If r is an integer and 9q = 243^r, which of the following expresses q

Question

If r is an integer and 9q = 243^r, which of the following expresses q in terms of r?

A. q=27^r
B. q=81^(r−9)
C. q=3^(r−3)
D. q=3^(5(r−2))
E. q=3^(5r−2)

Vinayak Shenoy · Answer

IMO E
9q= 243^r can be simplified as q= (3^5r)/3^2
q=3^(5r-2)

gracie90 · Answer

I say E as well. I plugged in numbers (q=27, r=1) and then looked at which answer choice yields q.

(E) q=3^(5r−2)

27=3^3

chetan2u · Answer

hi..

9q = 243^r.... 3^2*q=(3^5)^r...........q=\frac{3^{5r}}{3^2}=3^{5r-2} 
E

Abhishek009 · Answer

9q = 243^r

Or,  3^2q = 3^{5r}

So,  q = 3^{5r-2}

Thus, answer will be (E)  q=3^(5r−2)

souvonik2k · Answer

9q=243^r 
 3^2q = 3^{5r} 
 q=\frac{3^{5r}}{3^2} 
 q=3^{5r-2} 
Answer E.

saswata4s · Answer

9q = 243^r
=> q = 243^r/9 = 3^5r/3^2 = 3^(5r-2)

Ans: E.

calappa1234 · Answer

I went with this first. But picking those numbers also allows for A to be correct which it is in fact not.

If testing numbers, be careful to test all the choices guys! If you get a duplicate, switch the numbers up.

PriyanshuR · Answer

9q= 243^r can be simplified as q= (3^5r)/3^2
 q=3^(5r-2)

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