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Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
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x and y are positive numbers
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27 Jan 2022, 11:02
27 Jan 2022, 11:02
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\(x\) and \(y\) are positive numbers
\(\frac{x}{3} < \frac{y}{6} – 1\)
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.
\(\frac{x}{3} < \frac{y}{6} – 1\)
Quantity A |
Quantity B |
\(x\) |
\(y\) |
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.
x and y are positive numbers
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29 Jan 2022, 10:08
29 Jan 2022, 10:08
2
\(\frac{x}{3}<\frac{y}{6} -1\)
\(x< \frac{y}{2} -3\)
Here, irrespective of the values of x and y, it is clear that x< y.
Hence, answer is B.
\(x< \frac{y}{2} -3\)
Here, irrespective of the values of x and y, it is clear that x< y.
Hence, answer is B.
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: x and y are positive numbers
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30 Jan 2022, 09:12
30 Jan 2022, 09:12
1
GreenlightTestPrep wrote:
\(x\) and \(y\) are positive numbers
\(\frac{x}{3} < \frac{y}{6} – 1\)
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.
\(\frac{x}{3} < \frac{y}{6} – 1\)
Quantity A |
Quantity B |
\(x\) |
\(y\) |
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.
Given: \(\frac{x}{3} < \frac{y}{6} – 1\)
Eliminate the fractions by multiplying both sides of the inequality by \(6\) (the LCM of 3 and 6) to get: \(2x < y - 6\)
Add \(6\) to both sides: \(2x + 6 < y\)
Since \(2x < 2x + 6\), we can add this to our inequality to get: \(2x< 2x + 6 < y\)
Useful property: If \(k > 0\), then \(k < 2k < 3k < 4k …etc. \)
Since we're told \(x\) is positive, we can add another component to our inequality to get: \(x < 2x< 2x + 6 < y\)
At this point, it's clear that x < y, which means the answer is B
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