Sumon1 Posted September 13, 2011 Share Posted September 13, 2011 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 Quote Link to comment Share on other sites More sharing options...
Brent Hanneson Posted September 15, 2011 Share Posted September 15, 2011 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 Quote Link to comment Share on other sites More sharing options...
Lav Posted September 23, 2011 Share Posted September 23, 2011 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. Quote Link to comment Share on other sites More sharing options...
sandeep_chads Posted February 10, 2012 Share Posted February 10, 2012 Thanks Brent - I got this question in MGMAT and was wondering there was something wrong with the question stem :) Quote Link to comment Share on other sites More sharing options...
krusta80 Posted March 2, 2012 Share Posted March 2, 2012 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 Quote Link to comment Share on other sites More sharing options...
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