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If r and t are positive integers, what is the value of t?

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If r and t are positive integers, what is the value of t? [#permalink] New post  Updated on: 28 Dec 2020, 07:54
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If r and t are positive integers, what is the value of t?

(1) \(t^{r-1} = 1\)

(2) \(r ≠ 1\)
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Originally posted by MHIKER on 22 Jan 2012, 08:44.
Last edited by MHIKER on 28 Dec 2020, 07:54, edited 2 times in total.
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Re: If r and t are positive integers, what is the value of t? [#permalink] New post  22 Jan 2012, 08:51
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Baten80 wrote:
If r and t are positive integers, what is the value of t?
(1) t^(r-1) = 1
(2) r ≠ 1



If r and t are positive integers, what is the value of t?

Note that r and t are positive integers.

(1) \(t^{r-1}=1\) --> if \(r=1\), then \(t\) can be any positive integer as in this case we would have \(t^0=1\). Not sufficient.
(2) \(r\neq{1}\). Clearly insufficient as no info about \(t\).

(1)+(2) As \(r\neq{1}\) then in order \(t^{r-1}=1\) to hold true \(t\) must be 1. Sufficient.

Answer: C.
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Re: If r and t are positive integers, what is the value of t? [#permalink] New post  17 Jan 2015, 04:59
Hi All,

Can you please advise if we can write t^(r-1) as t^r/t?

Thanks
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Re: If r and t are positive integers, what is the value of t? [#permalink] New post  17 Jan 2015, 06:39
aj0809 wrote:
Hi All,

Can you please advise if we can write t^(r-1) as t^r/t?

Thanks



Yes, we can.

t^(r-1) = t^r * t^(-1)

and t ^ (-1) = 1/t

so...


t^(r-1) = t^r / t

I hope it's clear.

Thanks
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Re: If r and t are positive integers, what is the value of t? [#permalink] New post  17 Jan 2015, 12:14
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Hi All,

DesiGmat is correct, but for the sake of removing any confusion on the subject, I'm just going to add some parentheses:

T^(R-1) = (T^R)/T

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Re: If r and t are positive integers, what is the value of t? [#permalink] New post  08 Mar 2016, 21:34
aj0809 wrote:
Hi All,

Can you please advise if we can write t^(r-1) as t^r/t?

Thanks



See in solving the questions pertaining to exponents we need to remember the EXPONENT 1 rules
1=> (1)^anything =1
2=> (-1)^any even positive number =1
3=> (any number) ^0 =1 (any number ≠0)

Hope this helps

regards
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If r and t are positive integers, what is the value of t? [#permalink] New post  28 Dec 2020, 07:53
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MHIKER wrote:
If r and t are positive integers, what is the value of t?

(1) \(t^{r-1} = 1\)

(2) \(r ≠ 1\)



(1) If r=1, them \(t^{1-1}=t^0=1\), t can take any value. Insufficient.

(2) We don't have any information about t. Insufficient.

Considering both:

\(t^{r-1} = 1\), and \(r ≠ 1\), then t must 1 as any exponent of 1 will result 1. Sufficient.

The answer is \(C.\)
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Re: If r and t are positive integers, what is the value of t? [#permalink] New post  12 Apr 2023, 00:34
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Re: If r and t are positive integers, what is the value of t? [#permalink]
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