2001 AMC 10 Problem 10

Attempt Problem 10 of the 2001 AMC 10 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2001 AMC 10 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

10.

x,

y,

and

z

are positive with

xy=24,

xz=48,

and

yz=72,

then

x+y+z

18

19

20

22

24

Divide

xz=48

xy=24

to relate

y

and

z

From

z=2y

and

yz=72,

solve for

y

Dividing

xz=48

xy=24

gives

z=2y.

Then

yz=2y^2=72,

y=6,

z=12,

and

x=\frac{24}{y}=4.

Hence

x+y+z=22.

Thus, the correct answer is D.

Problem 10 in other years