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.
Nov 2007:30 AM PST
-08:30 AM PST
Learn what truly sets the UC Riverside MBA apart and how it helps in your professional growth
Nov 2001:30 PM EST
-02:30 PM IST
Learn how Kamakshi achieved a GMAT 675 with an impressive 96th %ile in Data Insights. Discover the unique methods and exam strategies that helped her excel in DI along with other sections for a balanced and high score.
Nov 1912:30 PM EST
-01:30 PM EST
Learn how Keshav, a Chartered Accountant, scored an impressive 705 on GMAT in just 30 days with GMATWhiz's expert guidance. In this video, he shares preparation tips and strategies that worked for him, including the mock, time management, and more
Nov 2211:00 AM IST
-01:00 PM IST
Do RC/MSR passages scare you? e-GMAT is conducting a masterclass to help you learn – Learn effective reading strategies Tackle difficult RC & MSR with confidence Excel in timed test environment- Nov 23
11:00 AM IST
-01:00 PM IST
Attend this free GMAT Algebra Webinar and learn how to master the most challenging Inequalities and Absolute Value problems with ease. 
Nov 2407:00 PM PST
-08:00 PM PST
Full-length FE mock with insightful analytics, weakness diagnosis, and video explanations!
Nov 2510:00 AM EST
-11:00 AM EST
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.
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
28% (02:36) correct
72%
(02:45)
wrong
based on 471
sessions
History
Date
Time
Result
Not Attempted Yet
If a, b are integers, and \((a-b)^2 + 8b^2=108\), what is the number of the ordered pairs (a,b)?
A. 2
B. 4
C. 6
D. 8
E. 10
A. 2
B. 4
C. 6
D. 8
E. 10
17 May 2017, 20:47
Kudos
Bookmarks
Amby02
Hi MikeMighty and AMahmoodi
The approach is correct but you are faltering at two places.
1) you are looking for ordered pairs a,b so you cannot find combinations by simply multiplying. Each value of a and b, combined, should satisfy equation.
2) 100 is also a perfect square..
now the solution
Let's look at 8b^2.... B can take value as 0,1,2,3...
When b=4, 8b^2 becomes 128, more than Right Hand side..
When we subtract 108-8b^2, it should give us a perfect square as (a-b)^2 is a perfect square.
1) b=0,
\(108-8b^2=108..\)... NOT a perfect square.... OUT
2) b=1 or -1,
\(108-8*1^2=100... So.. (a-b)^2=100=10^2..\)...
# a-b=10....b=1,a=11 ; b=-1,a=9….....SO 2 ordered pairs
#a-b=-10...Again 2 ordered pairs
So 4 pairs here.
3) b= 2 or -2
\(108-8*2^2=76\)..... NOT a perfect square.... OUT
4) b=3 or -3..
\(108-8*3^2=36=6^2 ..or ..(-6)^2\)
#a-b=6.......2 ordered pairs
#a-b=-6..... Again 2 ordered pairs
So 4 pairs
Overall ordered pairs =4+4=8..
Just for info these are
a-b=10………(11,1);(9,-1)
a-b=-10………(-9,1);(-11,-1)
a-b=6………(9,3);(3,-3)
a-b=-6………(-3,3);(-9,-3)
D
12 Jan 2018, 13:38
Kudos
Bookmarks
Hi All,
While this question 'looks' complex, it can be organized into some simple ideas; those ideas - along with a bit of BRUTE FORCE arithmetic - can get you to the solution without too much trouble.
We're told that (A - B)^2 + 8(B^2) = 108 and that A and B are both INTEGERS.
In simple terms:
(A perfect square) + 8(A perfect square) = 108
Since perfect squares cannot be negative, and that second perfect square is multiplied by EIGHT, there can't be that many solutions to this equation. Let's focus on that second perfect square....If the first perfect square was 0, then we'd have....
0 + 8(a perfect square) = 108
(a perfect square) = 108/8 = 13.5
Since B is an INTEGER, we know that this equation is NOT possible - but we can use it to determine that that perfect square is less than 13.5. Thus, we really only have to think about 0, 1, 4 and 9 for that second perfect square. Let's start 'big' and work our way down...
IF.... B = 3 or -3, then we have...
(A-B)^2 + 72 = 108
(A-B)^2 = 36
(A-B) = +6 or -6
Thus, we could have FOUR solutions here:
A = 9, B = 3
A = -3, B = 3
A = -9, B = -3
A = 3, B = -3
IF.... B = 2 or -2, then we have...
(A-B)^2 + 32 = 108
(A-B)^2 = 76
76 is NOT a perfect square though, so there are no solutions here.
IF.... B = 1 or -1, then we have...
(A-B)^2 + 8 = 108
(A-B)^2 = 100
(A-B) = +10 or -10
Thus, we could have FOUR solutions here:
A = 11, B = 1
A = -9, B = 1
A = 9, B = -1
A = -11, B = -1
IF.... B = 0, then we have...
(A-0)^2 + 0 = 108
(A)^2 = 108
108 is NOT a perfect square though, so there are no solutions here.
Total solutions = four + four = 8
Final Answer:
GMAT assassins aren't born, they're made,
Rich
While this question 'looks' complex, it can be organized into some simple ideas; those ideas - along with a bit of BRUTE FORCE arithmetic - can get you to the solution without too much trouble.
We're told that (A - B)^2 + 8(B^2) = 108 and that A and B are both INTEGERS.
In simple terms:
(A perfect square) + 8(A perfect square) = 108
Since perfect squares cannot be negative, and that second perfect square is multiplied by EIGHT, there can't be that many solutions to this equation. Let's focus on that second perfect square....If the first perfect square was 0, then we'd have....
0 + 8(a perfect square) = 108
(a perfect square) = 108/8 = 13.5
Since B is an INTEGER, we know that this equation is NOT possible - but we can use it to determine that that perfect square is less than 13.5. Thus, we really only have to think about 0, 1, 4 and 9 for that second perfect square. Let's start 'big' and work our way down...
IF.... B = 3 or -3, then we have...
(A-B)^2 + 72 = 108
(A-B)^2 = 36
(A-B) = +6 or -6
Thus, we could have FOUR solutions here:
A = 9, B = 3
A = -3, B = 3
A = -9, B = -3
A = 3, B = -3
IF.... B = 2 or -2, then we have...
(A-B)^2 + 32 = 108
(A-B)^2 = 76
76 is NOT a perfect square though, so there are no solutions here.
IF.... B = 1 or -1, then we have...
(A-B)^2 + 8 = 108
(A-B)^2 = 100
(A-B) = +10 or -10
Thus, we could have FOUR solutions here:
A = 11, B = 1
A = -9, B = 1
A = 9, B = -1
A = -11, B = -1
IF.... B = 0, then we have...
(A-0)^2 + 0 = 108
(A)^2 = 108
108 is NOT a perfect square though, so there are no solutions here.
Total solutions = four + four = 8
Final Answer:
GMAT assassins aren't born, they're made,
Rich
