How many roots does x6 –12x4 + 32x2 = 0 have?(A) 1(B) 3(C) 4(D) 5(E) 2Solution:x^6 –12(x^4) + 32(x^2) = x^2 (x^4 – 12x^2 + 32) = x^2 (x^2 – 4)(x^2 – 8)The roots are 0, ±2, and ±2√2: a total of 5.Please remember that ‘0’ is also a root.The correct answer is D … [Read more...] about Equations – roots and powers
powers
GMAT Problem Solving : Number Properties
This question is an interesting Number Properties Problem Solving GMAT prep question . How many digits does the product of 412 and 523 contain? A. 12 B. 13 C. 23 D. 24 E. 35 The correct answer is choice D. We can rewrite the given numbers as 224 * 523. i.e., 2 * 223 * 523 = 2 * 1023. This is a 24 digit number. … [Read more...] about GMAT Problem Solving : Number Properties