tester2 Posted September 7, 2008 Share Posted September 7, 2008 The sum of the first 50 positive even integers is 2,550. What is the sum of the even integers from 102 to 200 inclusive? a)5100 b) 7550 c) 10100 d) 15500 e) 20100 OK, sometimes these ridiculous number sums come up and i never know how to hand them. I guessed the correct answer of B only because I figured A was a trap. How do you do this problem? Thanks! Quote Link to comment Share on other sites More sharing options...
Shooter Posted September 7, 2008 Share Posted September 7, 2008 I am not sure how to use the given first information (i.e) 2550. I did as follows: number of terms b/w 102 and 200 (200-102+1) = 98. 50 terms are even n=50;a=102;d=2 substitute in n/2[2a+(n-1)d] Gives you 7550 Quote Link to comment Share on other sites More sharing options...
shobby Posted September 7, 2008 Share Posted September 7, 2008 (1) For 1 to 100, terms are 2, 4, 6, ..so on (2) For 101 to 200, terms are 102, 104, 106, .. so on Every term in (2) is 100 more than its corresponding term in (1). So, sum of terms of (2) is 2550 + 50(100) = 7550 Quote Link to comment Share on other sites More sharing options...
Retake_GMAT Posted September 8, 2008 Share Posted September 8, 2008 Just apply formula for AP.No tricks at all!! 200 = 102 + (n-1) d 200= 102 + 2n -2 202=102 + 2n 100=2n n = 50 25 * ( 2*102 + 49*2)= 25* ( 204 + 98) = 302*25 =7550 Quote Link to comment Share on other sites More sharing options...
ankitharish Posted September 9, 2008 Share Posted September 9, 2008 The first info can be used to derive the formulae for AP. But better learn the formulae plain and simple. Quote Link to comment Share on other sites More sharing options...
Gymat Posted September 10, 2008 Share Posted September 10, 2008 What is AP? I'm not sure that I understand where did you get D=2? Quote Link to comment Share on other sites More sharing options...
bose Posted September 11, 2008 Share Posted September 11, 2008 sum of first 50 even # i.e. from 2-100=2550 sum of 102 - 200=here each term is added with 100, so 100*50+2550 since 50 even terms are there in 102-200 ans 7550 Quote Link to comment Share on other sites More sharing options...
gmat_magic_prep Posted September 11, 2008 Share Posted September 11, 2008 sum of first 50 even # i.e. from 2-100=2550 sum of 102 - 200=here each term is added with 100, so 100*50+2550 since 50 even terms are there in 102-200 ans 7550 sum of first 50 +ve even integers = 2550 2 + 4 + .. + 100 = 2550 Given sum = G = 2(1+2+ .. + 50) = 2550 Required sum = S = 102 + 104 + .. + 200 => S = 2(51 + 52 + ... + 100) Now, G + S = 2550 +S = 2(1+ .. +50) +2(51+ .. +100) => S + 2550 = 2(1+2+3+ ..100) = 2 * 100 * 101 / 2 = 10100 => S = 10100 - 2550 = 7550 This appears long but the easiest way. Quote Link to comment Share on other sites More sharing options...
mail2jkd Posted September 11, 2008 Share Posted September 11, 2008 Step 1: Find the average of the even series - (102+200)/2 = 151 Step 2: Find the number of even integers in the series - Easy way, 200-102=98+1=99 integers in the series. 99/2+1=50 even integers because it starts and ends with a even number. 50x151=7550. Ans:B Or you can use the AP nth digit formula to get the number of even integers in a series. Tn=(a+n-1)d 200=102+(n-1)2 n=50 Quote Link to comment Share on other sites More sharing options...
gcvbt7t Posted September 12, 2008 Share Posted September 12, 2008 7550 is the an swer Quote Link to comment Share on other sites More sharing options...
karthikvela Posted September 12, 2008 Share Posted September 12, 2008 Yeah the answer is 7550. The simplest way is given by mail2jkd. The same kind of problem can be found in OG11 PS portion Q.no:204. Quote Link to comment Share on other sites More sharing options...
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