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# t is an integer

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t is an integer [#permalink]  25 May 2018, 16:26
Expert's post
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Question Stats:

92% (01:08) correct 7% (00:07) wrong based on 13 sessions
$$t$$ is an integer

 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.
[Reveal] Spoiler: OA

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Kudos [?]: 1138 [0], given: 7

Re: t is an integer [#permalink]  26 May 2018, 10:07
Expert's post
Carcass wrote:
$$t$$ is an integer

 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

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Re: t is an integer   [#permalink] 26 May 2018, 10:07
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