Ratio is a math concept that is vital in your post-MBA journey. It allows you to compare variables and provide a means to divide the variable with a common factor. “The ratio of boys to girls is seven to two” can be expressed as the proportion: B/G = 7/2. Do with this what you like: 7G = 2B or B = 7G/2, whatever. Forget the “:” with ratios.
GMAT writers love to provide ratios (which are multiplicative relationships) and then add an absolute component (addition/subtraction). Note that when you have a ratio like B/G = 7/2, we don’t actually know the number of girls and boys. There can be 14 boys and 4 girls, or 70 boys and 20 girls. Questions that insert absolute numbers should be taken with caution. For example:
At a certain restaurant, the ratio of the number of cooks to the number of waiters is 3 to 13. When 12 more waiters are hired, the ratio of the number of cooks to the number of waiters changes to 3 to 16. How many cooks does the restaurant have?
A. 4
B. 6
C. 9
D. 12
E. 15
The key here is setting up the equation. Since we don’t know the initial scale of the number of cooks and waiters, we can express this scale by “x”.
C/W = 3x/13x.
Notice that whatever x is, the ratio will hold true. (x must be an integer, since you can’t have a portion of a cook, unless of course he chops his finger off by accident!)
“When 12 more waiters are hired” is the insertion of an absolute. Adding the 12 waiters, the new ratio becomes:
C/W = 3x/(13x + 12)
“The ratio of the number of cooks to the number of waiters changes to 3 to 16” defines this new ratio:
C/W = 3x/(13x + 12) = 3/16
STOP! Before we cross multiply and solve for x, we want to cancel out the 3’s in both the numerator. (More on this below.) After cross-multiplying, we get:
16x = 13x + 12
3x = 12
x = 4
Sweet. Answer A, right? Well, recall that x represents the scaling factor. The stimulus asks for the number of cooks, which we originally represented by 3x. So, 3*4 = 12 cooks. That’s 120 fingers. Choice D.
About the Author
I am Atul Jose, Founding Consultant of F1GMAT, an MBA admissions consultancy that has worked with applicants since 2009.
For the past 15 years I have edited the application files of admits to the M7 programs: Harvard Business School, Stanford Graduate School of Business, the Wharton School, MIT Sloan, Chicago Booth, Kellogg School of Management, and Columbia Business School, together with admits to Berkeley Haas, Yale School of Management, NYU Stern, Michigan Ross, Duke Fuqua, Darden, Tuck, IMD, London Business School, INSEAD, SDA Bocconi, IESE Business School, HEC Paris, McCombs, and Tepper, plus other programs inside the global top 30.
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