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18 Jun 2018, 03:10
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B
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Difficulty:
15%
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Question Stats:
88% (01:34) correct
12%
(01:55)
wrong
based on 52
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If \(-8 < x < -6\) and \(2 < y < 3\), which of the following could be the value of \(\sqrt{-xy}\)?
A. 3
B. 4
C. 5
D. 6
E. 7
A. 3
B. 4
C. 5
D. 6
E. 7
18 Jun 2018, 03:10
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Official Solution:
If \(-8 < x < -6\) and \(2 < y < 3\), which of the following could be the value of \(\sqrt{-xy}\)?
A. 3
B. 4
C. 5
D. 6
E. 7
Multiplying \(-8 < x < -6\) by \(-1\) yields \(6 < -x < 8\). Since \(2 < y < 3\), it follows (by multiplication) that \(12 < (-x)y < 24\). Taking square roots (since all numbers are positive) yields \(\sqrt{12} < \sqrt{-xy} < \sqrt{24}\). Since \(3 < \sqrt{12}\) and \(5 > \sqrt{24}\), 4 is one possible value of \(\sqrt{-xy}\).
Answer: B
If \(-8 < x < -6\) and \(2 < y < 3\), which of the following could be the value of \(\sqrt{-xy}\)?
A. 3
B. 4
C. 5
D. 6
E. 7
Multiplying \(-8 < x < -6\) by \(-1\) yields \(6 < -x < 8\). Since \(2 < y < 3\), it follows (by multiplication) that \(12 < (-x)y < 24\). Taking square roots (since all numbers are positive) yields \(\sqrt{12} < \sqrt{-xy} < \sqrt{24}\). Since \(3 < \sqrt{12}\) and \(5 > \sqrt{24}\), 4 is one possible value of \(\sqrt{-xy}\).
Answer: B
16 Aug 2019, 03:32
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Ok, so i came up with a much simpler solution...
Since it is a "could be" we don't have to be accurate.
Let's take x = -7 ( it's given -8<x<-6)
Now, we need to keep 2 things in mind.
1. We need a perfect square - since answers are integers
2. y needs to be little more than 2 but less than 3.
With this in mind, we can say -7*y = integer. From here i immediately thought of getting rid of 7. One way to do that is to take y = Something/7
Now, this something needs to be slightly larger than 7 times 2 i.e 14 and also a perfect square. 16 fits perfectly.
You have your answer.
This looks like a long explanation BUT it took about 30-40 seconds in total.
Since it is a "could be" we don't have to be accurate.
Let's take x = -7 ( it's given -8<x<-6)
Now, we need to keep 2 things in mind.
1. We need a perfect square - since answers are integers
2. y needs to be little more than 2 but less than 3.
With this in mind, we can say -7*y = integer. From here i immediately thought of getting rid of 7. One way to do that is to take y = Something/7
Now, this something needs to be slightly larger than 7 times 2 i.e 14 and also a perfect square. 16 fits perfectly.
You have your answer.
This looks like a long explanation BUT it took about 30-40 seconds in total.
