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27 Feb 2020, 00:24
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
68% (01:35) correct
32%
(01:43)
wrong
based on 106
sessions
History
Date
Time
Result
Not Attempted Yet
If r, a and b are positive integers, is r a product of two consecutive odd integers?
(1) r = 4a^2 - b^2
(2) b = 1
(1) r = 4a^2 - b^2
(2) b = 1
03 Mar 2020, 05:56
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A.
r = 4a^2 - b^2
r = (2a)^2 - b^2
r = (2a+b)(2a-b)
This means that r is the product of an even number minus b and that even number plus b.
If b is even, then r is the product of two even numbers while if b is odd, r is the product of two odd numbers.
Hence, INSUFFICIENT.
B.
Clearly INSUFFICIENT.
Combining A and B, we get r = (2a+1)(2a-1) which is the product of two odd numbers.
Hence, SUFFICIENT.
r = 4a^2 - b^2
r = (2a)^2 - b^2
r = (2a+b)(2a-b)
This means that r is the product of an even number minus b and that even number plus b.
If b is even, then r is the product of two even numbers while if b is odd, r is the product of two odd numbers.
Hence, INSUFFICIENT.
B.
Clearly INSUFFICIENT.
Combining A and B, we get r = (2a+1)(2a-1) which is the product of two odd numbers.
Hence, SUFFICIENT.
General Discussion
Updated on: 06 Mar 2023, 01:20
Originally posted by GMATinsight on 27 Feb 2020, 01:07.
Last edited by Bunuel on 06 Mar 2023, 01:20, edited 2 times in total.
Last edited by Bunuel on 06 Mar 2023, 01:20, edited 2 times in total.
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Bunuel
Question: Is r product of two consecutive odd inetegers?
Statement 1: r = 4a^2 - b^2
@a = 1 and b = 1, r = 3 = 1*3 i.e. Answer to Question is YES
@a = 2 and b = 2, r = 12 = 3*4 i.e. Answer to Question is NO
NOT SUFFICIENT
Statement 2: b = 1
No connection between r and b hence
NOT SUFFICIENT
COmbining the two statements
@a = 1 and b = 1, r = 3 = 1*3 i.e. Answer to Question is YES
@a = 2 and b = 1, r = 15 = 3*5 i.e. Answer to Question is YES (Induction says SUFFICIENT)
ALGEBRA: r = 4a^2 - b^2 = r = 4a^2 - 1 = (2a+1)*(2a-1) which is product of two ODD integers hence
SUFFICIENT
Answetr: Option C
