GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 16 Oct 2019, 00:09

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

### Hide Tags

Intern
Joined: 20 Jan 2013
Posts: 33
SliceCo, a company that sells knives, is structured so that each of it  [#permalink]

### Show Tags

13 Nov 2014, 23:22
16
00:00

Difficulty:

95% (hard)

Question Stats:

41% (02:41) correct 59% (02:26) wrong based on 137 sessions

### HideShow timer Statistics

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.

_________________
_________________

KUDOS is always a good way to thank anyone.
It encourages someone to post more questions and also answers.

KUDOS Please if My post helps you in anyway. Your Kudos keep me alive [/color]
Intern
Joined: 04 Jul 2014
Posts: 45
Schools: Smeal" 20
Re: SliceCo, a company that sells knives, is structured so that each of it  [#permalink]

### Show Tags

14 Nov 2014, 00:16
3
2
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.

------------

Please give Kudos if this post helps
##### General Discussion
Manager
Joined: 01 Jan 2015
Posts: 62
Re: SliceCo, a company that sells knives, is structured so that each of it  [#permalink]

### Show Tags

31 Oct 2015, 18:28
3
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.

Senior SC Moderator
Joined: 14 Nov 2016
Posts: 1348
Location: Malaysia
SliceCo, a company that sells knives, is structured so that each of it  [#permalink]

### Show Tags

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 $$A$$.
_________________
"Be challenged at EVERY MOMENT."

“Strength doesn’t come from what you can do. It comes from overcoming the things you once thought you couldn’t.”

"Each stage of the journey is crucial to attaining new heights of knowledge."

Non-Human User
Joined: 09 Sep 2013
Posts: 13162
Re: SliceCo, a company that sells knives, is structured so that each of it  [#permalink]

### Show Tags

17 Jun 2019, 08:24
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: SliceCo, a company that sells knives, is structured so that each of it   [#permalink] 17 Jun 2019, 08:24
Display posts from previous: Sort by