HOT Competition (Instagram) 31 Aug/11:00AM: On a certain farm, the rat

On a certain farm, the ratio of pigs to ostriches is 7 to 5. Are there more than 14 llamas on the farm?

(1) The ratio of ostriches to llamas is 4 to 3.
(2) There are five more ostriches than llamas, and there are 8 more pigs than ostriches.

Solution:

Pigs = P, Ostriches = O, and Illamas = I;

From Statement 1

P:O = 7:5 ; O: I = 4:3

therefore, combining them, the ratio becomes P:O:I = 28: 20: 15

Therefore the minimum number of Illmas = 15 ( Since animals have to be a whole number)

So, I> 14

So, 1 is sufficient

From Statement 2

P:O = 7:5 , P - O = 8 , O - I = 5;

Therefore, 7x/12 - 5x/12 = 8 or x/6 = 8 or x = 48;
so P = 28 and O = 20

O - I = 5 ; or I = 15;

So I > 14

So, 2 is also sufficient

IMO D is the correct answer

Posted from my mobile device

D
Is L > 14


1. P : O : L = 28:20:15 .
Hence llamas denoted by L are multiple of 15 , which is more than 14. Hence, sufficient.

2. Similarly O-L = 5 and P-O = 8.
We already know P:O = 7:5.
Solving further,
P : O : L = 28:20:15 .
Hence L are multiple of 15 , which is more than 14. Hence, sufficient.

Posted from my mobile device

Solution:
Let's consider Pigs= P , Ostriches=O , Llamas= L

From question stem we know
\(\frac{P}{O}=\frac{7}{5} =\frac{7X}{5X}\)

P can be 7, 14, 21, 28,35,42,49..... equation(1)
O can be 5,10,15,20,25,30,35,40.... equation(2)

Option1.
\(\frac{Ostriches}{Llamas}=\frac{O}{I}=\frac{4}{3}=\frac{4Y}{3Y}\)

O= 4,8,12,16,20,24.......40.... etc. --equation(3)

First common term between equation(2) and equation (3) is 20 so minimum number of Ostriches can be 20 i.e. 4*5. So minimum number of Llamas 3*5=15.

15>14.
Are there more than 14 llamas on the farm->YES

option2.
\(\frac{P}{O}=\frac{7X}{5X}\)
There are five more ostriches than llamas, and there are 8 more pigs than ostriches.
=>P=O+8=>7X=5X+8=>X=4
=>O=L+5 => 5X=L+5=> 5*4=L+5 =>L=15

Are there more than 14 llamas on the farm->YES

Both options individually are sufficient get answer.

IMO Answer is D

Posted from my mobile device

Let's assume number of pigs = P

No of Ostriches = 5P / 7

=> P should be divisible by 7 & number of Ostriches is a multiple of 5

=> Possible values for no of Ostriches = 5, 10, 15 .....(1)

Statement 1:

Llama = [3 * (no of Ostriches)] / 4

=> No of Ostriches should be a multiple of 4........(2)

After combining eq 1 & 2 possible values of Ostriches =

20, 40......

Possible values of Llama = 15, 30...etc.

We can say no of Llama is more than 14.

Statement 1 is sufficient.


Statement 2:

Let's assume number of Llama = x

No of Ostriches = 5+x

No of Pigs = 8+5+x

We know pigs to ostrich ratio

We can calculate x

=> (13+x)/(5+x) = 7/5

=> x = 30/2 = 15.

No of Llama is 15 30 which is more than 14.

Statement 2 is also sufficient.

Therefore, both statements are sufficient

Therefore, answer should be D option.

Posted from my mobile device

On a certain farm, the ratio of pigs to ostriches is 7 to 5. Are there more than 14 llamas on the farm?

(1) The ratio of ostriches to llamas is 4 to 3.
P:O = 7:5
O:L = 4:3
P:O:L = 28:20:15 (lcm (4,5) = 20)
P = 28x O = 20x L = 15x , where x ≥ 1
Therefore, minimum number of Llamas = 15.
Sufficient.

(2) There are five more ostriches than llamas, and there are 8 more pigs than ostriches.
O = L + 5
P = O + 8 = L + 13

P = 7x and L = 5x
Solving 7x = L + 13 & 5x = L + 5, x = 4 and L = 15
Sufficient.

Choice D is the answer.

Posted from my mobile device

On a certain farm, the ratio of pigs to ostriches is 7 to 5. Are there more than 14 llamas on the farm?

(1) The ratio of ostriches to llamas is 4 to 3.
(2) There are five more ostriches than llamas, and there are 8 more pigs than ostriches.

The number of pig : ostriches is
7x : 5x

st1 : ostrich to ill : 4:3

pig : ostr - (1)
7 : 5

ostr : ill ---(2)

4 3

multiply eq 1 by 4 and eq 2 by 5

pig : ostr : ill
28: 20 : 15

so the minimum ill is more than 14
hence st1 is sufficient.


