In the sequence d_1, d_2, d_3, . . ., for all positive integers n, d_

Question

In the sequence d_1 , d_2 , d_3 , . . ., for all positive integers n, d_n = n^2 − 25n + 150 If k is a positive integer, is d_k > 0? 1) 5 < k < 25 2) k > 10

WannaManaConsult · Answer

We can factor the left side to

(n-10)(n-15)

Because the coefficient of n^2 is positive (1 in this case), we know (n-10)(n-15)>0 when n<10 or n>15 and (n-10)(n-15)<0 when 15>n>10.

1) insufficient. n could be between 10 and 15 or greater than 15 (or less than 10).
2) insufficient. n could be greater than 15 (making (n-10)(n-15)>0) or between 10 and 15 (making (n-10)(n-15)<0)

Put 1) and 2) together and we have 10<k<25. Still insufficient for same reason 2) is insufficient.

Answer: E.

nislam · Answer

chetan2u ,  BrentGMATPrepNow 
The problem seems very hard to me, I even did not get the answer explanation. Could you please give me a detail and easier solution.

Thanks!

BrentGMATPrepNow · Answer

Given : c Target question : Is d_k > 0 ? This is a good candidate for rephrasing the target question. Take: d_n=n^2 − 25n + 150 The factor to get: d_n=(n-10)(n-15) Now recognize that: -When 15 < n , we get: d_n=(n-10)(n-15)=(positive)(positive)= positive -When 10 < n < 15 , we get: d_n=(n-10)(n-15)=(positive)(negative)=negative -When 0 0 when 15 < k OR when k < 10 . So.... REPHRASED target question : Is k EITHER greater than 15 OR less than 10? Aside: the video below has tips on rephrasing the target question When I scan the two statements, they both feel insufficient, AND I’m pretty sure I can identify some cases with conflicting answers to the REPHRASED target question . So, I’m going to head straight to…… Statements 1 and 2 combined Statement 1 tells us that 5 < k < 25 Statement 2 tells us that k > 10 Case a : If k = 20 , the answer to the REPHRASED target question is YES Case b : If k = 12 , the answer to the REPHRASED target question is NO Since we can’t answer the REPHRASED target question with certainty, the combined statements are NOT SUFFICIENT Answer: E VIDEO ON REPHRASING THE TARGET QUESTION: https://www.youtube.com/watch?v=MyG1K3ee69w

chetan2u · Answer

The question has changed n to k as n could be anything 1, 2 etc, and now we are looking for: whether kth term >0? So d_k = k^2 − 25k + 150= k^2-15k-10k+150=(k-15)(k-10) . That is, the question becomes: Is (k-15)(k-10)>0 ? When will this be true? Case 1: When k<10, both k-10 and k-15 are negative so (k-10)(k-15) will be positive Case 2: When 100 and k-15<0, so (k-10)(k-15) will be negative. Case 3: When k>15, both k-10 and k-15 are positive so (k-10)(k-15) will be positive Let us see whether we can find a definite range as per above cases of k. 1) 5 < k < 25 All 3 cases possible Insufficient 2) k > 10 Again case 2 and case 3 are possible, giving us both yes and no as the answer Insufficient Combined Range= 10

In the sequence d_1, d_2, d_3, . . ., for all positive integers n, d_

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GMAT Data Sufficiency (DS) Questions

In the sequence d_1, d_2, d_3, . . ., for all positive integers n, d_

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