Events & Promotions
|
|
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Apr 2610:00 AM EDT
-11:00 AM EDT
The Target Test Prep course represents a quantum leap forward in GMAT preparation, a radical reinterpretation of the way that students should study. Try before you buy with a 5-day, full-access trial of the course for FREE!
Apr 2711:00 AM EDT
-12:00 PM EDT
Prefer video-based learning? The Target Test Prep OnDemand course is a one-of-a-kind video masterclass featuring 400 hours of lecture-style teaching by Scott Woodbury-Stewart, founder of Target Test Prep and one of the most accomplished GMAT instructors
Apr 2808:00 AM PDT
-11:00 AM PDT
Whether you are just beginning your MBA journey or fine-tuning your path to a 700+ score, GMAT Day is designed to give you a competitive edge.
03 Sep 2024, 02:12
Kudos
Bookmarks
A: 0
B: 0
A and B are integers, and the equation \(((5 - 3 - A)^2 + 3 - 6)^B = 1\) must hold true.
Select for A a value of A that ensures the equation is true for any integer value of B, and select for B a value of B that ensures the equation is true for any integer value of A. Make only two selection, one for each column.
Select for A a value of A that ensures the equation is true for any integer value of B, and select for B a value of B that ensures the equation is true for any integer value of A. Make only two selection, one for each column.
| A | B | |
| -2 | ||
| -1 | ||
| 0 | ||
| 1 | ||
| 2 | ||
| 3 |
ShowHide Answer
Official Answer
A: 0
B: 0
04 Sep 2024, 02:20
Kudos
Bookmarks
Official Solution:
\(((5 - 3 - A)^2 + 3 - 6)^B = 1\) to be true for any integer value of B, the expression in the parenthesis, the base, must be 1: \(1^{any \ integer} = 1\)
\((5 - 3 - A)^2 + 3 - 6=1\)
\((5 - 3 - A)^2 =4\)
\(5 - 3 - A =2\) or \(5 - 3 - A =-2\)
\(A =0\) or \(A=4\)
Since only 0 is present among the options, select 0 for A.
\(((5 - 3 - A)^2 + 3 - 6)^B = 1\) to be true for any integer value of A, the exponent must be 0: \((any \ nonzero \ number)^0 = 1\)
Thus, B must be 0. Note that \((5 - 3 - A)^2 + 3 - 6 = 0\) when A is not an integer, specifically when \(A = 2 + \sqrt{3}\) or \(A = 2 - \sqrt{3}\). This ensures that we avoid the case of \(0^0\) (a scenario not tested on the GMAT) for integer values of A.
Correct answer:
A "0"
B "0"
Bunuel
\(((5 - 3 - A)^2 + 3 - 6)^B = 1\) to be true for any integer value of B, the expression in the parenthesis, the base, must be 1: \(1^{any \ integer} = 1\)
\((5 - 3 - A)^2 + 3 - 6=1\)
\((5 - 3 - A)^2 =4\)
\(5 - 3 - A =2\) or \(5 - 3 - A =-2\)
\(A =0\) or \(A=4\)
Since only 0 is present among the options, select 0 for A.
\(((5 - 3 - A)^2 + 3 - 6)^B = 1\) to be true for any integer value of A, the exponent must be 0: \((any \ nonzero \ number)^0 = 1\)
Thus, B must be 0. Note that \((5 - 3 - A)^2 + 3 - 6 = 0\) when A is not an integer, specifically when \(A = 2 + \sqrt{3}\) or \(A = 2 - \sqrt{3}\). This ensures that we avoid the case of \(0^0\) (a scenario not tested on the GMAT) for integer values of A.
Correct answer:
A "0"
B "0"
14 Dec 2024, 09:40
Kudos
Bookmarks
I have revised the question, solution, and formatting by adding more details to enhance clarity.
