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The product of positive integers f, g, and h is even and the
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02 Sep 2018, 07:18
02 Sep 2018, 07:18
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The product of positive integers f, g, and h is even and the product of integers f and g is odd.
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Quantity A |
Quantity B |
The remainder when f is divided by 2 |
The remainder when h is divided by 2 |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
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Re: The product of positive integers f, g, and h is even and the
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05 Nov 2019, 06:42
05 Nov 2019, 06:42
sandy wrote:
The product of positive integers f, g, and h is even and the product of integers f and g is odd.
Quantity A |
Quantity B |
The remainder when f is divided by 2 |
The remainder when h is divided by 2 |
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
GIVEN: The product of integers f and g is odd
In other words: (f)(g) = ODD
Rule #4 tells us that f is ODD, and g is ODD
GIVEN: The product of positive integers f, g, and h is even
In other words: (f)(g)(h) = EVEN
Replace (f)(g) with ODD to get: (ODD)(h) = EVEN
Rule #5 tells us that h is EVEN
QUANTITY A: The remainder when f is divided by 2
Since f is ODD, the remainder will be 1
QUANTITY B: The remainder when h is divided by 2
Since h is EVEN, the remainder will be 0
1 > 0, so the correct answer is A
Cheers,
Brent
Re: The product of positive integers f, g, and h is even and the
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23 Feb 2024, 21:56
23 Feb 2024, 21:56
1
The product of any two odds will result in an odd. So f and g are odd. And the only way the product of f,g and h will be even is when h is even.
Quantity A: The remainder when f is divided by 2. When an odd number is divided by 2 the remainder will be 1.
Quantity B: The remainder when h is divided by 2. When an even number is divided by 2, the remainder will be 0.
Therefore, Quantity A is greater.
Quantity A: The remainder when f is divided by 2. When an odd number is divided by 2 the remainder will be 1.
Quantity B: The remainder when h is divided by 2. When an even number is divided by 2, the remainder will be 0.
Therefore, Quantity A is greater.
