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Difficulty:
5%
(low)
Question Stats:
85% (01:04) correct
15%
(01:05)
wrong
based on 127
sessions
History
Date
Time
Result
Not Attempted Yet
Which of the following fractions is the greatest ?
(A) \(-\frac{3}{2}\)
(B) \(-\frac{23}{22}\)
(C) \(-\frac{100}{99}\)
(D) \(-\frac{999}{998}\)
(E) \(-\frac{9999}{9998}\)
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(A) \(-\frac{3}{2}\)
(B) \(-\frac{23}{22}\)
(C) \(-\frac{100}{99}\)
(D) \(-\frac{999}{998}\)
(E) \(-\frac{9999}{9998}\)
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Bunuel
Many ways…
Simplify each
(A) \(-\frac{3}{2}=-1 -\frac{1}{2}\)
(B) \(-\frac{23}{22} =-1 -\frac{1}{22}\)
(C) \(-\frac{100}{99} =-1 -\frac{1}{99}\)
(D) \(-\frac{999}{998} =-1 -\frac{1}{998}\)
(E) \(-\frac{9999}{9998} =-1 -\frac{1}{9998}\)
-1/9998 is the least of what is being added to -1, so \(-1-\frac{1}{9998}\) will be closest to 0, and the largest.
Also look at fractions in the signature.
When the difference between numerator and denominator is SAME, here it is 1.
Let a be a positive integer.
If the fraction is positive and greater than 1, then \(\frac{3}{2}>\frac{3+a}{2+a}\).
So, if it is negative, it will be opposite. Hence -9999/9998 is the largest.
If the fraction is positive and lesser than 1, then \(\frac{1}{2}<\frac{1+a}{2+a}\).
So, if it is negative, it will be opposite. Hence, -1/2 > -499/500.
E
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