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505-555 (Easy)|   Algebra|                              
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shwetasood
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If a(a + 2) = 24 and b(b + 2) = 24, where a ≠ b, then a + b = 01 Sep 2023, 00:04
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alphaseeker
If a(a+2)=24 and b(b+2)=24
a(a+2)=b(b+2)
a^2+2a=b^2+2b
a^2-b^2=2b-2a
(a-b)(a+b)=2(b-a)
a+b=-2 (No need for smart numbers)
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can you please explain how it became minus 2 at the end. where did that minus sign come from
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Bunuel
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If a(a + 2) = 24 and b(b + 2) = 24, where a ≠ b, then a + b = 01 Sep 2023, 00:08
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shwetasood
alphaseeker
If a(a+2)=24 and b(b+2)=24
a(a+2)=b(b+2)
a^2+2a=b^2+2b
a^2-b^2=2b-2a
(a-b)(a+b)=2(b-a)
a+b=-2 (No need for smart numbers)

can you please explain how it became minus 2 at the end. where did that minus sign come from
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(a - b)(a + b) = 2(b - a)

Since (b - a) = -(a - b), then we get:

(a - b)(a + b) = -2(a - b)

Since a ≠ b, then a - b ≠ 0, and we can safely reduce by it to get:

a + b = -2

Hope it's clear.
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GMAT 1: 800 Q51 V49
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If a(a + 2) = 24 and b(b + 2) = 24, where a ≠ b, then a + b = 01 Sep 2023, 14:04
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shwetasood
alphaseeker
If a(a+2)=24 and b(b+2)=24
a(a+2)=b(b+2)
a^2+2a=b^2+2b
a^2-b^2=2b-2a
(a-b)(a+b)=2(b-a)
a+b=-2 (No need for smart numbers)



can you please explain how it became minus 2 at the end. where did that minus sign come from
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Hi shwetasood,

Any time you divide a non-zero integer by its 'opposite', you end up with -1. For example:

4/-4 = -1
-7/7 = -1
-X/X = -1
Etc.

In this prompt, the terms (A - B) and (B - A) are opposites, so at this point in the algebra...

(A - B)(A + B) = 2(B - A)

We can divide both sides by (A-B).

(A - B)(A + B)/(A-B) = 2(B - A)/(A - B)

This will 'cancel out' the terms on the 'left side' of the equation and create a "-1" on the 'right side'...

(A + B) = 2(-1)
(A + B) = -2

GMAT assassins aren't born, they're made,
Rich

Contact Rich at: [email protected]
www.empowergmat.com
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If a(a + 2) = 24 and b(b + 2) = 24, where a ≠ b, then a + b = 24 Sep 2024, 13:37
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shwetasood
shwetasood
alphaseeker
If a(a+2)=24 and b(b+2)=24
a(a+2)=b(b+2)
a^2+2a=b^2+2b
a^2-b^2=2b-2a
(a-b)(a+b)=2(b-a)
a+b=-2 (No need for smart numbers)



can you please explain how it became minus 2 at the end. where did that minus sign come from
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(b-a)/(a-b) will give you -1. 2*-1 is -2.
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If a(a + 2) = 24 and b(b + 2) = 24, where a ≠ b, then a + b = 29 Sep 2025, 11:16
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