If n denotes a number to the left of 0 on the number line such that the square of n is less than 1/100, then the reciprocal of n must be
A. Less than 10
B. Between 1 and 1/10
C. Between 1/10 and 0
D. Between 0 and 1/10
E. Greater than 10
Is there a strategic approach to this question? . Can any experts show?
If n denotes a number to the left of 0 on the number line su
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Let n = 1/20.ardz24 wrote:If n denotes a number to the left of 0 on the number line such that the square of n is less than 1/100, then the reciprocal of n must be
A. Less than 10
B. Between 1 and 1/10
C. Between 1/10 and 0
D. Between 0 and 1/10
E. Greater than 10
Is there a strategic approach to this question? . Can any experts show?
This works because (1/20)Â² = 1/400, which is less than 1/100.
In this case, the reciprocal of n = 20.
When the reciprocal of n is 20, only answer choice A is true, since 20 is less than 10.
The correct answer is A.
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We are given that n denotes a number to the left of 0 on the number line such that the square of n is less than 1/100. This means n is negative, and it is between 0 and 1/10 since (1/10)^2 = 1/100. Thus, n could be equal to values such as 1/11, 1/12, 1/13, etc. Notice that when we square these values, they are all less than 1/100.ardz24 wrote:If n denotes a number to the left of 0 on the number line such that the square of n is less than 1/100, then the reciprocal of n must be
A. Less than 10
B. Between 1 and 1/10
C. Between 1/10 and 0
D. Between 0 and 1/10
E. Greater than 10
Let's take the reciprocal of any of these values listed. The reciprocal of 1/11 is 11. Similarly, the reciprocal of 1/12 is 12 and the reciprocal of 1/13 is 13. Since these reciprocals are all less than 10, answer choice A is correct.
Answer: A
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STRATEGY: As with all GMAT Problem Solving questions, we should immediately ask ourselves, Can I use the answer choices to my advantage?BTGmoderatorAT wrote: ↑Tue Jan 09, 2018 7:14 amIf n denotes a number to the left of 0 on the number line such that the square of n is less than 1/100, then the reciprocal of n must be
A. Less than 10
B. Between 1 and 1/10
C. Between 1/10 and 0
D. Between 0 and 1/10
E. Greater than 10
Is there a strategic approach to this question? . Can any experts show?
In this case, the answer is a resounding yes, because we can just find a value of n that satisfies the given information, and then take the reciprocal of n.
From here, we should give ourselves about 20 seconds to identify a faster approach.
In this case, we can probably perform some algebra, but that will likely take longer than testing a value
We're told that the square of n is less than 1/100
In other words: n² < 1/100
So, for example, it could be the case that n = 1/20, since (1/20)² = 1/400, and 1/400 < 1/100
Important: The question also tells us that n denotes a number to the left of 0 on the number line
In other words, n is NEGATIVE, which means n = 1/20 doesn't satisfy this condition.
However, n = 1/20 meets all of the criteria since 1/20 is negative, and (1/20)² = 1/400, and 1/400 < 1/100
If n = 1/20, then the reciprocal of n = 20/1 = 20
Only answer choice A works.