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GRE Math Strategies Part III of VI: Illustration

The Illustration approach involves choosing workable numbers that substitute into
the question rather than using the given answer choices as with the Plug In strategy.

Illustration works best when the question provides some numerical information (like
percentages) but doesn’t supply you with absolute values.

Example #1:
At a public housing conference 15 percent of the attendees are male. After the speaker finishes, several female attendees but no males leave the conference and the total number of persons remaining is 60 percent of the original number. The number of female attendees who leave is what fraction of the original number of females attending the conference?
(A) 11/20
(B) 9/17
(C) 8/17
(D) 9/20
(E) 2/5

(C) is the correct answer.
Let 100 equal the total attendees. If 15 percent are men, and only females leave after the speaker, this leaves 60 percent of the original total in attendance.

Original #: 85 female, 15 male, 100 total
After Speaker Finishes: 45 female, 15 male, 60 total

The number of female attendees who leave [85 – 45 = 40] is what fraction of the original number of females? 40/85 = 8/17. (Note that we backed in to the 45 female number because we were given “remaining is 60 percent of the original number” and “all males remained (15).”)

Percents always conveniently add to 100 – for example, if 15 percent of the
attendees are male (given), then 85 percent are female (implied).
Always use 100 (or a multiple of 100) to illustrate percent problems.

The Illustration technique also works when a critical piece of information is not provided, thereby creating the possibility of providing it yourself. Here, the total number of people at the restaurant is an important piece of information.

Example #2:
Of the total number of people who ate in a restaurant one evening, 2/3 ordered salads. Of those who ordered salad, 1/3 had Italian dressing on their salad. If the total number of people who ate in the restaurant that night was T, which of the following expressions represents the number of people who did not eat any Italian dressing at the restaurant that evening?
(A) 2/9T
(B) 1/3T
(C) 1/2T
(D) 2/3T
(E) 7/9T

(E) is the correct answer.

A helpful choice for T should be a number that can be divided by 3 a couple of times.
Let T = 27, then 2/3 x 27 = 18 people ate salad that evening. Of these 18, 1/3 x 18 = 6 had Italian dressing. So 27 - 6 = 21 people did not have Italian dressing.
Now we need to look at the answers to see which fraction of T (our 27 people) the number 21 represents.
21/27 = 7/9, so (E) is the correct answer.

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