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.
Does a x (b + c) = a x b + c?
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- MartyMurray
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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.
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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- OptimusPrep
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Required: a(b + c) = ab + c?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.
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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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.
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!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.
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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.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!