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What is the sum of the integers from 190 to 195 inclusive? [#permalink]
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20 Oct 2010, 05:36
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What is the sum of the integers from 190 to 195 inclusive? A) 0 B) 5 C) 375 D) 875 E) 965
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Re: What is the sum of the integers from 190 to 195 inclusive? [#permalink]
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20 Oct 2010, 06:15
From 190 to +195 we know that all numbers from 1 to 190 will have both positive and negative terms. So they will just cancel each other out. The numbers that remain will be 191, 192,193, 194 and 195 whose sum can be easily calculated. The answer is E.
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Re: What is the sum of the integers from 190 to 195 inclusive? [#permalink]
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20 Oct 2010, 09:49
^^ Great explanation. My own approach was to use the formula (avg of 1st and last number) * total number . But I got stuck.
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Re: What is the sum of the integers from 190 to 195 inclusive? [#permalink]
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20 Oct 2010, 13:56
195  191/2 * 5 = 965
E



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Re: What is the sum of the integers from 190 to 195 inclusive? [#permalink]
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21 Oct 2010, 02:44
190+190=0 189+189=0 ... we still have 191+192+193+194+195=965 (E)



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What is the sum of the integers from 190 to 195, inclusive? [#permalink]
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20 Aug 2011, 06:20
What is the sum of the integers from 190 to 195, inclusive?
a) 0 b) 5 c) 375 d) 875 e) 965



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Re: What is the sum of the integers from 190 to 195, inclusive? [#permalink]
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20 Aug 2011, 08:51
This can be viewed as a sum of consecutive terms problem the sequence consists of integers between 191 and 196 the sequence starts at 190 and ends at +195 in an arithmetic progression, the nth term is given by tn=a+(n1)d here tn=195, a=190, d=1 hence, 195=190+(n1) or n=386 Sum of n terms can be calculated by sn=n/2(a+l) a=first term, l=last term, n=no. of terms sn=386*(190+195)/2 sn=193*5 sn=965
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Re: What is the sum of the integers from 190 to 195, inclusive? [#permalink]
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20 Aug 2011, 11:37
the series is in ap.
AP  sum of the series = (n/2)(2a+ (n1)d)
n = 190+1+195 (190 negative terms, 1 zero and 195 positive terms) = 386
a = 190 d = 1
=> sum of this series = (386/2)(380+385) = 965
Answer is E.



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Re: What is the sum of the integers from 190 to 195, inclusive? [#permalink]
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20 Aug 2011, 15:56
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Sum of 190 to +190 will be zero. You just have to sum up 191 t0 195 which is 965.



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Re: sum of the integers [#permalink]
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15 Dec 2011, 22:25
190+(189)+(188+).....+(4)+(3)+(2)+(1) + 0+1+2+3+4+........+188+189+190+191+192+193+194+195 Everything will cancel out except the last 5 numbers(191+192+193+194+195) So, the ans will be 965.
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Re: sum of the integers [#permalink]
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15 Dec 2011, 23:33
IMO E. 190 to +190 everything will cancel out. Sum of 191 to 195 = 965
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Re: sum of the integers [#permalink]
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16 Dec 2011, 11:39
as the list is consecutive integers, we can use following formulas:
sum/n= average. sum=(average)(n) average=a+b/2=190+195/2=2.5 number of items(n)=BA+1=195(190)+1=195+191=386. sum=average*n=2.5*386=965.
answer is E



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Re: sum of the integers [#permalink]
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16 Dec 2011, 21:19
190 to +190 will cancel out each other Sum= 190*5 +(1+2+3+4+5)= 950+15= 965 E
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What is the sum of integers from 190 to 195, inclusive? [#permalink]
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What is the sum of integers from 190 to 195, inclusive? A 0 B 5 C 375 D 875 E 965



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Re: What is the sum of integers from 190 to 195, inclusive? [#permalink]
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07 Feb 2017, 23:56
yuerchang wrote: What is the sum of integers from 190 to 195, inclusive? A 0 B 5 C 375 D 875 E 965 integers from 1 to 190 gets cancelled from similar negative values left only 191+192+193+194+195 = 965 Ans E



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Re: What is the sum of integers from 190 to 195, inclusive? [#permalink]
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08 Feb 2017, 00:54
The series is: 190, 189, 188,........ 2, 1, 0, 1, 2, ........ 188, 189, 190, 191, 192, 193, 194, 195; Hence, the ve and +ve values from 190 to +190 cancel each other leaving only 191, 192, 193, 194, 195; So, the sum of the series: 191 + 192 + 193 + 194 + 195 = 190*5 + (1+2+3+4+5) = 950 + 15 = 965; Answer E.
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What is the sum of integers from 190 to 195, inclusive? [#permalink]
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yuerchang wrote: What is the sum of integers from \(190\) to \(195\), inclusive? A 0 B 5 C 375 D 875 E 965 SUM = AVERAGE x NUMBER OF DATA POINTS \(Average = \frac{(190 + 195)}{2} = \frac{5}{2} = 2.5\) Number of data point \(= 195  (190) + 1 = 386\) \(Sum = 2.5 * 386 = 965\) The answer is E.
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Re: What is the sum of integers from 190 to 195, inclusive? [#permalink]
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08 Feb 2017, 05:02
yuerchang wrote: What is the sum of integers from 190 to 195, inclusive? A 0 B 5 C 375 D 875 E 965 Hi, We know 190 to 190 will cancel out.. now what is important is how fast you can calculate 191+192+193+194+195There are five terms which are close to 200, so ans will be close to 5*200=1000... 965 should be the answer.. If you want exact answer, it may be beneficial to calculate how far answer will be from 1000.. So they are 5+6+7+8+9 away, this is 35... And 100035=965... E
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Re: What is the sum of integers from 190 to 195, inclusive? [#permalink]
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08 Feb 2017, 07:39
yuerchang wrote: What is the sum of integers from 190 to 195, inclusive? A 0 B 5 C 375 D 875 E 965 Integers from 190 to 190 is  ( 190 , 189 , 188...........2 , 1 ,0 ) + ( 0 , 1 , 2 ............188 , 189 , 190) = 0Sum of integers from 190 to 195 = Sum of Integers from 190 to 190 ( ie, 0 ) + 191 + 192 + 193 + 194 + 195 => 965 Hence, answer must be (E) 965
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Re: What is the sum of integers from 190 to 195, inclusive? [#permalink]
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13 Feb 2017, 08:37
yuerchang wrote: What is the sum of integers from 190 to 195, inclusive? A 0 B 5 C 375 D 875 E 965 In determining the sum of the integers from 190 to 195 inclusive, we should recognize that all of the negative integers will cancel out with their positive counterparts. For instance, we have 190 and 190, 150 and 150, 10 and 10, etc. Thus, the only positive numbers that won’t cancel out with their negative counterparts are 191, 192, 193, 194, and 195. To determine the sum of these numbers, we can use this formula: sum = average x quantity. Since we have an evenly spaced set, the average is equal to the median, which is 193, and the quantity is 5. Thus, the sum = 193 x 5 = 965. Answer: E
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