Expert: Ahmed Salami - 9/28/2004

Question
Hi Ahmed,
This is a question from the GRE.

Question:
0 < X < 1

Colum A
X + X three-squared + X five-squared + X seven-squared

Colum B
X squared + X four-squared + X six-squared + X eight-squared

My answer:
I think the answer is Colum B. Since the sum of all the exponents in colum B (20) is greater than that of A (15).

Please advise.

Regards,

Maggis  

Answer
Hi Maggis,
I'm afraid column A is the greater. You would have been right if X were not between 0 and 1. Look at it this way, because of the value of X, X > X^2 (e.g 1/2 > 1/4). Generally, when 0<X<1 any term with the greater exponent is smaller. So by comparing all the terms in the two columns in the order in which they come, each term in column A is greater than the corresponding one in column B. You can also work it out by using say X = 1/3 and actually seeing the results.
I hope i have helped.
Good luck.
Regards.