Of the leopards at a certain zoo, 20% are both spotted and mature. If

Question

Of the leopards at a certain zoo, 20% are both spotted and mature. If all the leopards at the zoo are either spotted or not spotted, or mature or immature, is the ratio of the number of immature leopards who are spotted to the number of immature leopards who are not spotted greater than 1?

(1) If the number of immature spotted leopards doubled than there would be 102 total leopards at the zoo.

(2) If the number of immature but not spotted leopards were decreased by a half there would 86 total leopards at the zoo.

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Shwarma · Answer

Option C  ??

x= total animals
a= spotted immature
c= non-spotted immature 
Is a/c >1 ?
Yes/no

1. a+x=102
2. x-c/2= 86

1and 2 - a/c= 102-x/2x+172

so no matter any value of x(which will be positive, a/c is <1)  --  sufficient

Nidzo · Answer

Plotting the info provided in a 4x4 matrix.

\begin{tabular}{|l|l|l|l|}
    \hline
        ~ & M & I & Total \ \hline
        S & 20% &  ~ & ~ \ \hline
        nS & ~ & ~ & ~ \ \hline
        Total & ~ & ~ & 100% \ \hline
    \end{tabular}

For the ratio of the number of immature leopards who are spotted to the number of immature leopards who are not spotted to be greater than 1, the number of immature leopards who are spotted needs to be greater than the number of immature leopards who are not spotted.

(1) If the number of immature spotted leopards doubled than there would be 102 total leopards at the zoo.

Let the normal value of immature spotted leopards = x

\begin{tabular}{|l|l|l|l|}
    \hline
        ~ & M & I & Total \ \hline
        S & 20% &  2x & ~ \ \hline
        nS & ~ & ~ & ~ \ \hline
        Total & ~ & ~ & 102 \ \hline
    \end{tabular}

Simply plugging this info as above is wrong, because as one increases the total number of leopards the 20% for mature spotted leopards needs to decrease.

From this statement one cannot deduce if the number of immature leopards who are spotted is greater than the number of immature leopards who are not spotted.

INSUFFICIENT

(2) If the number of immature but not spotted leopards were decreased by a half there would 86 total leopards at the zoo.

Let the number of immature but not spotted leopards = y

\begin{tabular}{|l|l|l|l|}
    \hline
        ~ & M & I & Total \ \hline
        S & 20% &  ~ & ~ \ \hline
        nS & ~ 0.5y ~ & ~ \ \hline
        Total & ~ & ~ & 86 \ \hline
    \end{tabular}

As with statement 1, this does not provide sufficient info to find an answer to the question.

INSUFFICIENT

(1+2)

Putting the two statements together, one knows that if the number of immature spotted leopards doubled than there would be 102 total leopards, and if the number of immature but not spotted leopards were decreased by a half there would 86 total leopards. Without knowing how many leopards there are in total, it is impossible to use the info provided to find if the number of immature leopards who are spotted is greater than the number of immature leopards who are not spotted.

INSUFFICIENT

ANSWER E

Purnank · Answer

How can we equate x of both equation isn't that x will contain some of spotted immature, non-spotted immature of eiether of the conditons and those values will be different with respect to each statement?

fangjue987a · Answer

I calculated and I think it it C.

Suppose 
Spotted but immature=A,
Unspotted & immature=B,

Q: A/B>1?

Statement (1) 
(A+B)+All Mature=102, insufficient,

Statement (2)
A+B/2+All Mature=86, insufficient,

(1)+(2)
A+3/2B=16
2A+3B=32

All possible A & B could be:
A=13,B=2
A=10,B=4
A=7,B=6
A=4,B=8
A=1,B=10

Since Total animals= 102- (A+B), Total number of animals can be: 87,88,89,90,91
Only 90 satisfied coz 20%*90 is an integer ( the number of both spotted and mature).

so A/B < 1.

I think the answer is C, I donot know if I made mistakes in above steps.

pradeepbhuyan · Answer

denominator is not 2x+172 rather its 2x-172

Of the leopards at a certain zoo, 20% are both spotted and mature. If

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Of the leopards at a certain zoo, 20% are both spotted and mature. If

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