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800 level Difficult Exponent question.


Sumon1

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How can i solve this Data Sufficiency problem, anyone pull me out from the dark........

If m is a positive integer, is the value p+q at least twice the value of 3m+4m ?

1) p=3m+1 and q=22m+1

2) m=4

 

First, let's rewrite the target question as "Is p+q > 2(3^m + 4^m) ?"

 

Statement 1: If we replace p and q with their respective values, we can reword the target question as:

Is 3^(m+1)+2^(2m+1) > 2(3^m + 4^m) ? (do we have sufficient information to answer this question? let's find out)

 

To simplify the right-hand-side, first recognize that 4^m = (2^2)^m = 2^2m

So, we can reword the target question as: Is 3^(m+1)+2^(2m+1) > 2(3^m + 2^2m) ?

If we expand the right-hand-side, we get: Is 3^(m+1)+2^(2m+1) > (2)3^m + 2^(2m+1)?

At this point, we can subtract 2^(2m+1) from both sides to get: Is 3^(m+1) > (2)3^m?

Now, if we divide both sides by 3^m, we get: Is 3 > 2?

Yes, 3 is greater than 2.

Since we can answer the reworded target question with certainty, statement 1 is sufficient.

 

Statement 2: Since we have no information about p and q, we cannot answer the target questions. So, statement 2 is not sufficient and the answer is

A

.

 

Cheers,

Brent

 

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How can i solve this Data Sufficiency problem, anyone pull me out from the dark........

If m is a positive integer, is the value p+q at least twice the value of 3m+4m ?

1) p=3m+1 and q=22m+1

2) m=4

 

Obviously we need some help here, since we have no idea what p and q are.

 

Part (1)

p = 3^(m+1)

q= 2^(2m+1)

 

Now we know that p is a power of 3 greater than or equal to 9, and we know that q is an odd power of 2 greater than or equal to 8

 

p+q = 3*3^m+2*2^(2m) = 3*3^m + 2*4^m > 2*3^m + 2*4^m

 

SUFFICIENT

 

Part (2)

m = 4

 

Again, we have no idea what p and q are, so we can safely say INSUFFICIENT

 

A

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