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05 Oct 2020, 03:00
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C
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Difficulty:
55%
(hard)
Question Stats:
51% (01:12) correct
49%
(01:26)
wrong
based on 271
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Z is an infinite sequence of distinct positive real numbers. Is there a number in sequence Z that is greater than every other number in Z?
(1) No number in sequence Z is greater than 1.
(2) 1 is in sequence Z.
Are You Up For the Challenge: 700 Level Questions
Source:
(1) No number in sequence Z is greater than 1.
(2) 1 is in sequence Z.
Are You Up For the Challenge: 700 Level Questions
Source:
Ian Stewart
05 Oct 2020, 04:38
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Z is an infinite sequence of distinct positive real numbers. Is there a number in sequence Z that is greater than every other number in Z?
Explanation:
(S1) No number in sequence Z is greater than 1.
Not sufficient information to comment .
S1 insuffcient
(S2) 1 is in sequence Z.
Not sufficient information to comment .
S2 insuffcient
Combining S1 & S2
given that No number in sequence Z is greater than 1 & also given that 1 is in sequence
Hence 1 will be greater than every other number in Z( already given Z is an infinite sequence of distinct positive real numbers)
Thus C is the correct answer.
Explanation:
(S1) No number in sequence Z is greater than 1.
Not sufficient information to comment .
S1 insuffcient
(S2) 1 is in sequence Z.
Not sufficient information to comment .
S2 insuffcient
Combining S1 & S2
given that No number in sequence Z is greater than 1 & also given that 1 is in sequence
Hence 1 will be greater than every other number in Z( already given Z is an infinite sequence of distinct positive real numbers)
Thus C is the correct answer.
06 Oct 2020, 17:19
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Bunuel
Think of an infinite sequence as a gigantically large amount of numbers instead of "infinite". An infinite sequence can have a fixed range, such as \(f(n) = (0.5)^n\) with the input n being the integers 1 to infinity. The sequence starts off at 0.5 and keeps on getting smaller, it hits close to 0 but never actually reaches 0.
Statement 1:
Think of the example above, it is possible to have all integers greater than 0 yet no element of the sequence is equal to 0. Using this parody, it is possible that all numbers in Z are smaller than 1 but 1 is not within the sequence, therefore we would answer "no". Likewise, we can simply include 1 in Z and we would answer "yes".
Statement 2:
Insufficient.
Combined:
We confirmed 1 is in the sequence now so sufficient.
A good example to answer "no" with statement 1 alone is \(f(n) = 1 - (0.5)^n\), where \(n > 0\). When we get to very high values of n, \(f(n)\) will be close to 1 but we will always find a greater value by inputing the next n. Therefore there is no number within the sequence that is greater than the rest of the elements.
Ans: C
