If x ≥ 0.9, which of the following could be the value of (1 /√x)?
(A) 1.02
(B) 1.12
(C) 1.23
(D) 1.45
(E) 2.10
OA A
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If x ≥ 0.9,
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GMATGuruNY
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x ≥ 9/10jack0997 wrote:If x ≥ 0.9, which of the following could be the value of (1 /√x)?
(A) 1.02
(B) 1.12
(C) 1.23
(D) 1.45
(E) 2.10
10x ≥ 9
10 ≥ 9/x
10/9 ≥ 1/x
1/x ≤ 10/9
1/√x ≤ (√10)/3.
The only constraint is that x must be less than (√10)/3.
If B, C, D or E is correct -- implying that one of these answer choices is less than (√10)/3 -- then option A must also be correct, since it is even SMALLER than B, C, D, or E.
Implication:
Only the SMALLEST answer choice -- option A -- is viable, implying that none of the other answer choices is less than (√10)/3.
The correct answer is A.
Last edited by GMATGuruNY on Tue Jun 13, 2017 2:20 am, edited 1 time in total.
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Jay@ManhattanReview
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We have x ≥ 0.9.jack0997 wrote:If x ≥ 0.9, which of the following could be the value of (1 /√x)?
(A) 1.02
(B) 1.12
(C) 1.23
(D) 1.45
(E) 2.10
OA A
The value of 1/√x would be maximum if x = 0.9 and minimum = 0 if x = ∞.
Maximum value of 1/√x = 1/√0.9 = √(10/9) = √1.11
Since 1.11 > 1, the square root of 1.11 must be less than 1.11. We see that only option A qualifies, thus the correct answer.
The correct answer: A
Hope this helps!
-Jay
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Hi jack0997,
This question is a great 'concept' question - meaning that you don't have to do much math if you recognize the concepts involved.
Here, we're asked to consider the potential value of (1 /√x).....
IF....
X=1, then (1 /√1) = 1
As X gets BIGGER, the value of the fraction gets SMALLER.
As X gets SMALLER, the value of the fraction gets BIGGER.
The prompt tell us that X ≥ 0.9, so X can't get that much smaller than 1. However, since changing X just a little would change the value of the fraction just a little, we could conceivably hit every value of X up to whatever "limit" exists. The question asks us which of the 5 answers COULD be the value of X, so there can only be one possibility. IF 1.12 was the answer, then we should be able to get 1.02 as well, meaning that there would be TWO answers. Thus, the only possibility must be 1.02 (it's either the limit or the one answer that's within the limit.
Final Answer: A
GMAT assassins aren't born, they're made,
Rich
This question is a great 'concept' question - meaning that you don't have to do much math if you recognize the concepts involved.
Here, we're asked to consider the potential value of (1 /√x).....
IF....
X=1, then (1 /√1) = 1
As X gets BIGGER, the value of the fraction gets SMALLER.
As X gets SMALLER, the value of the fraction gets BIGGER.
The prompt tell us that X ≥ 0.9, so X can't get that much smaller than 1. However, since changing X just a little would change the value of the fraction just a little, we could conceivably hit every value of X up to whatever "limit" exists. The question asks us which of the 5 answers COULD be the value of X, so there can only be one possibility. IF 1.12 was the answer, then we should be able to get 1.02 as well, meaning that there would be TWO answers. Thus, the only possibility must be 1.02 (it's either the limit or the one answer that's within the limit.
Final Answer: A
GMAT assassins aren't born, they're made,
Rich
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Matt@VeritasPrep
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Since x is a range, 1/√x should also have a range. That means the answer is likely to be either the smallest or the largest of the five options. With that in mind, try A:
1/√x = 1.02
1 = 1.02√x
1/1.02 = √x
That number on the right I'd guesstimate at .98ish, so squaring it would still be > .9. Success!
1/√x = 1.02
1 = 1.02√x
1/1.02 = √x
That number on the right I'd guesstimate at .98ish, so squaring it would still be > .9. Success!
