Brian works as a consultant. His only work comes from three companies

Question

Brian works as a consultant. His only work comes from three companies: Company A, Company B, and Company C. He earns a daily rate of $500 when he works for company A, $600 when he works for company B, and $1000 when he works for company C. If Brian earned a total of $11,300 last month and worked less than five days for Company A, how many days did he work in total?

(1) Brian worked eight days for Company B last month.
(2) Brian worked five days for Company C last month.

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Official Answer

B

(1) Brian worked eight days for Company B last month.
(2) Brian worked five days for Company C last month.

dhruv23320 · Answer

Let the number of days Brian worked for Companies A, B, and C be a, b, and c.

His total earnings are:
500a + 600b + 1000c = 11,300 
We are also given that a < 5.

Statement (1): b = 8 
Substitute into the equation:
500a + 600(8) + 1000c = 11,300 
500a + 4,800 + 1000c = 11,300 
500a + 1000c = 6,500 
This simplifies to:
a + 2c = 13

Possible integer solutions with a < 5:
(a, c) = (3, 5) or (1, 6)

Total days worked = a + b + c:
For (3,5): 3 + 8 + 5 = 16 
For (1,6): 1 + 8 + 6 = 15

Different totals → statement (1) is not sufficient.

Statement (2): c = 5 
Substitute into the equation:
500a + 600b + 5000 = 11,300 
500a + 600b = 6,300 
Divide by 100:
5a + 6b = 63

Check integer solutions with a < 5:
a = 3 gives b = 8 (valid) 
Other values of a < 5 do not give integer b.

So a = 3, b = 8, c = 5.

Total days = 3 + 8 + 5 = 16, uniquely determined → statement (2) is sufficient.

Answer: B

annanyach · Answer

Why have we assumed that the number of days that Brian works with any given company has to be a whole number?

Edskore · Answer

Good catch on flagging that, annanyach. The problem says Brian "worked" a certain number of days — in real-world terms (and on the GMAT), the number of days someone works is always a non-negative integer. You can't work 2.5 days for a company in this context. So a, b, and c all have to be whole numbers (0, 1, 2, 3, ...).

This is actually a key move in Data Sufficiency problems involving rates and counts: when the problem talks about "number of days," "number of people," "number of items," etc., you should immediately recognize that those values are non-negative integers. That constraint is what makes the problem solvable.

Without the integer constraint, Statement (2) alone (5a + 6b = 63) would have infinitely many solutions (like a = 0.6, b = 10), and the answer would be E instead of B. The GMAT tests whether you catch that implicit constraint. I got tripped up by a similar thing early in my prep — always ask yourself whether the variable you're solving for has to be an integer.

Brian works as a consultant. His only work comes from three companies

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