St2: 7x - 5x = 8 ( as per statement)
2x = 8
x = 4
hence pigs = 28
ostr = 20
now ostr - ill = 5
hence ill = 15

hence statement two is sufficient .

Answer is D

Answer:D
Let number of ostriches=r
Number of pigs=p and number of illamas= i
Given p/r=7/5
Question: i >14 ?
Statement- 1:sufficient
Given r/i=4/3, also we know p/r=7/5
Now multiplying numerator and denominator in such a way that common ration can be deduced.
p/r=7*4/5*4=28/20, r/i=4*5/3*5=20/15
Hence p:r:i=28:20:15=28k:20k:15k
Where k is constant
Now it is clear i=15, 30,45....
That is i>14 sufficient

Statement-2:sufficient
Given r=i+5 and p=r+8
Then p/r=r+8/i+5=7/5 given
Putting value of r=i+5
(i+13) /(i+5) =7/5
i=15, which is greater than 14
Hence both statement sufficient

Posted from my mobile device

Ratio Question.

Given that the ratio of Pigs (P) to Ostriches (O) = 7:5 (P:O)
Question: llamas (L) > 14?

1) the ratio of Ostriches (O) to llamas (L) = 4:3 (O:L)
P:O = 7:5
O:L = 4:3
So we can find that P:O:L = 28:20:15.
So the least number of llamas is 15, which is more than 14.
Sufficient.

2) There are five more ostriches than llamas >> O - L = 5 ---- (1)
and there are 8 more pigs than ostriches. >> P - O = 8 ---- (2)
From P - O = 8 ---- (2) in P:O = 7:5 , P:O should be 28:20.
And from O - L = 5 ----(1), O:L should be 20:15.
So the number of llamas is 15, which is more than 14.
Sufficient.

I choose D.

Posted from my mobile device

On a certain farm, the ratio of pigs to ostriches is 7 to 5. Are there more than 14 llamas on the farm?

Remember : The number of pigs, ostriches, and llamas has to be positive integer.

(1) The ratio of ostriches to llamas is 4 to 3.

--> O:L=4:3, while P:O=7:5, so the least ratio of P:O:L=28:20:15

--> Then, the least number of llamas is 15.

SUFFICIENT.

(2) There are five more ostriches than llamas, and there are 8 more pigs than ostriches.

--> O=L+5 and P=O+8, so P=L+13

--> P:O=7:5, so \(\frac{L+13}{L+5}=\frac{7}{5}\)

--> Solve L; The least number of llamas is 15.

SUFFICIENT.

Posted from my mobile device

On a certain farm, the ratio of pigs to ostriches is 7 to 5. Are there more than 14 llamas on the farm?

(1) The ratio of ostriches to llamas is 4 to 3.
(2) There are five more ostriches than llamas, and there are 8 more pigs than ostriches.

Not a big fan of 'pigs, ostriches and ilamas', so I'm just going to use A, B and C instead

Our question stem: Is C >14 given A:B = 7:5

Statement 1:
B:C = 4:3

A:B = 7:5 (Ist part)
and B:C = 4:3, (IInd part)
since animals cannot be in fractions, for B to satisfy both the conditions, we need to multiply the first part by 5 and the second one with 4
Hence, A:B = 28:20 and B:C = 20:15
C> 14
Sufficient

Statement 2:
B = C+5
A = B+8

Also, A:B = 7x:5x

Using this in the condition given, x = 4 which means A = 28, B = 20 and C = 15
Hence sufficient

Both are sufficient, hence D

Given,

P/O = 7/5 -(1)

STATEMENT 1:

O/L = 4/3 -(2)

Now combining 1 and 2 we get the ratio of all three as

P:O:L = 28:20:15

Thus, minimum value of ratio component can be 1 and thus Llamams has to be 15 or greater. And thus we get a definite yes for our question asked.

STATEMENT 2:

Given, there are 8 more pigs than ostriches.

We already know,

P/O = 7/5

The component difference is 2(7-5)

To make it a difference of 8 we multiply the given ratio by 4 and the resultant will be

P/O = 28/20

Thus there are 28 pigs and 20 ostriches.

Also we are given that Llamas are 5 less than the ostriches, which make them 15 (20-5).
And thus we get a definite yes for our question asked.

Thus as both statements are independent to answer, we mark D as the correct option.

Posted from my mobile device

IMO Ans is D

On a certain farm, the ratio of pigs to ostriches is 7 to 5. Are there more than 14 llamas on the farm?

(1) The ratio of ostriches to llamas is 4 to 3.
(2) There are five more ostriches than llamas, and there are 8 more pigs than ostriches.

P=Pig, O=Ostrich, I= Ilamas
Option 1 :- P:O = 7:5; & O:I = 4:3
=>P:O:I= 28:20:15

SO =>P/I =28/15
=>I=15/28*P

As I is Integer , P must be multiple of 28
SO least value of I=15

Correct

Option II

O-I=5
P-O=8
P:O=7:5

So Solving all three we have O=20
and I=15

Option II Is Correct

So Option D