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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. # A retail business has determined that its net income, in ter  Question banks Downloads My Bookmarks Reviews Important topics
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A retail business has determined that its net income, in ter [#permalink]
Expert's post 00:00

Question Stats: 95% (00:56) correct 4% (02:00) wrong based on 43 sessions
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]
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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. Manager Joined: 26 Jan 2018
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Re: A retail business has determined that its net income, in ter [#permalink]
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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? Retired Moderator Joined: 07 Jun 2014
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Re: A retail business has determined that its net income, in ter [#permalink]
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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]
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. Intern Joined: 04 Oct 2018
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Re: A retail business has determined that its net income, in ter [#permalink]
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Here, x (Square)+x−380 = 0
Then, x (x+1) = 380
Then, x (x+1) = 19 * 20
Then, x (x+1) = 19 * (19+1)
So, x = 19
Ans: A
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Re: A retail business has determined that its net income, in ter [#permalink]
Expert's post
Column A: If the net income = 0, then x² + x - 380 = 0
Let's solve this equation by factoring: (x + 20)(x - 19) = 0
So, x = -20 or x = 19
Since x (the number of items sold) cannot be NEGATIVE, we can be certain that x = 19
So, Column A = 19
Column B = 10

[Reveal] Spoiler:
A

Cheers,
Brent
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Brent Hanneson – Creator of greenlighttestprep.com
If you enjoy my solutions, you'll like my GRE prep course. Manager Joined: 27 Sep 2017
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Re: A retail business has determined that its net income, in ter [#permalink]
First of all, we had to know that items can NOT be negative.

Then, for the net income $$x^{2}$$ + x - 380 to be 0. We can do the factorization (x+20)(x-19). We get x=19 or -20.

since items can not be negative. Quant A is 20 which is bigger than Quant B (10).
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Re: A retail business has determined that its net income, in ter [#permalink]
Thank you Re: A retail business has determined that its net income, in ter   [#permalink] 24 Feb 2020, 02:41
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