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Algebra

This topic has 3 expert replies and 0 member replies

Algebra

Post
If $$\left(3+a\right)\left(\frac{a}{10}-0.4\right)=-1$$ , then a could be

A. -4
B. -2
C. 1
D. 2
E. 4
What is the correct solution to this to get the right Option? Can any expert help out here?

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GMAT/MBA Expert

Post
Roland2rule wrote:
If $$\left(3+a\right)\left(\frac{a}{10}-0.4\right)=-1$$ , then a could be

A. -4
B. -2
C. 1
D. 2
E. 4
The decimals make this equation hard to solve .
So, let's first multiply both sides by 10.
We get: (3 + a)(10)(a/10 - 0.4) = (10)(-1)
Expand to get: (3 + a)(a - 4) = -10
Expand and simplify to get: a² - a - 12 = -10
Add 10 to both sides: a² - a - 2 = 0
Factor: (a - 2)(a + 1) = 0
So EITHER a = 2 OR a = -1

Check the answer choices....
Answer: D

Cheers,
Brent

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GMAT/MBA Expert

Post
Hi Roland2rule,
Lets take a look at your question.

$$\left(3+a\right)\left(\frac{a}{10}-0.4\right)=-1$$
In the first step, we will simplify the equation,
$$\left(3+a\right)\left(\frac{a-4}{10}\right)=-1$$

Multiply both sides of the equation by 10,
$$\left(3+a\right)\left(a-4\right)=-1\left(10\right)$$
$$\left(3+a\right)\left(a-4\right)=-10$$

Simplify the left hand side by multiplying the binomials,
$$3a-12+a^2-4a=-10$$
$$-a-12+a^2=-10$$
$$-a-12+a^2+10=0$$
$$a^2-a-2=0$$

Factorizing by grouping,
$$a^2-2a+a-2=0$$
$$a\left(a-2\right)+1\left(a-2\right)=0$$
$$\left(a-2\right)\left(a+1\right)=0$$
$$Either\ \left(a-2\right)=0\ or\ \left(a+1\right)=0$$
$$Either\ a=2\ or\ a\ =\ -1$$

If we see on the options given, we can only find 2 in the answer choices.
Therefore, Option D is correct.

I am available, if you'd like any follow up.

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Hi Roland2rule,

This question can be solved by TESTing THE ANSWERS. You can also take advantage of a particular Number Property to help you eliminate some of the answer choices. Since the product of the two parentheses is -1, one of those parentheses has to be POSITIVE while the other is NEGATIVE.

(3+A)(A/10 - .4) = -1

Answer A will make BOTH negative, while Answer E will make the second one equal 0. Thus, you can eliminate both of those options. From the remaining 3 choices, you just have to 'plug in' until you find the match. Based on these 3 remaining answers, the second parenthesis will be a one-decimal-place FRACTION, and the sum in the first will either be 1, 4 or 5, the correct answer will likely be the 5 (since we need the product to be an integer). TEST A=2 and you'll have your match.

Final Answer: D

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

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