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Events A, B, C and D are all possible outcomes of an experiment. In t

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Events A, B, C and D are all possible outcomes of an experiment. In t [#permalink]

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New post 11 Apr 2018, 05:54
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[GMAT math practice question] 4.11

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Events \(A, B, C\) and \(D\) are all possible outcomes of an experiment. In the table above, \(P(x)\) denotes the probability that event \(x\) occurs. What is \(P(A)\)?

\(1) P(A)+P(B)+P(C)=0.75\)
\(2) P(C)+P(D)=0.25\)
[Reveal] Spoiler: OA

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Re: Events A, B, C and D are all possible outcomes of an experiment. In t [#permalink]

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New post 11 Apr 2018, 07:06
total probability is 1
therefore, a+c+d=0.75

St1
a+0.25+c=0.75
a=0.5-c
Insufficient

St2
c+d=0.25
and we know that
a+c+d=0.75
a=0.5
Sufficient
Expert Post
Math Revolution GMAT Instructor
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Joined: 16 Aug 2015
Posts: 5267
GMAT 1: 800 Q59 V59
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Re: Events A, B, C and D are all possible outcomes of an experiment. In t [#permalink]

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New post 13 Apr 2018, 02:36
=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.

Since \(P(A) = a = 1 – ( c + d ) – 0.25 = 0.75 – (c + d)\), then \(P(A)\) can be determined from the value of \(c + d\). Thus, the answer is \(B\).

Condition 1)
If \(P(A) = 0.5, P(B) = 0.25\) and \(P(C) = 0\), then we have \(P(A) = 0.5.\)
If \(P(A) = 0.4, P(B) = 0.25\) and \(P(C) = 0.1\), then we have \(P(A) = 0.4.\)
Thus, condition 1) is not sufficient.

Condition 2)
Since \(P(A) + P(B) + P(C) + P(D) = 1, P(B) = 0.25\) and \(P(C) + P(D) = 0.25\) from condition 2), we have \(P(A) = 0.5.\)
Thus, condition 2) is sufficient.

Therefore, the answer is B.
Answer: B
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Re: Events A, B, C and D are all possible outcomes of an experiment. In t   [#permalink] 13 Apr 2018, 02:36
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