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30 Jun 2025, 21:12
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Statement 1 alone is sufficient because we know the range of x and y — we can determine the no. of integers in the interval.
For example, consider x = 1 and y = 10 (the range is 9, so there are 10 integers in total). Since both Ann and Bob are choosing randomly from the same set of 10 integers, we can calculate the exact probability that Ann's number is greater than Bob's. The total number of possible pairs is 10 × 10 = 100.
--> if Ann picks 10, then bob can pick anywhere from 1 to 9. So there are 9 options
--> if Ann picks 9, then bob can pick anywhere from 1 to 8. So there are 8 options
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--> if Ann picks 2, then bob can pick only 1. So there is 1 option
In total, there are 45 options (9 * 10 / 2)
So, the probability is 45/100 = 0.45.
Since the range is fixed, the probability is fixed — we don’t need to know the exact values of x and y.
Hence, Statement 1 alone is sufficient.
Statement 2 gives us the value of y alone. Since the number of possible values changes, the probability that Ann’s number is greater than Bob’s also changes.
So, Statement 2 alone is not sufficient.
I will go with option A.
For example, consider x = 1 and y = 10 (the range is 9, so there are 10 integers in total). Since both Ann and Bob are choosing randomly from the same set of 10 integers, we can calculate the exact probability that Ann's number is greater than Bob's. The total number of possible pairs is 10 × 10 = 100.
--> if Ann picks 10, then bob can pick anywhere from 1 to 9. So there are 9 options
--> if Ann picks 9, then bob can pick anywhere from 1 to 8. So there are 8 options
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--> if Ann picks 2, then bob can pick only 1. So there is 1 option
In total, there are 45 options (9 * 10 / 2)
So, the probability is 45/100 = 0.45.
Since the range is fixed, the probability is fixed — we don’t need to know the exact values of x and y.
Hence, Statement 1 alone is sufficient.
Statement 2 gives us the value of y alone. Since the number of possible values changes, the probability that Ann’s number is greater than Bob’s also changes.
So, Statement 2 alone is not sufficient.
I will go with option A.
30 Jun 2025, 21:20
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The total number of possible ordered pairs (Ann's choice, Bob's choice) is n * n.
The number of pairs where Ann not equal to Bob is n * (n - 1) (since for each of n choices Ann makes, Bob has n - 1 different choices).
Half of these will have Ann > Bob: so n(n - 1)/2.
P(Ann>Bob)=Favorable outcomes/Total outcomes=(n(n-1)/2)/n^2 =(n-1)/2n
(1) y - x = 9
n = 9+1 = 10
P = (10-1)/2*10 = 9/20
Statement is sufficient
(2) y = -20
Without a specific value for x, n can be any positive integer, and thus we cannot determine a unique value for the probability.
Statement is insufficient
The right answer is A
The number of pairs where Ann not equal to Bob is n * (n - 1) (since for each of n choices Ann makes, Bob has n - 1 different choices).
Half of these will have Ann > Bob: so n(n - 1)/2.
P(Ann>Bob)=Favorable outcomes/Total outcomes=(n(n-1)/2)/n^2 =(n-1)/2n
(1) y - x = 9
n = 9+1 = 10
P = (10-1)/2*10 = 9/20
Statement is sufficient
(2) y = -20
Without a specific value for x, n can be any positive integer, and thus we cannot determine a unique value for the probability.
Statement is insufficient
The right answer is A
samriddhi1234
Joined: 19 Aug 2022
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30 Jun 2025, 21:27
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Analysing the question stem first:
We know Ann and Bob randomly select an integer from the consecutive integers x to y, inclusive. We don't know the total number of outcomes yet.
Further, the probability that the integer Ann selects a number greater than Bob, denoted as \(P(A)\) will be half of the total outcomes. As one outcome is not favoured over the other, we can say that in half the outcomes she selects a greater integer and in half she selects the smaller integer.
So we just need the total number of outcomes to arrive at the answer. Now we look at the statements.
1) y - x = 9
y = 9 + x. if for example x is 1, y will be 10, so there are 10 total outcomes, regardless of what x and y are (take x=3 and y=12 and count the total outcomes).
Thus \(P(A)\) = 5/10 or 1/2. Sufficient.
2) y = -20.
This statement tells us nothing about the total number of outcomes. Insufficient.
Answer is option (A).
We know Ann and Bob randomly select an integer from the consecutive integers x to y, inclusive. We don't know the total number of outcomes yet.
Further, the probability that the integer Ann selects a number greater than Bob, denoted as \(P(A)\) will be half of the total outcomes. As one outcome is not favoured over the other, we can say that in half the outcomes she selects a greater integer and in half she selects the smaller integer.
So we just need the total number of outcomes to arrive at the answer. Now we look at the statements.
1) y - x = 9
y = 9 + x. if for example x is 1, y will be 10, so there are 10 total outcomes, regardless of what x and y are (take x=3 and y=12 and count the total outcomes).
Thus \(P(A)\) = 5/10 or 1/2. Sufficient.
2) y = -20.
This statement tells us nothing about the total number of outcomes. Insufficient.
Answer is option (A).
Bunuel
