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01 Jul 2022, 01:30
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
37% (02:20) correct
63%
(02:16)
wrong
based on 62
sessions
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If \(a, \ b, \ c, \ d\), and \(e\) are positive numbers and if \(\sqrt{a} + \sqrt{b} = \sqrt{c} + \sqrt{d} + \sqrt{e}\), then is \(b = d + e\) ?
(1) \(a = c\)
(2) \(a = d + e\)
Are You Up For the Challenge: 700 Level Questions
(1) \(a = c\)
(2) \(a = d + e\)
Are You Up For the Challenge: 700 Level Questions
09 Jul 2022, 04:52
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Given
a , b, c, d > 0
\(\sqrt[]{a} + \sqrt[]{b} = \sqrt[]{c} + \sqrt[]{d} + \sqrt[]{e}\)
Question
Is b = d + e ?
Statement 1
a = c
If a = c, then \(\sqrt[]{a} = \sqrt[]{c}\)
Cancelling, this from the base equation we get,
\(\sqrt[]{b} = \sqrt[]{d} + \sqrt[]{e}\)
Squaring both sides-
\((\sqrt[]{b})^2 = (\sqrt[]{d} + \sqrt[]{e})^2\)
\(b = d + e + 2 * \sqrt[]{de}\)
Hence, we can conclude that
\(b \neq d + e \)
Hence A is sufficient.
Statement 2
Statement 2 can be solved via observation, however let's take an example to make the thinking process relatively easy
We know that a = d + e
Say d = e = 1
Therefore a = 2
\(\sqrt[]{a} = \sqrt[]{2} \) = 1.414
\(1.414 + \sqrt[]{b} = \sqrt[]{c} + 1 + 1\)
Now if \(\sqrt[]{c}\) = 1.414
\( \sqrt[]{b} = 2\) , hence b = 4 and hence we can conclude that \(b \neq d + e \)
Alternatively,
if d = e = 1 and b = 2, a = 2
\(\sqrt[]{2} + \sqrt[]{2} = \sqrt[]{c} + 1 + 1\)
Hence, when
\(\sqrt[]{c} \approx 0.828 \), then b = d + e.
As we don't know the EXACT value of \(\sqrt[]{c}\), we can't conclude.
Hence the correct answer is A
a , b, c, d > 0
\(\sqrt[]{a} + \sqrt[]{b} = \sqrt[]{c} + \sqrt[]{d} + \sqrt[]{e}\)
Question
Is b = d + e ?
Statement 1
a = c
If a = c, then \(\sqrt[]{a} = \sqrt[]{c}\)
Cancelling, this from the base equation we get,
\(\sqrt[]{b} = \sqrt[]{d} + \sqrt[]{e}\)
Squaring both sides-
\((\sqrt[]{b})^2 = (\sqrt[]{d} + \sqrt[]{e})^2\)
\(b = d + e + 2 * \sqrt[]{de}\)
Hence, we can conclude that
\(b \neq d + e \)
Hence A is sufficient.
Statement 2
Statement 2 can be solved via observation, however let's take an example to make the thinking process relatively easy
We know that a = d + e
Say d = e = 1
Therefore a = 2
\(\sqrt[]{a} = \sqrt[]{2} \) = 1.414
\(1.414 + \sqrt[]{b} = \sqrt[]{c} + 1 + 1\)
Now if \(\sqrt[]{c}\) = 1.414
\( \sqrt[]{b} = 2\) , hence b = 4 and hence we can conclude that \(b \neq d + e \)
Alternatively,
if d = e = 1 and b = 2, a = 2
\(\sqrt[]{2} + \sqrt[]{2} = \sqrt[]{c} + 1 + 1\)
Hence, when
\(\sqrt[]{c} \approx 0.828 \), then b = d + e.
As we don't know the EXACT value of \(\sqrt[]{c}\), we can't conclude.
Hence the correct answer is A
13 Jul 2022, 05:29
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a, b, c, d and e are all positive numbers
Q. Is b = d + e ?
st 1. a = c implies sqrt a = sqrt c
given equation can be reduced to
sqrt b = sqrt d + sqrt e
Squaring both sides we get b = d + e + 2*sqrt(de). now sqrt (de) is a positive quantitly
therefore, we get a definite NO to the question, hence st 1 is Sufficient
St2. a = d + e
using this we can get a relationship between b and c but we cannot find the value of c or reduce the given equation to terms with b,d and e.
hence Insufficient.
Answer A
Q. Is b = d + e ?
st 1. a = c implies sqrt a = sqrt c
given equation can be reduced to
sqrt b = sqrt d + sqrt e
Squaring both sides we get b = d + e + 2*sqrt(de). now sqrt (de) is a positive quantitly
therefore, we get a definite NO to the question, hence st 1 is Sufficient
St2. a = d + e
using this we can get a relationship between b and c but we cannot find the value of c or reduce the given equation to terms with b,d and e.
hence Insufficient.
Answer A
