Author:
gmat and gre math
Mar
5
Which of the following could be true?(i) x = 1(ii) x = 3(iii) x = 5(A) i(B) ii(C) iii(D) i, ii(E) i, iiiSimple substitution will tell us which values of x yield a right triangle. (i) x = 1, triangle has side lengths 4, 3, and 5. This is a right triangle, so (i) is true.(ii) x = 3, triangle has side lengths 6, 9, and 11. This is not a right triangle, so (ii) is false.(iii) x = 5, triangle has
Author:
gmat and gre math
Feb
21
If (y-2)/(y-3) = 8/y, which of the following must be true?(i) |2y - 10| = 2(ii) y² - 9y + 14 = -24/y(iii) |5/24 - 1/y| = 1/24(A) i(B) i, ii(C) i, ii, iii(D) ii, iii(E) iiiThis question may look intimidating and complicated, but the key is to start from the beginning and solve the first clue: (y-2)/(y-3) = 8/y. If we cross multiply to clear the denominators, we gety(y-2) = 8(y-3) y² - 2y = 8y -
Author:
gmat and gre math
Feb
15
If x and y are positive numbers and (x + 12y)/(3x + y) = x/y, which of the following must be true?(i) x/y = 2(ii) x = 2 and y = 1(iii) x = y + 2(A) i(B) i, ii(C) i, iii(D) iii(E) noneThe first option can easily be checked by replacing x with 2y on the left hand side, and x/y with 2 on the right hand side, and then confirming that the equation is true.(2y + 12y)/(6y + y) = 2 ?(14y)/(7y) = 2 ?14/7
Filed under:
3-statements
Author:
gmat and gre math
Dec
23
Which of the following are true for all positive values of x and y?(i) sqrt(x+y) > |x-y|/6(ii) x+y > sqrt(2xy)(iii) x^y > x(A) i only(B) ii only(C) iii only(D) ii and iii(E) i, ii, and iiiWe should start by evaluating (ii) since it appears frequently and has a simple form. One way test its veracity is to plug in a few pairs of numbers for x and y to see if the statement is sometimes false. If
Author:
gmat and gre math
Dec
2
A rectangle with integer sides and a perimeter of 16 is inscribed within a circle. Which of the following must be true?(i) the area of the circle is less than 13π(ii) the area of the circle is at least 8π(iii) the circumference of the circle is less than 6π(A) iii(B) i and ii(C) i and iii(D) i, ii, and iii(E) noneWe should consider the extremes of rectangles that can be inscribed within a circle
Author:
gmat and gre math
Nov
18
Source: http://gmatgremath.blogspot.comWhich of the following must be true for positive integers m and n greater than 1?(i) (mn)! / (m+n)! is an integer(ii) (m+n)! / (n!m!) is an integer(iii) (m!)² / (n²)! is an integer, whenever m ≥ n(A) i and ii(B) i and iii(C) ii and iii(D) i, ii, and iii(E) noneStarting with (i), we should recall the following property of factorials: a!/b! is always an
Author:
gmat and gre math
Nov
18
Source: http://gmatgremath.blogspot.comFor positive numbers a and b, the operation Ω is defined by the equation a Ω b = (ab + 9)/(a + b). Which of the following must be true?(i) a² Ω a² = (a Ω a)²(ii) a Ω b = b Ω a(iii) a Ω 3 = 3(A) i(B) i and ii(C) ii(D) ii and iii(E) iiiTo evaluate (i), we can check with an actual number for a. Let's try a = 2. Then,2² Ω 2² = 4 Ω 4= (16 + 9)/(8) = 25/8, but(
Author:
gmat and gre math
Oct
23
If you are reading this post on a website other than http://gmatgremath.blogspot.com, then you are reading this post on a website that has scraped the RSS feed from my website, the "GMAT and GRE Math Blog." The site you currently viewing is a feed-scraping bottom feeder!
Filed under:
3-statements, Algebra, Area, Arithmetic, Factoring, charts, chuck norris, combination, combined work, coordinates, data sufficiency easy, data sufficiency hard, data sufficiency medium, exponents
Author:
gmat and gre math
Oct
22
If you are reading this post on a website that is not the GMAT and GRE Math Blog, it's because another site has scraped my site feed! Bad bottom feeders, you know who you are! You can full GMAT and GRE questions with explanations here.
Filed under:
3-statements, Algebra, Area, Arithmetic, Factoring, charts, chuck norris, combination, combined work, coordinates, data sufficiency easy, data sufficiency hard, data sufficiency medium, exponents
