Forum Home > GMAT > Quantitative > Problem Solving (PS)
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.
Dec 1310:00 AM EST
-12:00 PM EST
Have you ever wondered how to score a PERFECT 805 on the GMAT? Meet Julia, a banking professional who used the Target Test Prep course to achieve this incredible feat. Julia's story is nothing short of an inspiration.
Dec 1207:30 AM PST
-08:30 AM PST
Join the conversation to learn more about INSEAD vs LBS
Dec 1410:00 AM EST
-12:00 PM EST
Think a 100% GMAT Verbal score is out of your reach? Target Test Prep will make you think again! Our course uses techniques such as topical study and spaced repetition to maximize knowledge retention and make studying simple and fun.
Dec 1411:00 AM IST
-01:00 PM IST
Attend this session to learn how to Deconstruct arguments, Pre-Think Author’s Assumptions, and apply Negation Test.- Dec 15
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. - Dec 16
08:00 AM PST
-11:59 PM PST
GMAT Club 12 Days of Christmas is a 4th Annual GMAT Club Winter Competition based on solving questions. This is the Winter GMAT competition on GMAT Club with an amazing opportunity to win over $40,000 worth of prizes! - Dec 17
09:00 AM PST
-10:00 AM PST
Join Manhattan Prep instructor Whitney Garner for a fun—and thorough—review of logic-based (non-math) problems, with a particular emphasis on Data Sufficiency and Two-Parts. - Dec 18
10:00 AM PST
-11:00 AM PST
Here is the essential guide to securing scholarships as an MBA student! In this video, we explore the various types of scholarships available, including need-based and merit-based options.
11 Mar 2020, 12:13
Kudos
Bookmarks
C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
41% (01:57) correct
59%
(02:32)
wrong
based on 53
sessions
History
Date
Time
Result
Not Attempted Yet
How many pairs of positive integers (a, b) satisfy the equation the equation a^2 = 135 + b^2?
A. 2
B. 3
C. 4
D. 5
E. 6
Posted from my mobile device
A. 2
B. 3
C. 4
D. 5
E. 6
Posted from my mobile device
11 Mar 2020, 12:26
Kudos
Bookmarks
Dillesh4096
How many pairs of positive integers (a, b) satisfy the equation the equation a^2 = 135 + b^2?
A. 2
B. 3
C. 4
D. 5
E. 6
Posted from my mobile device
A. 2
B. 3
C. 4
D. 5
E. 6
Posted from my mobile device
\(a^2 = 135 + b^2\)
\(=> a^2 - b^2 = 135 \)
\(=> (a+b)(a-b) = 135\)
Since a and b are positive integers, we must have: \(a + b > a - b\)
Thus, breaking 135 as a product of its 2 factors, we have:
#1. a+b = 135, a-b = 1
#2. a+b = 45, a-b = 3
#3. a+b = 27, a-b = 5
#4. a+b = 15, a-b = 9
Thus, there are 4 pairs
(Note: each pair above is a combination of 2 odd numbers, which when solved, would ensure integer values of a and b)
Alternative approach:
Number of factors of 135 (= \(3^3 * 5^1\)) is: (3 + 1)*(1 + 1) = 8
=> Number of ways 135 can be broken as a product of 2 factors = 8/2 = 4
Note: This would not necessarily work if there was an even number in place of 135 - think why
shameekv1989
11 Mar 2020, 12:44
Kudos
Bookmarks
sujoykrdatta
Dillesh4096
How many pairs of positive integers (a, b) satisfy the equation the equation a^2 = 135 + b^2?
A. 2
B. 3
C. 4
D. 5
E. 6
Posted from my mobile device
A. 2
B. 3
C. 4
D. 5
E. 6
Posted from my mobile device
\(a^2 = 135 + b^2\)
\(=> a^2 - b^2 = 135 \)
\(=> (a+b)(a-b) = 135\)
Since a and b are positive integers, we must have: \(a + b > a - b\)
Thus, breaking 135 as a product of its 2 factors, we have:
#1. a+b = 135, a-b = 1
#2. a+b = 45, a-b = 3
#3. a+b = 27, a-b = 5
#4. a+b = 15, a-b = 9
Thus, there are 4 pairs
(Note: each pair above is a combination of 2 odd numbers, which when solved, would ensure integer values of a and b)
Alternative approach:
Number of factors of 135 (= \(3^3 * 5^1\)) is: (3 + 1)*(1 + 1) = 8
=> Number of ways 135 can be broken as a product of 2 factors = 8/2 = 4
Note: This would not necessarily work if there was an even number in place of 135 - think why
sujoykrdatta :- Is it because if a number is even then it might have an Even*Odd combination in which case, solving a+b and a-b will not result in an integer for a and b?
For odd numbers, all the factors are odd and thus a-b and a+b will both be odd numbers and when we solve these equations it will result in an integer for a and b.
