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# Thread: 800 level Difficult Exponent question.

1. ## 800 level Difficult Exponent question.

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  Reply With Quote

2. Originally Posted by Sumon1 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
SPOILER: A
.

Cheers,
Brent  Reply With Quote

3. A it is.

from (1) p + q = 3(m+1) + 2(2m+1) = 3m.3 + 4m.2 = 2(3m + 4m) + 3m
since m is a positive integer, (1) is clearly suff.

(2) tell us nothing abt p & q. So insuff.  Reply With Quote

4. Thanks Brent - I got this question in MGMAT and was wondering there was something wrong with the question stem   Reply With Quote

5. Originally Posted by Sumon1 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  Reply With Quote