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# The sum of all integers from 19 to 59, inclusive

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The sum of all integers from 19 to 59, inclusive [#permalink]  22 Aug 2018, 09:02
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Question Stats:

37% (01:04) correct 62% (00:55) wrong based on 8 sessions
 Quantity A Quantity B The sum of all integers from 19 to 59, inclusive The sum of all integers from 22 to 60, inclusive

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

Kudos for R.A.E
[Reveal] Spoiler: OA

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Kudos [?]: 496 [0], given: 86

Re: The sum of all integers from 19 to 59, inclusive [#permalink]  29 Aug 2018, 04:01
Carcass wrote:
 Quantity A Quantity B The sum of all integers from 19 to 59, inclusive The sum of all integers from 22 to 60, inclusive

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

Kudos for R.A.E

Let's take sum of numbers from 1 to 59 = $$\frac{{59*60}}{2}= 59 * 30$$

Now the sum of numbers from 1 to 18 = $$\frac{{18 * 19}}{2} = 19 * 9$$ (18 because the number 19 is inclusive)

so QTY A = Sum of nos. from 19 to 59 = $$59 * 30 - 19 * 9 = 1599$$

Let's take sum of numbers from 1 to 60 = $$\frac{{60 * 61}}{2}= 61 * 30$$

Now the sum of numbers from 1 to 21 = $$\frac{{21 * 22}}{2} = 21 * 11$$(18 because the number 19 is inclusive)

so QTY A = Sum of nos. from 22 to 60 =$$61 * 30 - 21 * 11 = 1599$$

i.e option C
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Re: The sum of all integers from 19 to 59, inclusive   [#permalink] 29 Aug 2018, 04:01
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