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If t> 1
[#permalink]
13 Jul 2020, 07:44
13 Jul 2020, 07:44
Expert Reply
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Question Stats:
81% (00:52) correct
18% (00:37) wrong based on 32 sessions
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\(t>1\)
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Kudos for the right answer and explanation
Quantity A |
Quantity B |
\(\frac{1}{1+\frac{3}{2^t}}\) |
\(\frac{1}{1+\frac{3}{3^t}}\) |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Kudos for the right answer and explanation
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Re: If t> 1
[#permalink]
16 Jul 2020, 09:53
16 Jul 2020, 09:53
Both the Quantities have similar looking fraction but their denominators are bit different. As both are positive fractions so we just need to figure out whose denominator is smaller (=> Fraction is bigger). We also know that t > 1
=> \(2^t\) and \(3^t\) will be greater than 1
and \(3^t\) > \(2^t\) as 3 > 2 and t > 1
=> \(\frac{1}{3^t}\) < \(\frac{1}{2^t}\) [Property: In case of two +ve fractions with same numerator, the fraction with larger denominator is smaller ]
=> \(\frac{3}{3^t}\) < \(\frac{3}{2^t}\) [Property: Multiplying with a +ve number on both the sides of an inequality DOES NOT change the sign of the inequality]
=> 1 + \(\frac{3}{3^t}\) < 1 + \(\frac{3}{2^t}\)
=> \(\frac{1}{1+\frac{3}{3^t}}\) > \(\frac{1}{1+\frac{3}{2^t}}\)
=> Quantity B > Quantity A
So, Answer will be B
Hope it helps!
=> \(2^t\) and \(3^t\) will be greater than 1
and \(3^t\) > \(2^t\) as 3 > 2 and t > 1
=> \(\frac{1}{3^t}\) < \(\frac{1}{2^t}\) [Property: In case of two +ve fractions with same numerator, the fraction with larger denominator is smaller ]
=> \(\frac{3}{3^t}\) < \(\frac{3}{2^t}\) [Property: Multiplying with a +ve number on both the sides of an inequality DOES NOT change the sign of the inequality]
=> 1 + \(\frac{3}{3^t}\) < 1 + \(\frac{3}{2^t}\)
=> \(\frac{1}{1+\frac{3}{3^t}}\) > \(\frac{1}{1+\frac{3}{2^t}}\)
=> Quantity B > Quantity A
So, Answer will be B
Hope it helps!
gmatclubot
Re: If t> 1 [#permalink]
16 Jul 2020, 09:53
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