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Difficulty:
45%
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Question Stats:
58% (01:23) correct
42%
(01:17)
wrong
based on 518
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If x > 0.9, which of the following could be the value of x?
A. √0.81
B. √0.9
C. (0.9)^2
D. (0.9)(0.99)
E. 1 - √0.01
A. √0.81
B. √0.9
C. (0.9)^2
D. (0.9)(0.99)
E. 1 - √0.01
If you decide to choose B, please tell me why E doesn't work, since the \sqrt{0.01} can be negative and the entire answer choice becomes greater than 1. However, B can be negative, which is smaller than 0.9.
11 Sep 2014, 21:45
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pohkid
If x > 0.9, which of the following could be the value of x?
A. √0.81
B. √0.9
C. (0.9)2
D. (0.9)(0.99)
E. 1 - √0.01
If you decide to choose B, please tell me why E doesn't work, since the \sqrt{0.01} can be negative and the entire answer choice becomes greater than 1. However, B can be negative, which is smaller than 0.9.
A. √0.81
B. √0.9
C. (0.9)2
D. (0.9)(0.99)
E. 1 - √0.01
If you decide to choose B, please tell me why E doesn't work, since the \sqrt{0.01} can be negative and the entire answer choice becomes greater than 1. However, B can be negative, which is smaller than 0.9.
You are missing a critical point here:
\(\sqrt{x}\) implies the principal square root i.e. the positive square root of x only.
For example:
\(\sqrt{9} = 3\) only.
\(\sqrt{9}\) is not -3.
When the question wants the negative square root, it will be written as \(-\sqrt{9} = -3\).
It might be against what you might have learnt in school but by convention (and certainly as far as GMAT is concerned), \(\sqrt{x}\) implies the positive square root only.
On the same lines, \(\sqrt{x^2} = |x|\) (only the positive value of x)
Therefore, √0.9 is a positive value greater than 0.9
and √0.01 has only one value which is 0.1 so option (E) becomes 1-0.1 = 0.9. It is not greater than 0.9
Answer (B) only.
12 Jan 2015, 16:39
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Hi All,
This question is built around a great Number Property rule that you might see on Test Day (although its usage is relatively rare).
When dealing with positive fractions (0 < X < 1).....what happens when you SQUARE a positive fraction?
eg
(1/3)^2 = (1/3)(1/3) = 1/9
Squaring a positive fraction makes the result SMALLER.
Since "squaring" and "square-rooting" are 'opposite' functions, what happens when you SQUARE-ROOT a positive fraction?
√(1/9) = √(1)/√(9) = 1/3
Square-rooting a positive fraction makes the result BIGGER.
In this question, you'll notice that the answer choices revolve around the use of 0.9
I want to focus on Answers B and C
Without doing the math, what happens when you SQUARE 0.9.....? The result will get SMALLER.
Without doing the math, what happens when you SQAURE ROOT 0.9....? The result will get BIGGER.
Since the question is asking which of the following values could be X (meaning....could be greater than 0.9), we don't have to do any more work...
Final Answer:
GMAT assassins aren't born, they're made,
Rich
This question is built around a great Number Property rule that you might see on Test Day (although its usage is relatively rare).
When dealing with positive fractions (0 < X < 1).....what happens when you SQUARE a positive fraction?
eg
(1/3)^2 = (1/3)(1/3) = 1/9
Squaring a positive fraction makes the result SMALLER.
Since "squaring" and "square-rooting" are 'opposite' functions, what happens when you SQUARE-ROOT a positive fraction?
√(1/9) = √(1)/√(9) = 1/3
Square-rooting a positive fraction makes the result BIGGER.
In this question, you'll notice that the answer choices revolve around the use of 0.9
I want to focus on Answers B and C
Without doing the math, what happens when you SQUARE 0.9.....? The result will get SMALLER.
Without doing the math, what happens when you SQAURE ROOT 0.9....? The result will get BIGGER.
Since the question is asking which of the following values could be X (meaning....could be greater than 0.9), we don't have to do any more work...
Final Answer:
GMAT assassins aren't born, they're made,
Rich
