The Quest for 700: Weekly GMAT Challenge (Answer)

Yesterday, Integrated Learning posted a 700 level GMAT question on our blog. Today, they have followed up with the answer:


At Integrated Learning we call this kind of question an “overlapping group” question.  To solve it, we advocate the Grouping

Grid™, a handy way to line up all the elements of a grouping question and get the answer quickly.  We won’t go into all the details here, but this is how it works for this question.

1. Start with the grid.  Label as shown, though it doesn’t matter if England is on the top or on the side.


2. Next, fill in the squares that correspond with the data given in the problem.  This problem is tougher because we only know that 80 people were in either England or France, but not both.  You can see how we solve that issue with algebra.


3. In the Grouping Grid™, every column adds down and every row adds across.  So you can now fill in all the boxes that you can infer from the given data.


4. Finally, to solve this problem, give one of the still-empty boxes the variable y and solve the two variables with two equations.


x + y = 70
(80 – x) + y = 40
Do the math and you will see that x = 55 and y = 15. Thus, we can further manipulate the
grid and fill it in completely.  The answer for who has been to both France and England is in the corresponding box, 35.


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