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SliceCo, a company that sells knives, is structured so that each of it

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SliceCo, a company that sells knives, is structured so that each of it  [#permalink]

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New post 13 Nov 2014, 23:22
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SliceCo, a company that sells knives, is structured so that each of its x regional sales directors has y salespeople working for that director. If, for the month of May, SliceCo sold exactly 2,200 knives, how many regional directors worked for SliceCo that month?

(1) Each regional director sold 150 knives, and each salesperson sold 80 knives.

(2) Each regional director had 5 salespeople.

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Re: SliceCo, a company that sells knives, is structured so that each of it  [#permalink]

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New post 14 Nov 2014, 00:16
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devmillenium2k wrote:
SliceCo, a company that sells knives, is structured so that each of its x regional sales directors has y salespeople working for that director. If, for the month of May, SliceCo sold exactly 2,200 knives, how many regional directors worked for SliceCo that month?

(1) Each regional director sold 150 knives, and each salesperson sold 80 knives.

(2) Each regional director had 5 salespeople.


SOLUTION:

This is slightly a tricky question.

Let the no. of sales director be X and the no. of sales people under each of these sales directors be Y

S1: 150x + 80xy = 2200

x(150 +80Y) = 2200

The prime factors of 2200 is 5^2*2^3*11.

So either X should have 11 as its prime factor or (150+80Y) should have 11 as the prime factor.

Scenario 1 -> consider x as 11. So now (150+80Y) should be 200 to get 2200...but even if take Y as 1...we get 230 . Hence we can conclude that this scenario is not possible and x can't 11.

Scenario 2 -> Now try to get 11 as prime factor of the term (150+80Y)...this becomes possible only when Y=5...i.e. the term becomes (150+80*5)=550

From scenario 2, we get Y=5 & X=4

Hence S1 is sufficient.

S2: This info is not sufficient to find the no. of sales directors.


Therefore Answer 'A'


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Re: SliceCo, a company that sells knives, is structured so that each of it  [#permalink]

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New post 31 Oct 2015, 18:28
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devmillenium2k wrote:
SliceCo, a company that sells knives, is structured so that each of its x regional sales directors has y salespeople working for that director. If, for the month of May, SliceCo sold exactly 2,200 knives, how many regional directors worked for SliceCo that month?

(1) Each regional director sold 150 knives, and each salesperson sold 80 knives.

(2) Each regional director had 5 salespeople.


Evaluating Statement 1:

\(150x+80(xy)=2200\) --> \(15x+8(xy)=220\) --> \(x(15+8y)=2^2*11*5\)

We know that x and y must be integers because the variables represent regional sales directors and salespeople respectively, which are people.

Since y is an integer, \(15+8y\), must be odd. Since \(15+8y\) is odd, x must be even; x must contain both primes of 2, otherwise \(15+8y\) would be even.

Now the question is:
Is \(x=2^2\) or \(x=2^2*5\) or \(x=2^2*11\) or \(x=2^2*5*11\)?

Since y is greater than or equal to 0, \(15+8y\) must be at least 15. Only when \(x=2^2\), \(15+8y\) is at least 15.
So \(15+8y\) is equal to 55 --> y= 5.

Statement 1 is sufficient.
Statement 2 is clearly insufficient since no information about how many knives were sold by each director and/or salespeople.

Correct answer is answer choice A.
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SliceCo, a company that sells knives, is structured so that each of it  [#permalink]

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New post 06 Feb 2017, 01:46
devmillenium2k wrote:
SliceCo, a company that sells knives, is structured so that each of its x regional sales directors has y salespeople working for that director. If, for the month of May, SliceCo sold exactly 2,200 knives, how many regional directors worked for SliceCo that month?

(1) Each regional director sold 150 knives, and each salesperson sold 80 knives.

(2) Each regional director had 5 salespeople.


Official solution from Veritas Prep.

A. This problem includes many elements of "Leverage Assets" and "Beware the C Trap". Statement 1 allows you to set up an equation for the number of knives sold; since each of the \(x\) directors has \(y\) salespeople, the total number of salespeople is then \(xy\), making the equation:

Directors * 150 knives each + Salespeople * 80 knives each = 2200

\(150x+80xy=2200\)

Which may not look sufficient at first given that it's one equation with two variables. But look at what Statement 2 gives you - the exact number of salespeople which would allow you to plug in 5 for y above and easily solve for the variable \(x\). (And note - statement 2 is not sufficient on its own as without knowing how many knives each class of employees sold you can't get anywhere near the totals for the number of people). So you should beware of the "easy C" here and make sure to invest time working on the equation from Statement 1, which reduces to:

\(15x+8xy=220\)

Note that the values for \(x\) and \(y\) must be integers (we're talking about people, so we can't have 2.5 or 8.333), and that you'll need numbers for which the sum ends in \(0\). This doesn't give you many options, and as it turns out the only combination that works is \(x=4\),\(y=5\), which allows for each term to end in \(0\) and keeps the total down to \(220\). Accordingly, since statement 1 alone is enough to solve for the number of regional directors (4), the correct answer is \(A\).
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Re: SliceCo, a company that sells knives, is structured so that each of it  [#permalink]

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