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

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6386
GMAT 1: 760 Q51 V42
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Events A, B, C and D are all possible outcomes of an experiment. In t  [#permalink]

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11 Apr 2018, 05:54
00:00

Difficulty:

45% (medium)

Question Stats:

55% (01:06) correct 45% (01:22) wrong based on 100 sessions

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[GMAT math practice question] 4.11

Attachment:

4.11.png [ 2.07 KiB | Viewed 625 times ]

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 $$P(A)$$?

$$1) P(A)+P(B)+P(C)=0.75$$
$$2) P(C)+P(D)=0.25$$

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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $99 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Intern Joined: 28 Apr 2014 Posts: 49 GMAT 1: 640 Q50 V25 Re: Events A, B, C and D are all possible outcomes of an experiment. In t [#permalink] ### Show Tags 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 Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6386 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Events A, B, C and D are all possible outcomes of an experiment. In t [#permalink] ### Show Tags 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 _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$99 for 3 month Online Course"
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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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25 Apr 2018, 23:03
P(x)=P(a)+P(b)+P(c)+P(d)=1
=P(a)+P+0.25+P(c)+P(d)=1
=P(a)+P(c)+P(d)=0.75

Require c and d values

B clearly gives this Vue, A does not

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Intern
Joined: 08 Jul 2018
Posts: 22
Location: India
Concentration: General Management, Marketing
GPA: 4
Re: Events A, B, C and D are all possible outcomes of an experiment. In t  [#permalink]

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21 Sep 2018, 23:43
MathRevolution wrote:
[GMAT math practice question] 4.11

Attachment:
4.11.png

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 $$P(A)$$?

$$1) P(A)+P(B)+P(C)=0.75$$
$$2) P(C)+P(D)=0.25$$

Looking at St. 1 -
We know that P(B)=.25
and from the st. P(A)+P(B)+P(C)=0.75

So, P(A)+P(C) =.25

No other way to find out the value of P(A).
Insufficient

So, options A & D are out

Now, for st.2
P(C)+P(D)=0.25
and it is given that P(B)=.25

Now, we also know that

P(A)+P(B)+P(C)+P(D)=1

replacing the values,

P(A)+.25+.5=1

P(A) =.25

Hence, B

Hit Kudos if this helps!
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Joined: 24 Dec 2017
Posts: 118
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Concentration: Strategy, Real Estate
Schools: Johnson '21
Re: Events A, B, C and D are all possible outcomes of an experiment. In t  [#permalink]

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22 Sep 2018, 22:57
First of all, I am not that good at probability. So please let me know if my approach is correct or not.

We need to P(A).

St 1: P(A)+P(B)+P(C)=0.75
=>P(B) = 0.25
=>P(A) + P(B) = 0.50
=> We cannot determine the value of P(A) from the given data. Hence insufficient.

St 2: P(C) + P(D) = 0.25
=>P(A)+P(B)+P(C)+P(D)=1
=>P(A)+0.25+0.25=1
=>P(A)=1-0.25-0.25
=>P(A)=0.50

Hence I chose B
Re: Events A, B, C and D are all possible outcomes of an experiment. In t &nbs [#permalink] 22 Sep 2018, 22:57
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# Events A, B, C and D are all possible outcomes of an experiment. In t

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