Problem Solving

Aman verma wrote:Q:In the upcoming Delhi Elections only two major parties are fighting the elections-The Aam-Aadmi Party headed by Arvind kejriwal and The Aam-Aurat party headed by Dr. Sanjay HarshaVardan. 45% of the population support the Aam-Aadmi Party and 30% of the population support The Aam-Aurat Party. One citizen is selected at random from the population named Aman Verma. Find the probability that he supports the Aam-Admi party if it is known that he supports the Aam-Aurat Party.

(A)1/3
(B)2/3
(C)5/6
(D)4/7
(E)5/9

Hi Aman,

As it stands, there is not enough information to answer this question.

Cheers,
Brent

Aman verma wrote:Q:In the upcoming Delhi Elections only two major parties are fighting the elections-The Aam-Aadmi Party headed by Arvind kejriwal and The Aam-Aurat party headed by Dr. Sanjay HarshaVardan. 45% of the population support the Aam-Aadmi Party and 30% of the population support The Aam-Aurat Party and 20% of the population support both the parties. One citizen is selected at random from the population named Aman Verma. Find the probability that he supports the Aam-Admi party if it is known that he supports the Aam-Aurat Party.

(A)1/3
(B)2/3
(C)5/6
(D)4/7
(E)5/9

We can solve this question using the Double Matrix Method. This technique can be used for most questions featuring a population in which each member has two characteristics associated with it.
Here, we have a population of voters, and the two characteristics are:
- pro Aam-Aadmi or not pro Aam-Aadmi
- pro Aam-Aurat or not pro Aam-Aurat

To learn more about this technique, watch our free video: https://www.gmatprepnow.com/module/gmat- ... ems?id=919

Since the question does not ask us to find specific numbers of voters, we can assign a "nice" value to the entire population. Let's say that there are 100 voters altogether.

So, we can set up our diagram as follows:


45% of the population support the Aam-Aadmi Party and 30% of the population support The Aam-Aurat Party
We can add this information to our diagram.



20% of the population support both the parties
We'll add that information as well.


At this point, we can determine the number of voters in each box.


Find the probability that he supports the Aam-Aadmi party if it is known that he supports the Aam-Aurat Party.

So, Aman verma is one of the 30 Aam-Aurat supporters.
Of the 30 Aam-Aurat supporters, 20 also support Aam-Aadmi
So, the required probability = [spoiler]20/30 = 2/3 = B[/spoiler]

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Here are some additional practice questions that can be solved using the Double Matrix Method:
- https://www.beatthegmat.com/mba/2011/05 ... question-1
- https://www.beatthegmat.com/mba/2011/05 ... question-2
- https://www.beatthegmat.com/mba/2011/05 ... question-3
- https://www.beatthegmat.com/ds-quest-t187706.html
- https://www.beatthegmat.com/overlapping ... 83320.html
- https://www.beatthegmat.com/finance-maj ... 67425.html
- https://www.beatthegmat.com/ds-french-j ... 22297.html
- https://www.beatthegmat.com/sets-t269449.html#692540
- https://www.beatthegmat.com/in-costume- ... tml#692116

Cheers,
Brent

Ha - after all of that work, I didn't interpret my own diagram correctly
I edited the last sentence accordingly.

Cheers,
Brent