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If pq is different from zero
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29 Jan 2020, 09:56
29 Jan 2020, 09:56
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\(pq \neq 0\)
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.
Kudos for the right answer and explanation
Quantity A |
Quantity B |
\((p+q)^3\) |
\(p^3+q^3\) |
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.
Kudos for the right answer and explanation
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Re: If pq is different from zero
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Updated on: 29 Jan 2020, 11:18
Updated on: 29 Jan 2020, 11:18
1
Carcass wrote:
\(pq \neq 0\)
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.
Kudos for the right answer and explanation
Quantity A |
Quantity B |
\((p+q)^3\) |
\(p^3+q^3\) |
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.
Kudos for the right answer and explanation
Quantity A: \((p+q)^3 = p^3 + q^3 + 3pq(p+q)\)
Quantity B: \(p^3 + q^3\)
We need to compare:
\(p^3 + q^3 + 3pq(p+q)\) VS \(p^3 + q^3\)
Subtracting \(p^3 + q^3\) from both sides, we have:
\(3pq(p + q)\) VS 0
# If \(p > 0\) and \(q > 0\): \(3pq(p+q) > 0\) => Quantity A is greater than Quantity B
# If \(p < 0\) and \(q < 0\): \(3pq(p+q) < 0\) (since \(pq > 0\) and \((p+q)<0\)) => Quantity A is smaller than Quantity B
Thus, there is no relation
Answer D
Originally posted by sujoykrdatta on 29 Jan 2020, 11:03.
Last edited by sujoykrdatta on 29 Jan 2020, 11:18, edited 1 time in total.
Last edited by sujoykrdatta on 29 Jan 2020, 11:18, edited 1 time in total.
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If pq is different from zero
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29 Jan 2020, 11:05
29 Jan 2020, 11:05
1
Carcass wrote:
\(pq \neq 0\)
Quantity A |
Quantity B |
\((p+q)^3\) |
\(p^3+q^3\) |
One option here is to expand and simplify Quantity A. The problem is that this approach could take a while.
Instead, I'm going to test some values
case i: Since \(pq \neq 0\), it COULD be the case that \(p = -1\) and \(q = 1\)
We get:
Quantity A: \((p+q)^3=((-1)+1)^3=0^3=0\)
Quantity B: \(p^3+q^3=(-1)^3+1^3=(-1)+1=0\)
In this case, the two quantities are equal
case ii: Alternatively, it could be the case that \(p = 1\) and \(q = 1\)
We get:
Quantity A: \((p+q)^3=(1+1)^3=2^3=8\)
Quantity B: \(p^3+q^3=1^3+1^3=1+1=2\)
In this case, Quantity A is greater
Answer: D
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