Author:
gmat and gre math
Jul
18
The function | |2x - 4| - 6 | is graphed above. Which of the following functions are completely equivalent to | |2x - 4| - 6 |?(i) | 6 - |4 - 2x| |(ii) 2(| |x - 2| + 3 |)(iii) |2x + 2| + |2x - 10| - |2x - 4| - 6(A) i and ii(B) i and iii(C) ii and iii(D) i, ii, and iii(E) noneThe expression in (i) is the easiest to check. We can apply the principle that |a-b| = |b-a| is always true no matter
Author:
gmat and gre math
Jul
7
a and b are prime numbers, and the legs of a right triangle are a*sqrt(b) and b*sqrt(a). If c is the hypotenuse of the right triangle, which of the following must be true?(i) c2 is composite(ii) c is not an integer(iii) c2 is odd(A) i only(B) ii only(C) i and ii(D) i and iii(E) ii and iiiLet's evaluate (i) since it occurs in three answer choices. Since we are dealing with a right triangle, we
Author:
gmat and gre math
May
7
n and m are odd prime numbers. Which of the following can never be prime?(i) |m-n|(ii) m+n(iii) mn-5(A) i only(B) i and ii(C) i and iii(D) ii only(E) ii and iiiThe fact that n and m are prime and odd will help use rule out many possibilities. Let's start by testing |m-n|. We know that this is always an even number. However, 2 is the only even number that is also prime. If we have m=5 and n=3
Author:
gmat and gre math
Apr
11
If |2x-5| ≤ 25 and |y+11| ≤ 19, which of the following must be true?(i) xy ≤ 120(ii) -40 ≤ x+y ≤ 23(iii) |2x + y + 6| ≤ 44(A) i, ii(B) ii(C) i, iii(D) ii, iii(E) iiiIf |2x-5| ≤ 25, then we can solve for the range of values of x by solving the equations2x-5 ≤ 25 and 2x-5 ≥ -25. This gives us -10 ≤ x ≤ 15.Similarly, we can find the range of y by solvingy+11 ≤ 19 and y+11 ≥ -19. This gives us -30 ≤
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
