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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2506
Given Kudos: 1055
GPA: 3.39
If P is an odd integer and if Q is an even integer, which of
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19 Mar 2020, 21:27
19 Mar 2020, 21:27
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If P is an odd integer and if Q is an even integer, which of the following expressions CANNOT represent an even integer?
(A) 3P - Q
(B) 3P * Q
(C) 2Q * P
(D) 3Q - 2P
(E) 32P - 2Q
(A) 3P - Q
(B) 3P * Q
(C) 2Q * P
(D) 3Q - 2P
(E) 32P - 2Q
Re: If P is an odd integer and if Q is an even integer, which of
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07 May 2020, 08:45
07 May 2020, 08:45
1
GeminiHeat wrote:
If P is an odd integer and if Q is an even integer, which of the following expressions CANNOT represent an even integer?
(A) 3P - Q
(B) 3P * Q
(C) 2Q * P
(D) 3Q - 2P
(E) 32P - 2Q
(A) 3P - Q
(B) 3P * Q
(C) 2Q * P
(D) 3Q - 2P
(E) 32P - 2Q
Here,
We know,
ODD * EVEN = EVEN
ODD * ODD = ODD
ODD + EVEN = ODD
(A) 3P - Q = (ODD * ODD) - EVEN = ODD
(B) 3P * Q = (ODD * ODD) * EVEN = EVEN
(C) 2Q * P = (EVEN * EVEN) * ODD = EVEN
(D) 3Q - 2P = (ODD * EVEN) - (EVEN * ODD) = EVEN
(E) 32P - 2Q = (EVEN * ODD) - (EVEN * ODD) = EVEN
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: If P is an odd integer and if Q is an even integer, which of
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08 Jun 2021, 14:39
08 Jun 2021, 14:39
1
GeminiHeat wrote:
If P is an odd integer and if Q is an even integer, which of the following expressions CANNOT represent an even integer?
(A) 3P - Q
(B) 3P * Q
(C) 2Q * P
(D) 3Q - 2P
(E) 32P - 2Q
(A) 3P - Q
(B) 3P * Q
(C) 2Q * P
(D) 3Q - 2P
(E) 32P - 2Q
Some important rules:
#1. ODD +/- ODD = EVEN
#2. ODD +/- EVEN = ODD
#3. EVEN +/- EVEN = EVEN
#4. (ODD)(ODD) = ODD
#5. (ODD)(EVEN) = EVEN
#6. (EVEN)(EVEN) = EVEN
(A) 3P - Q
Since P is odd and Q is even we get: (ODD)(ODD) - EVEN
By rule #4, we get: ODD - EVEN
By rule #2, we get: ODD
Since 3P - Q must be ODD, we can also say that 3P - Q CANNOT represent an even number
Answer: A
Cheers,
Brent
