If 12 birds sit on each branch of a tree, 6 birds don’t have a place

Question

If 12 birds sit on each branch of a tree, 6 birds don’t have a place to sit. If 15 birds sit on each branch, 2 branches are left vacant. The number of birds are how many more than the number of branches?

(A) 148
(B) 138
(C) 128
(D) 118
(E) 108

(A) 148 
(B) 138 
(C) 128 
(D) 118
(E) 108

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GMATinsight · Answer

Let, number of trees = x

Total Birds = 12x+6

Total Birds = 15*(x-2)

i.e. 12x+6 = 15(x-2)

i.e. 3x = 36

i.e. trees, x = 12
i.e. Birds = 12x+6 = 1150

Birds - Branches = 150-12 = 138

Answer: Option B

yashikaaggarwal · Answer

Answer is supposedly B.
Let k be the no. Of branches.
If 12 birds are sitting on each branch. 6 birds Don't have space.
12k+6 -----(1)

If 15 birds sit on each branch. 2 branches remain vacant.
15(k-2) -----(2)

Equating 1&3
12k+6=15k-30
36=3k
K=12. So there are 12 branches 
And putting value of k in any equation. We get 150 as the birds no.
Now birds more than branches are 150-12=138
Answer should be B

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Lucky1994 · Answer

let number of birds = x and branches=y.
12y+6=x (from 1st statement)
15(y-2)=x (from 2nd statement)

solving both equation
x= 138 and y=12.

Difference = 138.

Option B

neshantz · Answer

Is there any way to solve this faster by other methods also?

I noticed intuitively in my head that the total birds being 150 made sense as it's a multiple of 15 and also 12*12 + 6 = 150.

But I couldn't figure out how to confirm this quickly by checking the answers etc.

sujoykrdatta · Answer

Let the number of branches be b:

From the first scenario: Total number of birds = 12b + 6

Note:  We need to determine the difference between the number of birds and the number of branches.

Thus: Total number of birds - Number of branches =  12b + 6 - b = 11b + 6

Only option B is of the above form: 6 more than a multiple of 11: 138 = 6 + 11 * 12

Note: It makes sense to ask yourself a couple of questions before jumping into the solution:
Why have they asked for the difference and not just the number of birds etc. 
Why are all options in a pattern

Answer B

However, if this observation does not click:

From the second scenario: Total number of birds = 15(b - 2)

Equating total number of birds:  15(b - 2) = 12b + 6  
=> b = 12

=> Number of birds = 15(b - 2) = 150
=> Difference = 150 - 12 = 138

Archit3110 · Answer

an alternate way than using linear expression method ..
 neshantz

If 12 birds sit on each branch of a tree, 6 birds don’t have a place to sit
means that for every multiple of 12 birds, 6 other birds dont get a place
if observed then then birds total would be a factor of 15 considering branch >1 ; eg we get 12x+6/15 which can be written as 2 * (2x+1)/5 ; x can be 2,12,7,17

secondly we know that If 15 birds sit on each branch, 2 branches are left vacant.
which means that for every multiple value of bird , the total branches are +2 ; i.e for 15 birds we have 3 branches ; 30 birds ; 4 branches
45 birds; 5 branches ; 60 birds 6 branches 
75 --7
90--8
105-9
120-10
135-11
150-12
target of question is The number of birds are how many more than the number of branches?
seeing options we see only option which matches ; 150-12 ; 138 and also since value of x can be ( 2,7,12,17) so only 12 branches match

OPTION B 138

lacktutor · Answer

Let x be the number of branches :
Number of birds if 12 birds on each branch: (12x +6 ) 
Number of birds if 15 birds on each branch: 15(x -2)

(12x +6 )= 15(x -2)
12x + 6= 15x -30
x = 12 (branches)
12x +6 = 150 birds

150- 12= 138 
Answer (B)

AnirudhaS · Answer

Let b= number of branches, and t=total number of birds
Therefore,
12b+6=t....(i)
15(b-2)=t.....(ii)
Solving (i) and (ii), b=12, t=150
So difference = 150-12=138

Answer:  B

ScottTargetTestPrep · Answer

We can let b = the number of birds on the branches of the tree and r = the number of branches on the trees. We can create the equations:

b = 12r + 6

and

b = 15*(r - 2)

b = 15r - 30

Equating the right hand side of these two equations (since they are both equal to b), we have:

12r + 6 = 15r - 30

36 = 3r

12 = r

So there are 12 branches on the tree and 12(12) + 6 = 144 + 6 = 150 birds on the tree. Therefore, the number of birds is 150 - 12 = 138 more than the number of branches.

Answer: B

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If 12 birds sit on each branch of a tree, 6 birds don’t have a place

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