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a = b + 1 and 5 < ab < 8
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01 Dec 2020, 03:06
01 Dec 2020, 03:06
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\(a = b + 1\) and \(5 < ab < 8\)
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 |
\(2a+b^2\) |
\(a^2+2b\) |
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
Re: a = b + 1 and 5 < ab < 8
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01 Dec 2020, 03:59
01 Dec 2020, 03:59
2
column A: 2a+b^2 ? column B: a^2+2b
plug in the value a=b+1 in both column
2b+2+b^2 ? b^2+2b+1+2b
2 ? 1+2b [eliminating the common terms]
1 ? 2b [subtacting 1]
1/2 ? b [divide by 2]
case-1: if b= 2 then a=3 ab=6 [greater than 1/2]
case-2: if b=-3 then a=-2 ab=6 [less than 1/2]
b can be both positive and negative and still satisfies the condition 5<ab<8
therefore, D will be the answer.
plug in the value a=b+1 in both column
2b+2+b^2 ? b^2+2b+1+2b
2 ? 1+2b [eliminating the common terms]
1 ? 2b [subtacting 1]
1/2 ? b [divide by 2]
case-1: if b= 2 then a=3 ab=6 [greater than 1/2]
case-2: if b=-3 then a=-2 ab=6 [less than 1/2]
b can be both positive and negative and still satisfies the condition 5<ab<8
therefore, D will be the answer.
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a = b + 1 and 5 < ab < 8
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04 Dec 2020, 08:58
04 Dec 2020, 08:58
1
Carcass wrote:
\(a = b + 1\) and \(5 < ab < 8\)
Quantity A |
Quantity B |
\(2a+b^2\) |
\(a^2+2b\) |
We can solve this question using matching operations (my favorite Quantitative Comparison strategy)
Given:
Quantity A: \(2a+b^2\)
Quantity B: \(a^2+2b\)
Since we're told \(a = b + 1\), we can replace \(a\) with \(b + 1\) to get:
Quantity A: \(2(b + 1)+b^2\)
Quantity B: \((b + 1)^2+2b\)
Expand and simplify both quantities:
Quantity A: \(b^2+2b+2\)
Quantity B: \(b^2+4b+1\)
Subtract \(b^2\) from both quantities:
Quantity A: \(2b+2\)
Quantity B: \(4b+1\)
Subtract \(2b\) from both quantities:
Quantity A: \(2\)
Quantity B: \(2b+1\)
Subtract \(1\) from both quantities:
Quantity A: \(1\)
Quantity B: \(2b\)
Divide both quantities by \(2\):
Quantity A: \(0.5\)
Quantity B: \(b\)
We're told that 5 < ab < 8, however there are infinitely many values of a and b that satisfy this inequality.
For example, it could be the case that a = -2 and b = -3, in which case, Quantity A is greater
It could also be the case that a = 3 and b = 2, in which case, Quantity B is greater
Answer: D
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