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kiran120680
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Joined: 18 Feb 2019
Last visit: 27 Jul 2022
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Schools: AGSM '20 EDHEC Sept 2019 Intake Great Lakes '21 IE
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Updated on: 17 Apr 2019, 08:40
Originally posted by kiran120680 on 17 Apr 2019, 04:53.
Last edited by kiran120680 on 17 Apr 2019, 08:40, edited 1 time in total.
Last edited by kiran120680 on 17 Apr 2019, 08:40, edited 1 time in total.
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A
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35% (02:38) correct
65%
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wrong
based on 150
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If A and B are integers, is the product AB even?
I. A + B = √(10A+3B)
II. (66B-2)/A= 13A-B
I. A + B = √(10A+3B)
II. (66B-2)/A= 13A-B
17 Apr 2019, 08:31
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If A and B are integers, is the product AB even?
If any of A and B is even, AB will be even.
I. A + B = √10A+3B
A-2B=√10A.... Square both sides.. \(A^2+4B^2-4AB=10A...........A^2=10A+4AB-4B^2=2(5A+2AB-2B^2)\)..
Therefore, A is a multiple of 2. So, AB is even.
Sufficient
Edited version.. A+B=√(10A+3B)
Square both sides.. \(A^2+B^2+2AB=10A+3B\)... Let us see if both A and B are odd
\(odd^2+odd^2+2*odd*odd=10*odd+3*odd....O+O+E=E+O.....E+E=E+O...E=O\)..Not possible
So at least one is even. Which one is not required, we can say AB will be even
Sufficient
II. (66B-2)/A= 13A-B
66B-2=13A^2-AB......\(AB=66B-2-13A^2\)..
Therefore if A is even \(even=even*B-2-13*even\).. possible
If A and B are odd..\(odd*odd=66*odd-even-13*odd......odd=even-even-odd\)... possible
So AB can be even or Odd
Insufficient
A
If any of A and B is even, AB will be even.
I. A + B = √10A+3B
A-2B=√10A.... Square both sides.. \(A^2+4B^2-4AB=10A...........A^2=10A+4AB-4B^2=2(5A+2AB-2B^2)\)..
Therefore, A is a multiple of 2. So, AB is even.
Sufficient
Edited version.. A+B=√(10A+3B)
Square both sides.. \(A^2+B^2+2AB=10A+3B\)... Let us see if both A and B are odd
\(odd^2+odd^2+2*odd*odd=10*odd+3*odd....O+O+E=E+O.....E+E=E+O...E=O\)..Not possible
So at least one is even. Which one is not required, we can say AB will be even
Sufficient
II. (66B-2)/A= 13A-B
66B-2=13A^2-AB......\(AB=66B-2-13A^2\)..
Therefore if A is even \(even=even*B-2-13*even\).. possible
If A and B are odd..\(odd*odd=66*odd-even-13*odd......odd=even-even-odd\)... possible
So AB can be even or Odd
Insufficient
A
kiran120680
Moderator - Masters Forum
Joined: 18 Feb 2019
Last visit: 27 Jul 2022
Posts: 706
Own Kudos:
Given Kudos: 276
Location: India
Schools: AGSM '20 EDHEC Sept 2019 Intake Great Lakes '21 IE
GMAT 1: 460 Q42 V13
GPA: 3.6
Schools: AGSM '20 EDHEC Sept 2019 Intake Great Lakes '21 IE
GMAT 1: 460 Q42 V13
Posts: 706
Kudos:
2,720
17 Apr 2019, 08:40
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chetan2u
Edited Statment I.
