A lottery is played by selecting X distinct single digit numbers from GMAT data sufficiency

Question: A lottery is played by selecting X distinct single digit numbers from 0 to 9 at once such that order does not matter. What is the probability that a player will win playing the lottery?

Statement (1) Players must match at least two numbers with machine to win.
Statement (2) X = 4

A) Statement (1) ALONE is sufficient, but statement (2) ALONE is not sufficient.
B) Statement (2) ALONE is sufficient, but statement (1) ALONE is not sufficient.
C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D) EACH statement ALONE is sufficient.
E) Statements (1) and (2) TOGETHER are not sufficient.

Answer: C

Solution and Explanation:

Approach Solution 1:
Case I: There is no overlap at all between the machine's four options and mine.
The computer is unable to select four of my specified digits. The machine must choose one of the following six digits:
first preference P = 6/10 = 3/5 as a backup option.
P = 5/9
Third choice, P = 4/8 = ½
Option four = 3/7
P1=3/5×5/9×1/2×3/7 =
P1=1/1×1/1×1/2×1/7=1/14
The Case I probability is that.
Case II: Each of the machine's four options matches exactly one of mine.
The first match is the one of my digits, which can be made on any of the four options. The other three options adhere to the aforementioned pattern. The first in the first line, the second in the second line, etc. are the options for the matching digit in the terms below.
P2=4/10 × 6/9 × 5/8 × 4/7
+6/10 × 4/9 × ⅝ × 4/7
+6/10 × 5/9 × 4/8 × 4/7
+6/10 × 5/9 × 4/8 × 4/7
P2=1/1 × ⅔ × 1/1 × 1/7
+2/1 × ⅓ × 1/1 ×1/7
+1/1 × ⅓ × 1/1 × 2/7
+1/1 × ⅓ × 1/1 × 2/7
P2=4∗2/(3∗7) = 8/21
The likelihood of Case II is that.
Including those two:
P(1,2) = 1/14 + 8/21 = 3/42 + 16/ 42 = 19/42
We deduct that from 1 in order to obtain the total probability of the condition of the question not being satisfied.
P=1− 19/42 = 23/42
Case I: There is no overlap at all between the machine's four options and mine.
The computer is unable to select four of my specified digits. The machine must choose one of the following six digits:
first preference P = 6/10 = 3/5 as a backup option. Third choice, P = 5/9 P = 4/8 = ½
Option four Equals 3/7
Correct option: C

Approach Solution 2:
First claim: To win, players must match at least two digits.
At least now we are aware of what winning entails. We don't know how many digits are chosen, which is the problem. If X = 9, the lottery will choose all the numbers from 1 to 9, and if I choose all the numbers from 1 to 9, I will have a 100% probability of matching at least two numbers and winning. That lottery wouldn't be very lucrative. It's harder if X = 3 because the lottery chooses three and I choose three. Clearly the likelihood of winning depends on the value of X, and we don't know that in Statement #1. This assertion is not sufficient on its own.
Second premise: X = 4.
We now know how many digits are chosen—the lottery chooses 4, and I choose 4—but I'm not sure what "winning" actually entails. (This is an illustration of a DS issue where it is essential important to completely disregard Statement #1 while examining Statement #2 separately.) We know how many digits are chosen in Statement 2, but we have no notion what winning looks like. This assertion is not sufficient on its own.
We now know that the lottery chooses four numbers, I choose four numbers, and if at least two of my numbers line up with two of the lottery's cards, I win. Now that the math problem has been clearly specified, we might, if we so desired, determine the probability's exact numerical value. Of course, given that this is DS, wasting time on that computation would be a grave error. We have enough information now. Together, the statements are adequate.
Correct option: C

Approach Solution 3:
You play the lottery by simultaneously choosing X unique single-digit numbers between 0 and 9—the order is irrelevant. What is the likelihood that a lottery participant will win?
1) In order to win, players must match at least two numbers.
(2) X = 4
There is a good possibility (C) will be the answer because there are 2 variables (x and how many to win) and 2 equations supplied.
When the requirements are combined, the likelihood of winning is 1-(10C4/104), which is distinct and makes the condition sufficient, hence the answer is (C).
For situations where we require two more equations, such as initial conditions with "2 variables," "3 variables and 1 equation," or "4 variables and 2 equations," we have one equation in each of cases 1) and 2). As a result, C has a 70% chance of being the correct response while E has a 25% chance. The vast majority are these two. There is a 5% probability that the answer will be from A, B, or D in the case of common error type 3, 4, though. Using 1) and 2) individually and the DS definition, C is the response that is most likely to be the case (It saves us time). Of course, there may be circumstances in which the response is A, B, D, or E.
Correct option: C

“A lottery is played by selecting X distinct single digit numbers from GMAT data sufficiency" - is a topic of the GMAT data sufficiency section of GMAT. This question has been borrowed from the book “GMAT Official Guide Quantitative Review”.

To understand GMAT data sufficiency questions, applicants must possess fundamental qualitative skills. Quant tests a candidate's aptitude in reasoning and mathematics. The GMAT Quantitative test's problem-solving phase consists of a question and two statements. By using mathematics to answer the question, the candidate must select the appropriate response among five choices which states which statement is sufficient to answer the problem. The data sufficiency section of the GMAT Quant topic is made up of very complicated math problems that must be solved by using the right math facts.

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