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If a, b, and c are integers and a(b - c) is odd, which of the followin
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06 Jul 2021, 08:06
06 Jul 2021, 08:06
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If a, b, and c are integers and a(b - c) is odd, which of the following must be odd?
A. b
B. c
C. ab
D. ab + c
E. abc
A. b
B. c
C. ab
D. ab + c
E. abc
If a, b, and c are integers and a(b - c) is odd, which of the followin
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06 Jul 2021, 08:57
06 Jul 2021, 08:57
1
Solution:
a(b-c)= odd
The above is possible when b-c= odd & a=odd
Now, note that b-c is odd also means that either of the two should be even and the other has to be odd.
Therefore, all the possibilities, suggesting above can be eliminated.
A. b- Can be even
B. c- Can be even
C. ab-Can be even- if b is even and a is odd the product would be even
D. ab + c= if b is odd then, odd*odd+even=odd+even= odd or if b is even, even*odd+odd=even+odd=odd--Correct option
E. abc- Can give us a even product.
IMO D
Hope this helps!
a(b-c)= odd
The above is possible when b-c= odd & a=odd
Now, note that b-c is odd also means that either of the two should be even and the other has to be odd.
Therefore, all the possibilities, suggesting above can be eliminated.
A. b- Can be even
B. c- Can be even
C. ab-Can be even- if b is even and a is odd the product would be even
D. ab + c= if b is odd then, odd*odd+even=odd+even= odd or if b is even, even*odd+odd=even+odd=odd--Correct option
E. abc- Can give us a even product.
IMO D
Hope this helps!
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Re: If a, b, and c are integers and a(b - c) is odd, which of the followin
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06 Jul 2021, 09:08
06 Jul 2021, 09:08
Carcass wrote:
If a, b, and c are integers and a(b - c) is odd, which of the following must be odd?
A. b
B. c
C. ab
D. ab + c
E. abc
A. b
B. c
C. ab
D. ab + c
E. abc
One approach here is to test some values that satisfy the initial condition
If a(b - c) is odd, then it COULD be the case that a = 1, b = 2 and c = 1
Now let's plug these values into our answer choices...
A. b = 2
2 is NOT odd, so eliminate A
B. c = 1
1 is odd, so keep B
C. ab = (1)(2) = 2
2 is NOT odd, so eliminate C
D. ab + c = (1)(2) + 1 = 3
3 is odd, so keep D
E. abc = (1)(2)(1) = 2
2 is NOT odd, so eliminate E
At this point, we're left with answer choices B and D
So that's test another set of values
If a(b - c) is odd, then it COULD be the case that a = 2, b = 1 and c = 1
Now let's plug these values into the remaining answer choices...
B. c = 2
2 is NOT odd, so eliminate B
By the process of elimination, the correct answer must be D
Cheers,
Brent
