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consecutive integers

by Johnrohit » Sun Oct 27, 2013 10:41 pm
the operation --> is defined by x -->y= x+(x+1)+(x+2)...+y. For example, 3-->7=3+4+5+6+7. What is the value of (100 -->150) - (125 -->150)?


[spoiler]OA=2800[/spoiler]
Last edited by Johnrohit on Sun Oct 27, 2013 11:08 pm, edited 1 time in total.
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by Matt@VeritasPrep » Sun Oct 27, 2013 11:06 pm
Let's get each term clear first, then look for a way to simplify.

100 → 150 = (100 + 101 + 102 + ... + 149 + 150)
123 → 150 = (123 + 124 + 125 + ... + 149 + 150)

So when I subtract the sum in green from the sum in red, everything will cancel except for (100 + 101 + 102 + ... + 121 + 122).

This means that the question is really asking me for the sum of the integers from 100 to 122, inclusive. The formula for this is (Smallest Integer + Greatest Integer)/2 times (Number of Integers), which here is

(100+122)
--------- * 23
2

Or 111 * 23, or 2553. (The OA is wrong, or there was a typo in the question: that answer would be right if the question was (100 → 150) - (125 → 150).)
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by Johnrohit » Sun Oct 27, 2013 11:09 pm
Sooo sorry matt! thank u for the help! tht was a typo!! edited it! wil check d posts b4 posting it 4m nw on! thanks again
Matt@VeritasPrep wrote:Let's get each term clear first, then look for a way to simplify.

100 → 150 = (100 + 101 + 102 + ... + 149 + 150)
123 → 150 = (123 + 124 + 125 + ... + 149 + 150)

So when I subtract the sum in green from the sum in red, everything will cancel except for (100 + 101 + 102 + ... + 121 + 122).

This means that the question is really asking me for the sum of the integers from 100 to 122, inclusive. The formula for this is (Smallest Integer + Greatest Integer)/2 times (Number of Integers), which here is

(100+122)
--------- * 23
2

Or 111 * 23, or 2553. (The OA is wrong, or there was a typo in the question.)
Johnrohit wrote:the operation --> is defined by x -->y= x+(x+1)+(x+2)...+y. For example, 3-->7=3+4+5+6+7. What is the value of (100 -->150) - (123 -->150)?


[spoiler]OA=2800[/spoiler]
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by GMATGuruNY » Mon Oct 28, 2013 2:41 am
Johnrohit wrote:the operation --> is defined by x -->y= x+(x+1)+(x+2)...+y. For example, 3-->7=3+4+5+6+7. What is the value of (100 -->150) - (125 -->150)?


[spoiler]OA=2800[/spoiler]
100-->150 = 100+101+...+123+124+125+126+...+149+150
125-->150 = .....................................+125+126+...+149+150
When we subtract, all of the values in red cancel (as Matt noted above).
Thus:
Difference = 100+101+....+123+124.

We need to calculate the sum of the CONSECUTIVE INTEGERS from 100 to 124, inclusive.

For any set of consecutive integers:
Number of integers = biggest - smallest + 1
Average = median = (biggest + smallest)/2
Sum = (number)(average).

Here:
Number of integers = 124-100+1 = 25.
Average = (124+100)/2 = 112.
Sum = 25*112 = 2800.

Similar problems:
https://www.beatthegmat.com/for-any-posi ... 59401.html
https://www.beatthegmat.com/sum-of-all-t ... 86631.html
https://www.beatthegmat.com/consecutive- ... 73388.html
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