The feel of technical power

Algebra Level 4

Assume $a$ and $b$ are both real numbers. Determine which of these statements must necessarily be true:

A) If $a>b$ , then $a^2>b^2$

B) If $|a|>b$ , then $a^2>b^2$

C) If $a>|b|$ , then $a^2>b^2$

D) If $a^2>b^2$ , then $a>b$

E) If $a\neq|b|$ , then $a^2\neq b^2$

B A E C D

2 solutions

Baby Googa
Feb 14, 2015

'A' doesn't work: 2 > -3, 4 < 9.

'B' doesn't work: |2| > -3, 4 < 9.

'C' works: since a > |b|, a must be positive, since b is positive. So a^2 > b^2.

'D' doesn't work: 9 > 4, -3 < 2.

'E' doesn't work: -2 != |2|, 4 = 4.

Note: != means "not equal to"

Alex Segesta
Feb 22, 2015

I think this is kind of overrated for level 3.