Hello, I need some help! I found this problem and I do not know what rule it was applied when solving the problem.
Is (y+3)^2 less than 4?
(1) y+3 is less than 2.
(2) y+3 is greater than .
They say, "The Inequality (y+3)^2 < 4 is equivalent to -2 < y+3 < 2. Will this be truth for any given exponent to have a two side inequality to the power? what if the power is negative? what direction should it be?
Your help will be appreciatted! correct Answer is C
inequalities with an exponent
This topic has expert replies
GMAT/MBA Expert
- Anurag@Gurome
- GMAT Instructor
- Posts: 3835
- Joined: Fri Apr 02, 2010 10:00 pm
- Location: Milpitas, CA
- Thanked: 1854 times
- Followed by:523 members
- GMAT Score:770
Is (y + 3)² less than 4?Taniuca wrote:Hello, I need some help! I found this problem and I do not know what rule it was applied when solving the problem.
Is (y+3)^2 less than 4?
(1) y+3 is less than 2.
(2) y+3 is greater than .
They say, "The Inequality (y+3)^2 < 4 is equivalent to -2 < y+3 < 2. Will this be truth for any given exponent to have a two side inequality to the power? what if the power is negative? what direction should it be?
Your help will be appreciatted! correct Answer is C
We can take examples to be more clear.
(1) (y + 3) < 2
If y = -2, then (y + 3)² = (-2 + 3)² = 1 < 4
If y = -6, then (y + 3)² = (-6 + 3)² = 9 > 4
No definite answer; NOT sufficient.
(2) I guess it is (y + 3) > -2
If If y = -2, then (y + 3)² = (-2 + 3)² = 1 < 4
If y = 4, then (y + 3)² = (4 + 3)² = 49 > 4
No definite answer; NOT sufficient.
Combining (1) and (2), we know that -2 < (y + 3) < 2. So, (y + 3)² < 4; SUFFICIENT.
The correct answer is C.
Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)
Join Our Facebook Groups
GMAT with Gurome
https://www.facebook.com/groups/272466352793633/
Admissions with Gurome
https://www.facebook.com/groups/461459690536574/
Career Advising with Gurome
https://www.facebook.com/groups/360435787349781/
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)
Join Our Facebook Groups
GMAT with Gurome
https://www.facebook.com/groups/272466352793633/
Admissions with Gurome
https://www.facebook.com/groups/461459690536574/
Career Advising with Gurome
https://www.facebook.com/groups/360435787349781/
- sl750
- Master | Next Rank: 500 Posts
- Posts: 496
- Joined: Tue Jun 07, 2011 5:34 am
- Thanked: 38 times
- Followed by:1 members
If the exponent,as in this case is 2, you have two real roots, one positive and one negative. Also, in this case, the inequality used is less than, hence the expression, y+3 is in between the range +/-2. Had it been the other way around, where (y+3)^2>4, the result would be (y+3>2 or (y+3)<-2.Taniuca wrote:Hello, I need some help! I found this problem and I do not know what rule it was applied when solving the problem.
Is (y+3)^2 less than 4?
(1) y+3 is less than 2.
(2) y+3 is greater than .
They say, "The Inequality (y+3)^2 < 4 is equivalent to -2 < y+3 < 2. Will this be truth for any given exponent to have a two side inequality to the power? what if the power is negative? what direction should it be?
Your help will be appreciatted! correct Answer is C
For higher order exponents, like say, n=4, you have 2 real roots and 2 complex roots
For n=3, you have one real root and 2 complex roots. Also for odd exponents it is possible to have negative real roots. Ex cuberoot(-8) = -2
The inequality sign changes when you multiply both sides by a negative quantity or divide by a nonzero negative number