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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2506
Given Kudos: 1055
GPA: 3.39
If k and t are integers and k^2 t^2 is an odd integer, which of the
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03 Jan 2023, 10:01
03 Jan 2023, 10:01
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Expert Reply
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Question Stats:
50% (01:25) correct
50% (02:22) wrong based on 4 sessions
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If k and t are integers and k^2 – t^2 is an odd integer, which of the following must be an even integer?
I. k + t + 2
II. k^2 + 2kt + t^2
III. k^2 + t^2
A. None
B. I only
C. II only
D. III only
E. I, II, and III
I. k + t + 2
II. k^2 + 2kt + t^2
III. k^2 + t^2
A. None
B. I only
C. II only
D. III only
E. I, II, and III
GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2506
Given Kudos: 1055
GPA: 3.39
Re: If k and t are integers and k^2 t^2 is an odd integer, which of the
[#permalink]
05 Jan 2023, 10:06
05 Jan 2023, 10:06
1
Expert Reply
If k and t are integers and k^2 – t^2 is an odd integer, which of the following must be an even integer?
I. k + t + 2
II. k^2 + 2kt + t^2
III. k^2 + t^2
A. None
B. I only
C. II only
D. III only
E. I, II, and III
k^2 -t^2 = odd
so, if k is even, t will be odd.
I. k+t+2 = even+odd+2 = odd
II. k^2 + 2kt+t^2 = even + even + odd = odd
III. k^2 + t^2 = even + odd = odd
Answer: A
I. k + t + 2
II. k^2 + 2kt + t^2
III. k^2 + t^2
A. None
B. I only
C. II only
D. III only
E. I, II, and III
k^2 -t^2 = odd
so, if k is even, t will be odd.
I. k+t+2 = even+odd+2 = odd
II. k^2 + 2kt+t^2 = even + even + odd = odd
III. k^2 + t^2 = even + odd = odd
Answer: A
gmatclubot
Re: If k and t are integers and k^2 t^2 is an odd integer, which of the [#permalink]
05 Jan 2023, 10:06
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