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Min/Max Problems

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Min/Max Problems

by swerve » Mon Jun 05, 2023 3:10 pm

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Five friends visited a used book store and each friend purchased one book. No two friends paid the same amount for a book, and the lowest book price was \(\$1\). If the sum of all book prices was \(\$25\), what is the maximum price that any one book cost, rounded to the nearest dollar?

A. \(\$15\)
B. \(\$17\)
C. \(\$19\)
D. \(\$21\)
E. \(\$23\)

The OA is D

Source: Veritas Prep
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Re: Min/Max Problems

by test_avoider » Mon Jun 26, 2023 8:43 pm
swerve wrote: ↑
Mon Jun 05, 2023 3:10 pm
 Five friends visited a used book store and each friend purchased one book. No two friends paid the same amount for a book, and the lowest book price was \(\$1\). If the sum of all book prices was \(\$25\), what is the maximum price that any one book cost, rounded to the nearest dollar?

A. \(\$15\)
B. \(\$17\)
C. \(\$19\)
D. \(\$21\)
E. \(\$23\)

The OA is D

Source: Veritas Prep
Let 0< x<y<z <1
A= max (to be found!!!)
B = 1.z
C= 1.y
D= 1.x
E= 1.0 (minimum, given)

A = 25.0 - (1.0+ 1.z +1.y +1.x )
= 21 - 0.a (where a = 0.x+0.y+0.z)

since A is to be maximized by taking round off therefore, A=21
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