The number of stamps that Kaye and Alberto had were in the ratio of 5:3 respectively. After Kaye gave Alberto 10 of her stamps, the ration of the number of Kaye had to the number of Alberto had was 7:5. As a result of the gift, Kaye had how many more stamps than Alberto?

The number of stamps that Kaye and Alberto had were in the ratio of 5:3 respectively. After Kaye gave Alberto 10 of her stamps, the ration of the number of Kaye had to the number of Alberto had was 7:5. As a result of the gift, Kaye had how many more stamps than Alberto?

(A) 20
(B) 30
(C) 40
(D) 60
(E) 90

In GMAT tutoring we teach the “ratio box”. It’s nothing groundbreaking but helpful for organizing GMAT ratio information. The Kaye and Alberto stamp question is a very specific type of ratio question that comes up reasonably often. I call it a “new ratio” question because usually you’re given a new ratio and then asked to solve for some of the real world values. Let’s take what we know about Kaye and Alberto and hopefully make some inferences. Here’s the ratio box with the information that we have:

We don’t know what the multiplier is so I’d always put in a variable. I usually use “M” for multiplier. Using variables that somewhat connect to what they represent is a good GMAT habit to get into. Then you can multiply across to get your real world values for the stamps that Kaye and Alberto have. To those you can add 10 stamps to Alberto and subtract 10 stamps from Kaye. After the stamp trading, the new ratio of stamps is 7:5. Now we can just solve for the “M” the multiplier and then solve for the difference of stamps (after the trade). Go ahead and comment with any questions or additions. Happy GMAT studies!