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If x < y, which of the following must be true?
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17 Dec 2017, 14:14
17 Dec 2017, 14:14
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47% (01:02) correct
52% (00:46) wrong based on 36 sessions
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If \(x < y\), which of the following must be true?
A. \(2x < y\)
B. \(2x > y\)
C. \(x^2 < y^2\)
D. \(2x-y < y\)
E. \(2x-y < 2xy\)
A. \(2x < y\)
B. \(2x > y\)
C. \(x^2 < y^2\)
D. \(2x-y < y\)
E. \(2x-y < 2xy\)
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Re: If x < y, which of the following must be true?
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31 Jan 2018, 20:50
31 Jan 2018, 20:50
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Expert Reply
In any question asking what must be true, you should try to imagine scenarios in which it isn't true. I'd start with the simplest looking answers and save the complex ones for last.
A. 2x < y
Does this have to be true? Let's pretend x = 5 and y = 6. So x<y but if you double x it's no longer smaller than y. This one's out.
B. 2x > y
OK this time let's imagine x = 1 and y = a billion. If we double x it's obviously not bigger than a billion, so this one's out.
C. x^2 < y^2
This one looks pretty good. It obviously could be true. But let's not settle for that. What if x was a large negative value and y a small positive value? For example, x = -10 and y = 2. This still fulfills the original inequality but when you square both you get 100 < 4, which isn't true. Out!
D. 2x-y < y
Always try to simplify equations and inequalities until they have the fewest number of terms possible. If we add y to both sides of this inequality, it turns into 2x < 2y. Dividing by 2 gets us x < y, which is the original inequality we were given. So this must be it!
E. 2x-y < 2xy
This one is meant to just waste your time. Luckily we already have the answer.
A. 2x < y
Does this have to be true? Let's pretend x = 5 and y = 6. So x<y but if you double x it's no longer smaller than y. This one's out.
B. 2x > y
OK this time let's imagine x = 1 and y = a billion. If we double x it's obviously not bigger than a billion, so this one's out.
C. x^2 < y^2
This one looks pretty good. It obviously could be true. But let's not settle for that. What if x was a large negative value and y a small positive value? For example, x = -10 and y = 2. This still fulfills the original inequality but when you square both you get 100 < 4, which isn't true. Out!
D. 2x-y < y
Always try to simplify equations and inequalities until they have the fewest number of terms possible. If we add y to both sides of this inequality, it turns into 2x < 2y. Dividing by 2 gets us x < y, which is the original inequality we were given. So this must be it!
E. 2x-y < 2xy
This one is meant to just waste your time. Luckily we already have the answer.
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Re: If x < y, which of the following must be true?
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06 May 2022, 07:58
06 May 2022, 07:58
Carcass wrote:
If \(x < y\), which of the following must be true?
A. \(2x < y\)
B. \(2x > y\)
C. \(x^2 < y^2\)
D. \(2x-y < y\)
E. \(2x-y < 2xy\)
A. \(2x < y\)
B. \(2x > y\)
C. \(x^2 < y^2\)
D. \(2x-y < y\)
E. \(2x-y < 2xy\)
When I scan the answer choices, I see that D looks promising.
D) 2x − y < y
Add y the both sides of the inequality: 2x < 2y
Divide both sides by 2 to get: x < y
So, D is equivalent to the original inequality x < y
Answer: D
Alternate approach: Test values
If x < y, then it could be the case that x = 1 and y = 2.
Plug these values into the five answer choices to get:
A. 2(1) < 2, which simplifies to 2 < 2. Not true. Eliminate.
B. 2(1) > 2, which simplifies to 2 > 2. Not true. Eliminate.
C. 1² < 2², which simplifies to 1 < 2. TRUE. Keep.
D. 2(1) − 2 < 2, which simplifies to 0 < 2. TRUE. Keep.
E. 2(1) − 2 < 2(1)(2), which simplifies to 0 < 4. TRUE. Keep.
We're down to options C, D and E.
Strategy: We first tested 2 positive values. Now that's test 1 negative and 1 positive.
We'll test x = -3 and y = 2.
Plug these values into the remaining answer choices to get:
C. (-3)² < 2², which simplifies to 9 < 4. Not true. Eliminate.
D. 2(-4) − 2 < 2, which simplifies to -10 < 2. TRUE. Keep.
E. 2(-3) − 2 < 2(-3)(2), which simplifies to -8 < -12. Not true. Eliminate.
By the process of elimination, the answer is D
