GMAT – Quant Test Questions and Answers

4^x + 4^-x = 2 To get reciprocals to equal 2, both must be 1, so x = 0 Point Q lies in the interior of a particular circle. Is point Q the center of the circle? (1) There exist points A, B, and C, all distinct points on the circle's circumference, such that the distances QA, QB, and QC are identical. Yes Point Q lies in the interior of a particular circle. Is point Q the center of the circle? (2) At least two different diameters of the circle contain point Q. Yes, All diameters of a circle intersect at the circle's center and nowhere else. Therefore, if Q is the point of intersection of two or more of the circle's diameters, then Q must be the center of the circle. The statement is sufficient. If x is a prime number, what is the value of x? (2) The average of any x consecutive integers is an integer. X must be odd Then there are an odd number of members in a consecutive set, the mean/median will be a member of the set and thus an integer (e.g. 5,6,7,8,9; mean/median = 7). In contrast when there are an even number of members in the set, the mean/median will NOT be a member of the set and thus NOT an integer (e.g. 5,6,7,8; mean/median = 6.5). 1 / (a+b) 1/a + 1/b If a and b are positive, then true Need to test a or b as 1 as well as 0(a or b - decimal) 1 If negative, then generally won't be true |a| + |b| = a + b a and b must be positive Rectangle inscribed in a circle -- what is radius circle? radius of circle equal to half the diagonal diameter equal to full diagonal, so can use pythagorean theorem to solve