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02 Jun 2025, 10:11
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D
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If \( k \) is a positive even integer, which of the following must be an odd integer?
I. \( k^2 - 3k + 4 \)
II. \( k^5 + 3 \)
III. \( 7k - 7 \)
(A) II only
(B) III only
(C) I and III only
(D) II and III only
(E) I, II, and III
Source: Quantitative Review 2025-26
I. \( k^2 - 3k + 4 \)
II. \( k^5 + 3 \)
III. \( 7k - 7 \)
(A) II only
(B) III only
(C) I and III only
(D) II and III only
(E) I, II, and III
Source: Quantitative Review 2025-26
02 Jun 2025, 10:31
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kingbucky
If \( k \) is a positive even integer, which of the following must be an odd integer?
I. \( k^2 - 3k + 4 \)
II. \( k^5 + 3 \)
III. \( 7k - 7 \)
(A) II only
(B) III only
(C) I and III only
(D) II and III only
(E) I, II, and III
Source: Quantitative Review 2025-26
I. \( k^2 - 3k + 4 \)
II. \( k^5 + 3 \)
III. \( 7k - 7 \)
(A) II only
(B) III only
(C) I and III only
(D) II and III only
(E) I, II, and III
Source: Quantitative Review 2025-26
I. \( k^2 - 3k + 4=even^2 - 3*even + even = even - even+even=even \)
II. \( k^5 + 3 =even^5 + odd= even + odd=odd\)
III. \( 7k - 7 =7*even - odd = even - odd=odd\)
Answer: D.
GraemeGmatPanda
Joined: 13 Apr 2020
Last visit: 04 Jul 2025
Posts: 70
Own Kudos:
Given Kudos: 18
Location: United Kingdom
Concentration: Marketing
Schools: LBS '16 (A$)
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02 Jun 2025, 11:10
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Another way of doing this one, is to replace k by 0 (which is an even number)
I = 0 - 0 + 4 = even
II = 0 + 3 = odd
III = 0 - 7 = odd
I = 0 - 0 + 4 = even
II = 0 + 3 = odd
III = 0 - 7 = odd
kingbucky
If \( k \) is a positive even integer, which of the following must be an odd integer?
I. \( k^2 - 3k + 4 \)
II. \( k^5 + 3 \)
III. \( 7k - 7 \)
(A) II only
(B) III only
(C) I and III only
(D) II and III only
(E) I, II, and III
Source: Quantitative Review 2025-26
I. \( k^2 - 3k + 4 \)
II. \( k^5 + 3 \)
III. \( 7k - 7 \)
(A) II only
(B) III only
(C) I and III only
(D) II and III only
(E) I, II, and III
Source: Quantitative Review 2025-26
