Question: From the even numbers between 1 and 9, two different even numbers are to be chosen at random, without replacement. What is the probability that their sum will be 8?

1. 1/12
2. 1/6
3. 1/4
4. 1/3
5. 1/2

Correct Answer: B
Solution and Explanation:
Approach Solution 1:
Even numbers between 1 and 9 are 2,4,6,8.
The sum of the two numbers should be 8, and the possible ways are (2,6), or, (6,2)
Probability of selecting the 1st number (between 2 or 6) = 2/4= ½
Probability of selecting the 2nd number (between 4,6,8 or 2,4,8)= 1/3
The required probability= 1/2∗1/3= 1/6

Approach Solution 2:
Ways to choose two even numbers out of four(2,4,6,8) = 1st*2nd = 4*3 = 12
Even numbers that sum 8 are 2 and 6.
(4 is not possible for once 4 is chosen first the other has to be 4 itself the 2nd time but it would require a replacement of 4, which is not possible AND 8 is also not possible since 0 is not available).
Ways to choose two even numbers that sum 8 = 2*1 = 2
Probability= 2/12= 1/6

Approach Solution 3:
Given 2,4,6,8, what is the probability that their sum will be 8, if we picked the numbers without replacement? The only options are...

a) 6 + 2
b) 2 + 6

Therefore,
1/4 x 1/3 = 1/12 <--- P(picking 6 followed by 2)
1/4 x 1/3 = 1/12 <--- P(picking 2 followed by 6)
Since these are mutually exclusive events we can add:
1/12 + 1/12 = 2/12 = 1/6

“From the even numbers between 1 and 9, two different even numbers”- is a topic of the GMAT Quantitative reasoning section of GMAT. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. GMAT Quant practice papers improve the mathematical knowledge of the candidates as it represents multiple sorts of quantitative problems.

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