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Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
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a-1/b+1 vs a/b
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24 Aug 2020, 14:13
24 Aug 2020, 14:13
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a and b are both positive.
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 |
\(\frac{a-1}{b+1}\) |
\(\frac{a}{b}\) |
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.
Retired Moderator
Joined: 20 Aug 2020
Posts: 49
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Re: a-1/b+1 vs a/b
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24 Aug 2020, 14:24
24 Aug 2020, 14:24
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GreenlightTestPrep wrote:
a and b are both positive.
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 |
\(\frac{a-1}{b+1}\) |
\(\frac{a}{b}\) |
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.
When we compare \(A\) and \(B\), we can try to figure out \(A - B\) is positive or negative, since \(A > B\) is equivalent to \(A - B > 0\) and \(A < B\) is equivalent to \(A - B < 0\).
We have \(A - B = \frac{{a-1}}{{b+1}} - \frac{a}{b} = \frac{{b(a-1)-a(b+1)}}{{b(b+1)}} = \frac{{ab-b-ab-a}}{{b(b+1)}} = -\frac{{a+b}}{{b(b+1)}} < 0\), since \(a\) and \(b\) are positive.
Thus we have \(A < B\).
\(B\) is greater than \(A\).
Therefore, B is the right answer.
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: a-1/b+1 vs a/b
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25 Aug 2020, 06:17
25 Aug 2020, 06:17
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GreenlightTestPrep wrote:
a and b are both positive.
Quantity A |
Quantity B |
\(\frac{a-1}{b+1}\) |
\(\frac{a}{b}\) |
We can solve this question using matching operations (my favorite Quantitative Comparison strategy)
Given:
Quantity A: \(\frac{a-1}{b+1}\)
Quantity B: \(\frac{a}{b}\)
Since we're told b is positive, we can safely multiply both quantities by b to get:
Quantity A: \(\frac{b(a-1)}{b+1}\)
Quantity B: \(a\)
Also, if b is positive, we can be certain that b+1 is positive, which means we can multiply both quantities by b+1 to get:
Quantity A: \(b(a-1)\)
Quantity B: \(a(b+1)\)
Expand:
Quantity A: \(ab-b\)
Quantity B: \(ab+a\)
Subtract ab from both quantities:
Quantity A: \(-b\)
Quantity B: \(a\)
Add b to both quantities:
Quantity A: \(0\)
Quantity B: \(a+b\)
Since we're told that a and b are both positive, we can conclude that a+b is POSITIVE, which means Quantity B > Quantity A
Answer: B
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