Functions

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BTGmoderatorRO: Moderator; Posts: 772; Joined: Wed Aug 30, 2017 6:29 pmFollowed by: 6 members

by BTGmoderatorRO » Sat Oct 28, 2017 2:31 am

Let function f(x)=(x-a)(x-b). If f(10)=f(20)=0, f(30)=?

A. 50
B. 100
C. 150
D. 200
E. 250
OA is d
what approach can we use to get the correct answer?

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Source: Beat The GMAT — Problem Solving | Sat Oct 28, 2017 2:31 am

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Sat Oct 28, 2017 3:06 am

Roland2rule wrote:Let function f(x)=(x-a)(x-b). If f(10)=f(20)=0, f(30)=?

A. 50
B. 100
C. 150
D. 200
E. 250

f(10) = 0 implies (10, 0) is a point on the graph of f(x)=(x-a)(x-b).
Implication:
f(x) = (x-10)(x-b), with the result that x=10 yields f(x)=0.

f(20) = 0 implies (20, 0) is a point on the graph of f(x)=(x-10)(x-b).
Implication:
f(x) = (x-10)(x-20), with the result that x=20 yields f(x)=0.

Substituting x=30 into f(x) = (x-10)(x-20), we get:
f(x) = (30-10)(30-20) = (20)(10) = 200.

The correct answer is D.

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8177; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Tue Nov 12, 2019 7:20 pm

BTGmoderatorRO wrote:Let function f(x)=(x-a)(x-b). If f(10)=f(20)=0, f(30)=?

A. 50
B. 100
C. 150
D. 200
E. 250
OA is d
what approach can we use to get the correct answer?

Since f(10) = f(20) = 0, this means a = 10 and b = 20, or vice versa. In other words, f(x) = (x - 10)(x - 20). Therefore, f(30) = (30 - 10)(30 - 20) = (20)(10) = 200.

Answer: D

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