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

Question

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

(2)  r ≠ 1

Bunuel · Accepted Answer

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
eq{1} . Clearly insufficient as no info about  t .

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

Answer: C.

aj0809 · Answer

Hi All,

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

Thanks

DesiGmat · Answer

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

EMPOWERgmatRichC · Answer

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

GMAT assassins aren't born, they're made,
Rich

stonecold · Answer

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

MHIKER · Answer

(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.

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

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GMAT Data Sufficiency (DS) Questions

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

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