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# A retail business has determined that its net income, in ter

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A retail business has determined that its net income, in ter [#permalink]  16 May 2018, 08:45
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A retail business has determined that its net income, in terms of x, the number of items sold, is given by the expression $$x^2 + x - 380$$.

 Quantity A Quantity B The number of items that must be sold for the net income to be zero 10

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.
[Reveal] Spoiler: OA

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Re: A retail business has determined that its net income, in ter [#permalink]  16 May 2018, 20:20
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I solved the problem using the quadratic formula, but I welcome other ways on how to do it faster.

a=1, b=1, c= -380

x= $$\frac{-1+-\sqrt{1^2-4(1)(-380)}}{2(1)}$$

x= $$\frac{-1+-\sqrt{1521}}{2}$$

x= $$\frac{-1+39}{2(1)}$$ and x= $$\frac{-1-39}{2}$$

X= $$\frac{38}{2}$$ and x= $$\frac{-40}{2}$$

x=19 and x=-20.

Since we are looking for a positive integer, we can disregard -20 and only look at x=19.

Quantity A = 19
Quantity B = 10

Quantity A is greater.

Last edited by PIneappleBoy2 on 17 May 2018, 00:27, edited 1 time in total.
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Re: A retail business has determined that its net income, in ter [#permalink]  16 May 2018, 21:41
PIneappleBoy2 wrote:
I solved the problem using the quadratic formula, but I welcome other ways on how to do it faster.

a=1, b=1, c= -380

x= $$\frac{-1+-\sqrt{1^2-4(1)(-380)}}{2(1)}$$

x= $$\frac{-1+-\sqrt{1521}}{2}$$

x= $$\frac{-1+39}{2(1)}$$ and x= $$\frac{-1-39}{2}$$

X= $$\frac{38}{2}$$ and x= $$\frac{-40}{2}$$

x=14 and x=-20.

Since we are looking for a positive integer, we can disregard -20 and only look at x=14.

Quantity A = 14
Quantity B = 10

Quantity A is greater.

38/2 is 19 BTW.

How do we know square root of 1521 is 39?

I think we can just consider about the symobl the number would have and conclude as positive vs negative. Correct me if I am wrong.

Also is that the only way to solve this problem?
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Re: A retail business has determined that its net income, in ter [#permalink]  16 May 2018, 21:50
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Expert's post
The quadratic method is indeed correct. There is a riskier plugging method.

Rewrite the equation: $$x^2+x-380=0$$ as $$x^2+x=380$$

$$x(x+1)=380$$.

So 380 is product of 2 consequtive integers x and x+1. Factorizing 380 we get 19, 5, 2, 2. So we can rewrite 380 as 19*20 (two consecutive integers).

Hence x=19.

PS: in real exam this method might be risky and might consume too much time to implement.
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Re: A retail business has determined that its net income, in ter [#permalink]  17 May 2018, 00:33
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mohan514 wrote:
PIneappleBoy2 wrote:
I solved the problem using the quadratic formula, but I welcome other ways on how to do it faster.

a=1, b=1, c= -380

x= $$\frac{-1+-\sqrt{1^2-4(1)(-380)}}{2(1)}$$

x= $$\frac{-1+-\sqrt{1521}}{2}$$

x= $$\frac{-1+39}{2(1)}$$ and x= $$\frac{-1-39}{2}$$

X= $$\frac{38}{2}$$ and x= $$\frac{-40}{2}$$

x=14 and x=-20.

Since we are looking for a positive integer, we can disregard -20 and only look at x=14.

Quantity A = 14
Quantity B = 10

Quantity A is greater.

38/2 is 19 BTW.

How do we know square root of 1521 is 39?

I think we can just consider about the symobl the number would have and conclude as positive vs negative. Correct me if I am wrong.

Also is that the only way to solve this problem?

Just edited my original post to reflect that the answer is actually 19, not 14. Thank you for that.

We are able to find that 39 is the square root of 1521 through the use of the GRE Calculator.

As for concluding the positive vs. negative, you are correct. I just wrote it out since it was a part of the quadratic equation.
Re: A retail business has determined that its net income, in ter   [#permalink] 17 May 2018, 00:33
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