A nonprofit group organizes its local fundraisers in teams,

Question

A nonprofit group organizes its local fundraisers in teams, with each of its L team leaders responsible for D group directors, and each of those D group directors responsible for F fundraisers. If the only three positions on each local team are team leaders, group directors, and fundraisers, and there are more group directors than team leaders, how many team leaders are on the Dallas team?

(1) There are 81 total members on the Dallas team

(2) There are 5 group directors on the Dallas team

(1) There are 81 total members on the Dallas team

(2) There are 5 group directors on the Dallas team

madhavsrinivas · Accepted Answer

I think you almost got it right with your analysis, but you just missed it. I am sorry. C is incorrect. Please find the answer below:

Each of L team leaders has D group directors, making the total number of group directors equal to (L)(D). And each of those group directors has F fundraisers, again requiring multiplication: that total is (L)(D)(F). (You can try this by plugging in small numbers - if each of 2 leaders has 3 directors, you know there would be 6 directors)

So while statement 1 is not sufficient (there are multiple combinations that could get you to 81, such as L = 1, D = 2, and F = 39; or L = 1, D = 5, and F = 15), statement 2 guarantees that there is only one team leader. This is because 5 is a prime number, and you know that the number of group directors = LD. The only possible way for LD to equal 5 is if L is 1 and D is 5, or if D is 1 and L is 5. And since the stimulus tells you that there are more directors than leaders, the combination must be 5 directors and 1 leader. Accordingly, statement 2 is sufficient.

ENGRTOMBA2018 · Answer

Look below.

The question tells us that there are L leads, each with D directors and each D has F fundraisers. The question is asking you L=?

Now assume some smaller values to make sense of the given information. Lets say there is 1 lead, 2 directors for this 1 lead and in turn each of the 2 directors has 3 fundraisers.

Thus the total number of people = 1+2+6 = 9 ---> Also equal to L+LD+DF (you can try with different combinations).

Per statement 1, L + L*D + L*D*F = 81 ---> L(1+D+DF) = 81 ---> 81/L MUST be an integer ---> L = multiple of 3 or 1

As mentioned above, the possible combinations are L = 1, D = 2, and F = 39; or L = 3, D = 13, and F = 1 or L = 1, D = 5, and F = 15 are the only possible cases.

Thus you get 2 different values of L. NOT sufficient.

Per statement 2, D=5 , this clearly eliminates 2 of the 3 cases we looked at in S1. Thus, this statement is sufficient.

B is thus the correct answer.

Hope this helps.

Paris75 · Answer

I got it wrong since I used the 81 to prove there was only one team leader but:

With statement B alone we can mange to find it:

Since there is L<D, L should be 1 2 3 or 4.

But if L is 2 than the number of D should be divided in 2, meaning ... That we have 2.5 directors. Impossible.

Same logic with 3 and 4...

The only possible answer is 1. Choice C only helps to confirm this answer!

Am I right here?

li220 · Answer

Hey... I'm not sure about this one, I feel A is sufficient too.

From the question we've got:

Total number of people on Dallas team = L + L*D + L*D*F = L * (D + D*F + 1) = L * (D(1+F) + 1) = 81

Given that 81 = 3^4, L must be either 1, 3, 9, 27, or 81. However we also know that L>D, so there's no need to check the combinations where L = 9 or higher.

There a bunch of combinations where L=1, as D can then be equal to any factor of 81-1.
However, there are no combinations where L=3 and where L>D, because in that case D must be a factor of 26, i.e. 1, 2, or 13. 3 is larger than 1 or 2, and 13 doesn't work because in that case F = 1, and 13 Directors can't split 1 fundraiser between them!

So I find that prompt A is sufficient to determine that L = 1.

But VeritasPrep's CAT says I'm wrong, as does this thread, so please explain what I'm missing here!

manpreetsingh86 · Answer

hi, the highlighted portion is wrong. it's actually the other way around. D>L. now try for L=3, we have D=13 and F=2.

i hope it helps.

li220 · Answer

Hey thanks Manpreet. You're right, i meant D>L. You've made me realise that actually my mistake was to confuse F and the total number of fundraisers. I assumed that F = 1 means there's only 1 fundraiser total, when actually that means there's 1 fundraiser per Director, which is entirely possible.

So i think what you mean is L = 3, D = 13, and F = 1

Thanks for quick response!

targetbusiness · Answer

Pls explain how the colored part is leading to 81?

abhimahna · Answer

Hey  siddreal  ,

Team Leaders, L = 1

If D = 2, that means total number of Group directors = L * D = 1*2 = 2 (Each Leader with D directors means if we have 5 leaders, we will have 5D directors)

Now, if F = 39, the total number of fund raisers = L * D * F = 1* 2 * 39 = 78 (Each Director has F fund raisers. We already know We have LD directors, so fund raisers = LD*F)

Total members in the team = Number of (Leaders + Directors + Fundraisers) = 1 + 2 + 78 = 81.

Does that make sense?

KarishmaB · Answer

ArupSR

All teams may not be on the same size but this is the structure of each team:
Each of its L team leaders responsible for D group directors, and each of those D group directors responsible for F fundraisers.

L leaders, each leader managing D directors and each Director managing F fundraisers

So team = L + LD + LDF

The value of L, D and F may be different for different teams.

We are concerned about the Dallas team only.

Stmnt 1: L + LD + LDF = 81
L(1 + D + DF) = 81
L = 1, D = 2, F = 39
L = 3, D = 13, F = 1
Not Sufficient

Stmnt 2 tells us that LD = 5 and since we know that L < D, 
L = 1 and D = 5
Sufficient.

AnirudhaS · Answer

if you get this question within 2 min, you deserve to get that 700!

This is the only possible way to distribute when LD=5=1*5
L1
D1 D2 D3 D4 D5

The example below makes D=6, with L=2
L1..........................L2
D1 D2 D3................D4 D5 D6

And, this makes D=4, with L=2
L1...........................L2
D1 D2.....................D3 D4

The only other way this would work of there are 5 team leaders, and 1 director each under them. But in the question it is pretty much given L<D, so even this wouldn't work but just giving you the visual representation below
L1.....L2.....L3.....L4.....L5
D1.....D2....D3.....D4....D5

Shrey08 · Answer

chetan2u   VeritasKarishma

In statement 2 can we simply say that since number of directors is some integer x multiplied by number of leaders (Because each of the L leader is responsible for D directors) ...... from (2) we know that total number of directors is 5, so 
either 1 leader is responsible for 5 directors or 
5 leaders are responsible for 1 director each.

Since there are fewer leaders than directors, the number of leader cannot be 5. There Number of leader is 1

KarishmaB · Answer

Yes, this is correct. Check here too: https://gmatclub.com/forum/a-nonprofit- ... l#p2674041

happypuppy · Answer

The total size of team = L + L*D + L*D*F

L, D and F are leaders, directors and fundraisers respectively.

We are talking about just one team here: Dallas team

St 1: L + L*D + L*D*F = 81
L(1 + D + D*F) = 81
Multiple solutions exist:
Let's take L=1, we need to get 80 in terms of L+D and D/L is an integer.
L = 1, D= 10, F=70
L = 1, D = 2, F = 39
L = 1, D = 20, F = 60
Hence, Not Sufficient

St 2: Given L*D = 5, or (1*5) only possible factor breakup and L < D
Since person can be only integer. 
L = 1 and D = 5, and F can be anything. 
But we got the no of Leaders: 1
Hence, Sufficient

shubs80 · Answer

Still unable to understand solution , what if 1 group director has more than 1 Team lead ?

A nonprofit group organizes its local fundraisers in teams,

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