rohitgoel15 wrote:
If x is positive, is x > 3 ?
(1) (x - 1)^2 > 4
(2) (x - 2)^2 > 9
Can someone point a mistake in my method?
(1)
Taking one of the equations:
(x - 1)^2 > 4
x^2 + 1 - 2x > 4
x^2 + 1 - 2x - 4 > 0
x^2 - 3x + 1x - 3 > 0
(x-3) (x+1) > 0
x > 3 and x > -1
while in the explanation given the ans is coming out to be x > 3 and x < -1
Please help ..
If x is positive, is x > 3 ?(1) (x - 1)^2 > 4 -->
(x+1)(x-3)>0 --> roots are -1 and 3. Now, ">" sign indicates that the solution lies to the left of a smaller root and to the right of the larger root:
x<-1 or
x>3. Since given that
x is positive then only one range is valid:
x>3. Sufficient.
(2) (x - 2)^2 > 9 -->
(x+1)(x-5)>0 --> roots are -1 and 5. Again, ">" sign indicates that the solution lies to the left of a smaller root and to the right of the larger root:
x<-1 or
x>5. Since given that
x is positive then only one range is valid:
x>5. Sufficient.
Answer: D.
Solving inequalities:
x2-4x-94661.html#p731476 (
check this one first)
inequalities-trick-91482.htmldata-suff-inequalities-109078.htmlrange-for-variable-x-in-a-given-inequality-109468.html?hilit=extreme#p873535everything-is-less-than-zero-108884.html?hilit=extreme#p868863Hope it helps.
Another approach:If x is positive, is x > 3 ?(1) (x - 1)^2 > 4 --> since both sides of the inequality are non-negative then we can take square root from both parts:
|x-1|>2.
|x-1| is just the distance between 1 and
x on the number line. We are told that this distance is more than 2:
--(-1)----1----3-- so,
x<-1 or
x>3. Since given that
x is positive then only one range is valid:
x>3. Sufficient.
(2) (x - 2)^2 > 9 -->
|x-2|>3. The same here:
|x-2| is just the distance between 2 and
x on the number line. We are told that this distance is more than 3:
--(-1)----2----5-- so,
x<-1 or
x>5. Since given that
x is positive then only one range is valid:
x>5. Sufficient.
Answer: D.
_________________
PLEASE READ AND FOLLOW: 11 Rules for Posting!!!
RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory
COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. NEW!!!
DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set. NEW!!!
What are GMAT Club Tests?
25 extra-hard Quant Tests
Find out what's new at GMAT Club - latest features and updates
close
49% (01:47) correct
