Percents and area

BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

This topic has expert replies

Post new topic Post Reply

Previous Topic Next Topic

moonlite: Senior | Next Rank: 100 Posts; Posts: 61; Joined: Fri Jun 06, 2008 5:58 am; Thanked: 1 times

Percents and area

by moonlite » Thu Apr 23, 2009 2:58 pm

A circle graph shows how the budget of a certain company was spent: 63 percent for salaries, 12 percent for research and development, 6 percent for utilities, 5 percent for equipment, 4 percent for supplies, and the remainder for transportation. If the area of each sector of the graph is proportional to the percent of the budget it represents, how many degrees of the circle are used to represent transportation?
(A) 10°
(B) 18°
(C) 36°
(D) 90°
(E) 324°

OA C

Please explain thanks.

Quote

Source: Beat The GMAT — Problem Solving | Thu Apr 23, 2009 2:58 pm

Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pm; Location: Toronto; Thanked: 1710 times; Followed by:614 members; GMAT Score:800

Re: Percents and area

by Stuart@KaplanGMAT » Thu Apr 23, 2009 3:19 pm

moonlite wrote:A circle graph shows how the budget of a certain company was spent: 63 percent for salaries, 12 percent for research and development, 6 percent for utilities, 5 percent for equipment, 4 percent for supplies, and the remainder for transportation. If the area of each sector of the graph is proportional to the percent of the budget it represents, how many degrees of the circle are used to represent transportation?
(A) 10°
(B) 18°
(C) 36°
(D) 90°
(E) 324°

Please explain thanks.

If the % for transportation is "t", we can say:

t = 100 - (63 + 12 + 6 + 5 + 4)

t = 100 - 90

t = 10

If 10% of funds were used for transportation, 10% of the area of the circle will be devoted to transportation. Using the circle sector formula:

degrees(t)/360 = area(t)/area(circle)

degrees(t)/360 = 1/10

degrees(t) = (1/10)(360) = 36

Or, using common sense (often quicker than formulas on test day!), if t makes up 10% of the circle, then t should contain 10% of the 360 degrees. Again:

10%(360) = 36