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t is an integer
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25 May 2018, 16:26
25 May 2018, 16:26
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74% (00:44) correct
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\(t\) is an integer
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Quantity A |
Quantity B |
\(\frac{1}{1+2^t}\) |
\(\frac{1}{1+3^t}\) |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
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Re: t is an integer
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26 May 2018, 10:07
26 May 2018, 10:07
2
Carcass wrote:
\(t\) is an integer
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Quantity A |
Quantity B |
\(\frac{1}{1+2^t}\) |
\(\frac{1}{1+3^t}\) |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
We can solve this question using matching operations
Given:
Quantity A: 1/(1 + 2^t)
Quantity B: 1/(1 + 3^t)
Since 2^t is POSITIVE for all integer values of t, we know that 1 + 2^t is also POSITIVE
This means we can safely multiply both quantities by (1 + 2^t) to get:
Quantity A: 1
Quantity B: (1 + 2^t)/(1 + 3^t)
Likewise, since (1 + 3^t) is POSITIVE, we can safely multiply both quantities by (1 + 3^t) to get:
Quantity A: 1 + 3^t
Quantity B: 1 + 2^t
Subtract 1 from both quantities to get:
Quantity A: 3^t
Quantity B: 2^t
From here, we can TEST some integer values of t
If t = 0, we get:
Quantity A: 3^0 = 1
Quantity B: 2^0 = 1
In this case, the two quantities are EQUAL
If t = 1, we get:
Quantity A: 3^1 = 3
Quantity B: 2^1 = 2
In this case, Quantity A is GREATER
Answer: D
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Re: t is an integer [#permalink]
26 May 2018, 10:07
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