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Multipe of 5 is 5, 10, 15, 20, etc. Those not divisible by 2 are 5, 15, 25, 35, etc.

So, there will be 1 number to include for every 10, so 1000 numbers / 10 = 100 numbers to include in the sum.

If you look at 5 + 995 = 1000, 15 + 985 = 1000, 25 + 975=1000, 35 + 965 = 1000...495+505=1000, You do this, then you have 50 pairs that add up to be 1000, so 50 * 1000 = 50,000 (i.e. D)

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There are 200 no's divisible by 5 upto 1000 and out of this only 100 nos are not divisible by 2. So the sum we need is (5+15+....+995) or 5(1+3+5+....199). The sum of consequtive n integers is n^2. Therefe for sum of 100 odd nos is 100^2.

Obtain the sum of all positive integers up to 1000, which are divisible by 5 and not divisible by 2.

a) 10050 b) 5050 c) 5000 d) 50000 e) 55000

My approach:

Step 1: Find out the sum of all integers divisible by 5. Number of such terms= \(\frac{(1000-0)}{5} + 1= 201\). Sum of all such integers= \(201*500\) (using the sum formula of terms in Arithmetic Progression).. (i) Step 2: Find out the sum of all integers divisible by 10: Number of such terms= \(\frac{(1000-0)}{10}= 101\). Sum of all such integers= \(101*500= 101*500\) .. (ii)

Now, the multiples of 10 are the ones which are divisible by both 5 and 2. Therefore, we need to subtract (ii) by (i) to arrive at the terms divisible only by 5 and not by 2

Re: Obtain the sum of all positive integers up to 1000, which [#permalink]

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13 Jan 2014, 19:25

100 possibilities, evenly spaced by 10. Since its an evenly spaced set, the median (500) is also the mean. Find the median: will be the average between the 50th observation (495) and the 51st observation (505), which is 500. Average * number of observations == total. 500*100 is 50,0000.

Obtain the sum of all positive integers up to 1000, which are divisible by 5 and not divisible by 2.

a) 10050 b) 5050 c) 5000 d) 50000 e) 55000

My approach:

Step 1: Find out the sum of all integers divisible by 5. Number of such terms= \(\frac{(1000-0)}{5} + 1= 201\). Sum of all such integers= \(201*500\) (using the sum formula of terms in Arithmetic Progression).. (i) Step 2: Find out the sum of all integers divisible by 10: Number of such terms= \(\frac{(1000-0)}{10}= 101\). Sum of all such integers= \(101*500= 101*500\) .. (ii)

Now, the multiples of 10 are the ones which are divisible by both 5 and 2. Therefore, we need to subtract (ii) by (i) to arrive at the terms divisible only by 5 and not by 2

Obtain the sum of all positive integers up to 1000, which are divisible by 5 and not divisible by 2.

a) 10050 b) 5050 c) 5000 d) 50000 e) 55000

My approach:

Step 1: Find out the sum of all integers divisible by 5. Number of such terms= \(\frac{(1000-0)}{5} + 1= 201\). Sum of all such integers= \(201*500\) (using the sum formula of terms in Arithmetic Progression).. (i) Step 2: Find out the sum of all integers divisible by 10: Number of such terms= \(\frac{(1000-0)}{10}= 101\). Sum of all such integers= \(101*500= 101*500\) .. (ii)

Now, the multiples of 10 are the ones which are divisible by both 5 and 2. Therefore, we need to subtract (ii) by (i) to arrive at the terms divisible only by 5 and not by 2

Can u explain in brief why do you multiply by 500. Thank you

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For every evenly spaced set (a.k.a. arithmetic progression), the sum equals to (mean)*(# of terms). 500 is the mean there: (mean)=(first+last)/2=(5+995)/2=500.

Re: Obtain the sum of all positive integers up to 1000, which [#permalink]

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05 Feb 2016, 04:19

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Re: Obtain the sum of all positive integers up to 1000, which [#permalink]

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05 Feb 2016, 07:37

Expert's post

puma wrote:

Obtain the sum of all positive integers up to 1000, which are divisible by 5 and not divisible by 2.

A. 10,050 B. 5,050 C. 5,000 D. 50,000 E. 55,000

Total Multiples of 5 from 1 through 1000 = 1000/5 = 200

Half of these 200 multiples of 5 will be even (i.e. divisible by 2) and remaining half will be odd multiples of 5

i.e. Question : 5+15+25+......+955=?

Since it's an Arithmetic Progression (In which difference between any two consecutive terms remain constant) in which sum of first and last term = Sum of second and Second last term = and so on...

100 such numbers i.e.e 50 such pairs and sum of each pair = 5+955 = 1000

i.e. Sum of all pairs = (100/2)*(5+955) = 50*1000 = 50,000

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Re: Obtain the sum of all positive integers up to 1000, which [#permalink]

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14 Mar 2016, 00:59

The question is basically asking us the sum of the AP series 5+15+......995 Number of terms can be calculated from A(n)= A+(n-1)D So N=100 Sum =100/2 * [5+995] = 50,000 hence D

gmatclubot

Re: Obtain the sum of all positive integers up to 1000, which
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14 Mar 2016, 00:59

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