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If r and q are integers, what is the value of (5^r)(3^(q+1))?

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If r and q are integers, what is the value of (5^r)(3^(q+1))? [#permalink] New post   29 Mar 2016, 03:13
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If r and q are integers, what is the value of (5^r)(3^(q+1))?

(1) (5^r)(3^q) = 729

(2) r + q = 6
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A
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FightToSurvive
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Re: If r and q are integers, what is the value of (5^r)(3^(q+1))? [#permalink] New post   29 Mar 2016, 04:01
If r and q are integers, what is the value of (5^r)(3^(q+1))?

(1) (5^r)(3^q) = 729

(2) r + q = 6
we can break the eqn as (5^r)(3^q)3

St(1) gives (5^r)(3^q) = 729. So answer is 729*3. Hence sufficient.
St(2) r + q = 6 doesnt help. Hence no sufficient.

Hence the answer is A.
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Re: If r and q are integers, what is the value of (5^r)(3^(q+1))? [#permalink] New post   10 Nov 2018, 14:47
Why is the 2nd statement not sufficient?

Couldn't we use substitution (i.e. - Q = 6 - R)

Thanks for posting!
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Re: If r and q are integers, what is the value of (5^r)(3^(q+1))? [#permalink] New post   29 Jun 2019, 14:42
I believe that the second equation is not sufficient because even if substitution is used the bases are not equivalent for you to solve for r and q.

Statement 2) r + q = 6
Say looking to substitute for r, r + q = 6 --> r = 6 - q
Try substituting into the problem question 5^r * 3^(q+1) = ? --> 5^(6-q) * 3^(q+1) = ?
The bases are not the same (5 and 3) so there is no way to drop the bases to solve for q.

Also, since we already know that Statement 1 is sufficient, then we know that C cannot an option, so if Statement 2 cannot solve by itself then the only option left is A.

Jake1991 wrote:
Why is the 2nd statement not sufficient?

Couldn't we use substitution (i.e. - Q = 6 - R)

Thanks for posting!
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Re: If r and q are integers, what is the value of (5^r)(3^(q+1))? [#permalink] New post   02 Feb 2022, 08:05
FightToSurvive wrote:
If r and q are integers, what is the value of (5^r)(3^(q+1))?

(1) (5^r)(3^q) = 729

(2) r + q = 6
we can break the eqn as (5^r)(3^q)3

St(1) gives (5^r)(3^q) = 729. So answer is 729*3. Hence sufficient.
St(2) r + q = 6 doesnt help. Hence no sufficient.

Hence the answer is A.


Hey, how did we multiply 729 with 3 in statement 1?
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Re: If r and q are integers, what is the value of (5^r)(3^(q+1))? [#permalink] New post   05 May 2022, 09:32
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Statement A
(5^r)(3^q) = 729
=> (5^r)(3^q)=3^6
So, in this case only if (5^r)=1 then only we can find the value of 3^q, which is 3^6 which is 729
So, here we can certainly say r=0 and then only (5^r) will be come 1
This gives certain values of r and q thus Statement A alone is sufficient

Statement B
Its an equation where both the variables are unknown so no certain values can be obtained for r and q, so Statement B alone is insufficient

Answer choice: A
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If r and q are integers, what is the value of (5^r)(3^(q+1))? [#permalink] New post   08 Jul 2022, 13:14
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The question can be rephrased:
(5^r)(3^q + 1) = (5^r)(3)(3^q)
= 3(5^r)(3^q)
The question then is really asking us to find a value of (5^r)(3^q).

(1) SUFFICIENT: This gives us the value of (5^r)(3^q).

(2) INSUFFICIENT: With r + q = 6, there are an infinite number of possibilities for the values of r and q. Each set of values would yield a very different value for (5^r)(3^q).

The correct answer is A.
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If r and q are integers, what is the value of (5^r)(3^(q+1))? [#permalink] New post   09 Jul 2022, 09:13
Preeeeeetika wrote:
FightToSurvive wrote:
If r and q are integers, what is the value of (5^r)(3^(q+1))?

(1) (5^r)(3^q) = 729

(2) r + q = 6
we can break the eqn as (5^r)(3^q)3

St(1) gives (5^r)(3^q) = 729. So answer is 729*3. Hence sufficient.
St(2) r + q = 6 doesnt help. Hence no sufficient.

Hence the answer is A.


Hey, how did we multiply 729 with 3 in statement 1?


Statement (2) only differs from the question stem by (3^1). (3^(q+1)) = (3^q)(3^1)

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If r and q are integers, what is the value of (5^r)(3^(q+1))? [#permalink]
09 Jul 2022, 09:13
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