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Jagan212
Joined: 06 Apr 2018
Last visit: 26 May 2024
Posts: 34
Given Kudos: 35
Location: India
Schools: IIMC MBAEx'23 (D) IIMA PGPX'23
GMAT 1: 620 Q43 V32
GPA: 3.2
07 Aug 2020, 20:10
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
43% (02:03) correct
57%
(01:41)
wrong
based on 203
sessions
History
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Not Attempted Yet
If \(a\) and \(b\) are positive integers, what is the value of \(a + b\)?
1. \(a^2-2ab+b^2 = 25\)
2. \(a^2-b^2 = -25\)
1. \(a^2-2ab+b^2 = 25\)
2. \(a^2-b^2 = -25\)
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
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Data Sufficiency Forum
If a and b are positive integers, what is the value of a+b?
1. a^2−2ab+b^2=25
Taking statement one alone,
(a-b)^2 = 25 ==> a-b = +-5
As multiple values are possible for a and b, statement 1 alone is not sufficient.
2. a^2−b^2=−25
Taking statement two alone,
=> a^2−b^2=−25
=> (a+b) (a-b) = -25
As a and b are positive integers, "b" has to be greater to get product of above as negative.
i.e. b>a and (a+b) (a-b) = -25.
Only possible positive integer values for a,b is 12,13 respectively.
Statement 2 is sufficient. Answer is B.
1. a^2−2ab+b^2=25
Taking statement one alone,
(a-b)^2 = 25 ==> a-b = +-5
As multiple values are possible for a and b, statement 1 alone is not sufficient.
2. a^2−b^2=−25
Taking statement two alone,
=> a^2−b^2=−25
=> (a+b) (a-b) = -25
As a and b are positive integers, "b" has to be greater to get product of above as negative.
i.e. b>a and (a+b) (a-b) = -25.
Only possible positive integer values for a,b is 12,13 respectively.
Statement 2 is sufficient. Answer is B.
08 Aug 2020, 01:40
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Jagan212
Hello guys!
Statement 1 says that,
\(a^2-2ab+b^2 = 25\)
\((a-b)^2= 25\)
\(a-b= +/- 5\)
It is not sufficient, because there is no unique solution available.
Statement 2 says that,
\(a^2-b^2 = -25\)
\((a+b) (a-b)= -25\)
After skimming it, it is evident that statement 2 is sufficient.
Still, the number at the place of 'b' should be greater for the final value to be negative, i.e. -25
So, this statement is sufficient with a= 12 and b=13 as its values.
Official Answer:- Option B
Thank you!
Regards,
Raunak Damle
