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Does a x (b + c) = a x b + c?

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Source: — Data Sufficiency |
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by MartyMurray » Fri Jun 17, 2016 10:04 pm
Statement 1: a = 1

If a = 1, look at what the question becomes.

Does 1 x (b + c) = 1 x b + c.

Standard order of operations puts multiplication ahead of addition. So 1 x b + c is the same as (1 x b) + c.

If we multiply out the two sides of the equation, the question becomes the following.

Does b + c = b + c?

For any values of b and c the answer to the question is "Yes."

So even though you have three variables and only two equations, you can answer the question with certainty.

Sufficient.

Statement 2: c = 0

If we plug into the equation 0 for c, the question becomes the following.

Does a x (b + 0) = a x b + 0?

Simplify the equation.

Does a x b = a x b?

For any values of a and b the answer is "Yes."

Sufficient.

The correct answer is D.
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by OptimusPrep » Sun Jun 19, 2016 3:13 am
Poisson wrote:Does a x (b + c) = a x b + c?

Statement 1: a = 1

Statement 2: c = 0

Please help me understand the logic behind this. Thanks so much.
Required: a(b + c) = ab + c?

Statement 1: a = 1
Hence a (b + c) = b + c
And, ab + c = b + c
These both are equal

SUFFICIENT

Statement 2: c = 0
a(b + c) = ab
And ab + c = ab
Again, these both are equal.

SUFFICIENT

Correct Option: D
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by Matt@VeritasPrep » Thu Jun 23, 2016 5:56 pm
Start with a little algebra:

a*b + a*c = a*b + c

a*c = c

a*c - c = 0

c * (a - 1) = 0

If this equation is true, we have c = 0 or (a - 1) = 0, i.e. a = 1. So the question becomes

"Is c = 0 and/or a = 1?"

From there, the statements are a snap!

This is very common the GMAT, so it's a good practice to do everything you can to simplify the problem first before attacking the statements.
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by Poisson » Fri Jul 01, 2016 6:26 am
Matt@VeritasPrep wrote:Start with a little algebra:

a*b + a*c = a*b + c

a*c = c

a*c - c = 0

c * (a - 1) = 0

If this equation is true, we have c = 0 or (a - 1) = 0, i.e. a = 1. So the question becomes

"Is c = 0 and/or a = 1?"

From there, the statements are a snap!

This is very common the GMAT, so it's a good practice to do everything you can to simplify the problem first before attacking the statements.
Thanks Matt! This helped me realize I could subtract ab from both sides. After that, it's easy. So this shows the importance of pulling as much information as possible from the stem. Thanks!
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by Matt@VeritasPrep » Fri Jul 08, 2016 2:31 pm
Poisson wrote:Thanks Matt! This helped me realize I could subtract ab from both sides. After that, it's easy. So this shows the importance of pulling as much information as possible from the stem. Thanks!
No problem! Extracting everything you can (and more!) from the stem is absolutely critical. In my experience, if I can't decode the stem, the statements tend to ADD confusion rather than remove it, so I do whatever I can to clear things up or phrase the problem in a friendlier way before addressing the statements.
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