branded shirts are priced at $20 per unit. On a certain day, the store sold a total of 30 shirts. What is the number of the branded shirts that the store sold on that day?
1. The store sold more than 20 branded shirts on that day.
2. On that day, the total sales from shirts were between $1604 and $1674.
Answer:
B
Source: e-GMAT
Given: All the branded shirts are priced at $60 per unit and all the non-branded shirts are priced at $20 per unit. On a certain day, the store sold a total of 30 shirts.
Let B = # of branded shirts sold
Let N = # of non-branded shirts sold
If a TOTAL of 30 shirts were sold, we can write:
N + B = 30
Target question: What is the value of B?
Statement 1: The store sold more than 20 branded shirts on that day.
All we know so far is that
N + B = 30
So, it's possible that
B = 21, B = 22, B = 23, etc
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: On that day, the total sales from shirts were between $1604 and $1674.
Branded shirts cost $60 each, and all the non-branded shirts cost $20 each
We can write:
20N + 60B = TOTAL sales
This means: 20N + 60B = some value between $1604 and $1674
Let's see if we can also use the fact that
N + B = 30 to help us answer the target question.
We can rewrite 60B as 20B + 40B and see what happens.
We get: 20N + 20B + 40B = some value between $1604 and $1674
Factor first two terms to get: 20(N + B)+ 40B = some value between $1604 and $1674
Replace
N + B with
30 to get: 20(
30)+ 40B = some value between $1604 and $1674
Evaluate: 600 + 40B = some value between $1604 and $1674
Subtract 600 from both sides to get: 40B = some value between $1004 and $1074
IMPORTANT: B is a POSITIVE INTEGER.
If B = 25, then 40B = 40(25) = 1000, which is NOT between $1004 and $1074
If B = 26, then 40B = 40(26) = 1040, which IS between $1004 and $1074
If B = 27, then 40B = 40(27) = 1080, which is NOT between $1004 and $1074
So, there's only 1 possible value that satisfies statement 2.
The answer to the target question is
B = 26
Since we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer: B
Cheers,
Brent
