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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:

52% (00:29) correct 48% (01:04) wrong based on 25 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.

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[Reveal] Spoiler: OA

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Re: The sum of all integers from 19 to 59, inclusive [#permalink]  29 Aug 2018, 04:01
1
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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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Director
Joined: 20 Apr 2016
Posts: 864
WE: Engineering (Energy and Utilities)
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Re: The sum of all integers from 19 to 59, inclusive [#permalink]  03 Apr 2019, 04:57
2
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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

The trick here is ,

QTY A, there are thee extra integers = 19 , 20 , 21 , and the sum of these integers = 60, which include the last integer in the QTY B

Hence QTY A = QTY B
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Re: The sum of all integers from 19 to 59, inclusive [#permalink]  04 Apr 2019, 10:34
2
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pranab01 wrote:

The trick here is ,

QTY A, there are thee extra integers = 19 , 20 , 21 , and the sum of these integers = 60, which include the last integer in the QTY B

Hence QTY A = QTY B

It was really great to see the same person come back six months later and show a quicker way to answer the same question. And this is a great trick, but it may be that not everyone sees this and it may be that this only applies to certain questions.

Here is a technique that works for all such questions. The equation is T = A * N ... I call it getting a "TAN" It stands for Total = Average * the Number of terms. This is easy to apply, especially since the GRE offers a calculator.

Quantity A is the sum (total) of integers from 19 to 59. We can get this total by multiplying the average by the number of terms.

The average of any set that has consistent spacing (such as integers, even integers, multiples of 7, etc) can be found by adding the smallest and largest terms and dividing by 2. So 19 + 59 = 78 / 2 = 39. So the average is 39.

The number of terms for an inclusive set is just the range / the spacing of the terms + 1. In this case we have 59 - 19 = 40 /1 (since we are counting all integers. If we were doing only even integers we would divide by 2 here) and then + 1 for inclusive = 41.

So the total is the average ( 39 ) * the number of terms ( 41 ). = 39 * 41 (At this point no need to multiply yet. Just leave it this way)

If we do the same for Quantity B, which is the sum of all integers from 22 to 60 we get an average of 22 + 60 = 82/2 = 41 and we get a number of terms of 60 - 22 = 38 + 1 = 39.

So the total for quantity B is 41 * 39.

Clearly 39 * 41 = 41 * 39 so the quantities are equal and answer is C!
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David Newland
Veritas Prep GRE Instructor

Re: The sum of all integers from 19 to 59, inclusive   [#permalink] 04 Apr 2019, 10:34
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