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04 Oct 2021, 03:15
Kudos
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
62% (01:21) correct
38%
(01:03)
wrong
based on 154
sessions
History
Date
Time
Result
Not Attempted Yet
The operation ? is defined on the set of real numbers by a?b = the larger of the numbers a and b. If a?0.5 = 0.5, which CANNOT be a value for a ?
I. \(\sqrt{2}\)
II. \(\sqrt{3}\)
III. \(\frac{1}{\sqrt{2}}\)
A. I only
B. II only
C. III only
D. I and II only
E. I, II, and III
I. \(\sqrt{2}\)
II. \(\sqrt{3}\)
III. \(\frac{1}{\sqrt{2}}\)
A. I only
B. II only
C. III only
D. I and II only
E. I, II, and III
04 Oct 2021, 09:06
Kudos
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Bunuel
a?0.5 = 0.5 => a is less than 0.5
I. \(\sqrt{2}\) => will be greater than 1, cannot be value of a
II. \(\sqrt{3}\) => will be greater than 1, cannot be value of a
III. \(\frac{1}{\sqrt{2}}\) => will be greater than \(\frac{1}{2\\
}\), cannot be value if a
Hence E
16 Jan 2022, 09:33
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Given that a?b = the larger of the numbers a and b and a?0.5 = 0.5 and we need to find which of the following cannot be the value of a
To find a?0.5 we need to compare a?0.5 with a?b
=> b = 0.5
=> to find the value of a?0.5 we need to replace b with 0.5 in a?b = the larger of the numbers a and b
=> a?0.5 = the larger of the numbers a and 0.5 = 0.5 (given)
=> a < 0.5
Now, lets take each answer choice and check which value is \(\geq\) 0.5
I. \(\sqrt{2}\) = 1.414 > 0.5 => a cannot be this value => TRUE
II. \(\sqrt{3}\) = 1.732 > 0.5 => a cannot be this value => TRUE
III. \(\frac{1}{\sqrt{2}}\)
Multiply numerator and denominator by \(\sqrt{2}\) we get
= \(\frac{\sqrt{2}}{ (\sqrt{2}* \sqrt{2}}\)
= \(\frac{\sqrt{2}}{2}\) = \(\frac{1.414}{2}\) = 0.707 > 0.5 => a cannot be this value => TRUE
=> All three values are > 0.5 => CANNOT be the value of a
So, Answer will be E
Hope it helps!
Watch the following video to learn the Basics of Functions and Custom Characters
To find a?0.5 we need to compare a?0.5 with a?b
=> b = 0.5
=> to find the value of a?0.5 we need to replace b with 0.5 in a?b = the larger of the numbers a and b
=> a?0.5 = the larger of the numbers a and 0.5 = 0.5 (given)
=> a < 0.5
Now, lets take each answer choice and check which value is \(\geq\) 0.5
I. \(\sqrt{2}\) = 1.414 > 0.5 => a cannot be this value => TRUE
II. \(\sqrt{3}\) = 1.732 > 0.5 => a cannot be this value => TRUE
III. \(\frac{1}{\sqrt{2}}\)
Multiply numerator and denominator by \(\sqrt{2}\) we get
= \(\frac{\sqrt{2}}{ (\sqrt{2}* \sqrt{2}}\)
= \(\frac{\sqrt{2}}{2}\) = \(\frac{1.414}{2}\) = 0.707 > 0.5 => a cannot be this value => TRUE
=> All three values are > 0.5 => CANNOT be the value of a
So, Answer will be E
Hope it helps!
Watch the following video to learn the Basics of Functions and Custom Characters
