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# Three consecutive integers have a sum of −84.

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Three consecutive integers have a sum of −84. [#permalink]  18 Jan 2016, 08:11
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Three consecutive integers have a sum of −84.

 Quantity A Quantity B The least of the threeintegers −28

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

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Re: Three consecutive integers have a sum of −84. [#permalink]  18 Jan 2016, 08:17
Expert's post
Solution

The best approach to the question is conceptually

3 consecutive integers are $$x, (x+1), (x+2) = -84$$. After calculation we do have: $$x= -29$$

$$-29 < -28$$ on the number line

The answer is $$B$$
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Re: Three consecutive integers have a sum of −84. [#permalink]  26 Jul 2017, 12:14
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Re: Three consecutive integers have a sum of −84. [#permalink]  13 Nov 2018, 19:43
Carcass wrote:
Solution

The best approach to the question is conceptually

3 consecutive integers are $$x, (x+1), (x+2) = -84$$. After calculation we do have: $$x= -29$$

$$-29 < -28$$ on the number line

The answer is $$B$$

After calculation ..... It is better if you show the calculation.
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Re: Three consecutive integers have a sum of −84. [#permalink]  15 Nov 2018, 02:32
If i consider the three integers as x-1,x,x+1 i get, x=-28

Under such a scenario, the integers become: -29,-28,-27
For this, the answer would be -27 > -28
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Re: Three consecutive integers have a sum of −84. [#permalink]  15 Nov 2018, 03:06
Expert's post
skjoshi267 wrote:
If i consider the three integers as x-1,x,x+1 i get, x=-28

Under such a scenario, the integers become: -29,-28,-27
For this, the answer would be -27 > -28

The least of the three integers -29,-28,-27 is -29 and not -27....

Let the three integers be x-1, X, X+1... So 3x=-84...X=-28
So numbers are -29,-28,-27
Least is -29 and is >-28
So A<B
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Some useful Theory.
1. Arithmetic and Geometric progressions : https://greprepclub.com/forum/progressions-arithmetic-geometric-and-harmonic-11574.html#p27048
2. Effect of Arithmetic Operations on fraction : https://greprepclub.com/forum/effects-of-arithmetic-operations-on-fractions-11573.html?sid=d570445335a783891cd4d48a17db9825
3. Remainders : https://greprepclub.com/forum/remainders-what-you-should-know-11524.html
4. Number properties : https://greprepclub.com/forum/number-property-all-you-require-11518.html
5. Absolute Modulus and Inequalities : https://greprepclub.com/forum/absolute-modulus-a-better-understanding-11281.html

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Re: Three consecutive integers have a sum of −84. [#permalink]  19 Nov 2018, 17:08
AE wrote:
Carcass wrote:
Solution

The best approach to the question is conceptually

3 consecutive integers are $$x, (x+1), (x+2) = -84$$. After calculation we do have: $$x= -29$$

$$-29 < -28$$ on the number line

The answer is $$B$$

After calculation ..... It is better if you show the calculation.

Basically it would be 3x + 3 = -84 so then it would be 3x = -87

x = -29 (the least of them)

Since -29 < -28.

The answer is B
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Re: Three consecutive integers have a sum of −84. [#permalink]  20 Nov 2018, 20:42
These integers are consecutive and their sum equals -84
Because they are consecutive they can’t have any arbitrary value, they should have such a shape:
x, x+1, x+2
x + x+1 + x+2 =
3x+ 3 = -84
3x = -84 -3 =-87
x = -29
A which is -29 is less than B which is -28. The answer is B.
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Re: Three consecutive integers have a sum of −84. [#permalink]  26 Nov 2018, 21:59
thank you
Re: Three consecutive integers have a sum of −84.   [#permalink] 26 Nov 2018, 21:59
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# Three consecutive integers have a sum of −84.

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