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TheRedSon
Joined: 26 May 2025
Last visit: 22 Sep 2025
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Location: India
Schools: CBS '26 Booth '26 Wharton '26 HBS '26 Stanford '26
30 Jun 2025, 08:49
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Number of integers available to pick= y-x+1 (inclusive of y and x).
Statement I says y-x=9. Plugging that in above, the total integers available becomes 10. Since Ann and Bob can each pick a number out of 10, the total outcomes can be calculated as 10x10(Ann picks 1, Bob picks 1, Ann picks 1, Bob picks 2... so on till A picks 10 and B picks 10.)
We're told to calculate probability that Ann picks a bigger number than Bob. Out of the 100 outcomes, 10 are such where Ann and Bob pick the same number, that leaves 45 outcomes where Bob picks a bigger number than Ann and 45 outcomes where Ann picks a bigger number than Bob.
So, probability is 45/100= 0.45
Statement I is sufficient
Statement II says y=-20. That data alone is insufficient to find out range of integers available to pick from. So, statement II is insufficient.
Therefore, Statement I ALONE is SUFFICIENT, while Statement II ALONE is NOT SUFFICIENT.
Statement I says y-x=9. Plugging that in above, the total integers available becomes 10. Since Ann and Bob can each pick a number out of 10, the total outcomes can be calculated as 10x10(Ann picks 1, Bob picks 1, Ann picks 1, Bob picks 2... so on till A picks 10 and B picks 10.)
We're told to calculate probability that Ann picks a bigger number than Bob. Out of the 100 outcomes, 10 are such where Ann and Bob pick the same number, that leaves 45 outcomes where Bob picks a bigger number than Ann and 45 outcomes where Ann picks a bigger number than Bob.
So, probability is 45/100= 0.45
Statement I is sufficient
Statement II says y=-20. That data alone is insufficient to find out range of integers available to pick from. So, statement II is insufficient.
Therefore, Statement I ALONE is SUFFICIENT, while Statement II ALONE is NOT SUFFICIENT.
30 Jun 2025, 08:50
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Information given:
- Ann & Bob each randomly pick an integer from x to y, inclusive
- We want the probability that Ann's number > Bob's number
- Statement 1: y - x = 9
- Statement 2: y = -20
Question:
- Is the probability that Ann's number is greater than Bob's number (uniquely) determinable?
Solution:
- The probability depends on the range size, e.g. the number of integers possible
- Total possible outcomes: n^2, where n = y - x + 1 (this is the number of 'options' that Ann and Bob have)
- Therefore, to find the probability that Ann's number > Bob's number, you need n
- Statement 1: y - x = 9
- n = (y - x) + 1 = 9 + 1 = 10
- We know how many integers there are, so we can calculate the probability that Ann's number > Bob's number
- P (Ann > Bob) = favorable pairs / (10^2)
- Therefore, statement 1 is sufficient
- Statement 2: y = -20
- However, x is unknown, so we can't find the range or n (see explanation under statement 1)
- For example, if x = -29, then n = 10
- If x = -50, then n is different
- The probability that Ann picks a greater number than Bob can change
- Therefore, statement 2 is insufficient
- Since statement 1 alone is sufficient, statement 1 and 2 together are also sufficient
Answer: A, statement 1 alone is sufficient
- Ann & Bob each randomly pick an integer from x to y, inclusive
- We want the probability that Ann's number > Bob's number
- Statement 1: y - x = 9
- Statement 2: y = -20
Question:
- Is the probability that Ann's number is greater than Bob's number (uniquely) determinable?
Solution:
- The probability depends on the range size, e.g. the number of integers possible
- Total possible outcomes: n^2, where n = y - x + 1 (this is the number of 'options' that Ann and Bob have)
- Therefore, to find the probability that Ann's number > Bob's number, you need n
- Statement 1: y - x = 9
- n = (y - x) + 1 = 9 + 1 = 10
- We know how many integers there are, so we can calculate the probability that Ann's number > Bob's number
- P (Ann > Bob) = favorable pairs / (10^2)
- Therefore, statement 1 is sufficient
- Statement 2: y = -20
- However, x is unknown, so we can't find the range or n (see explanation under statement 1)
- For example, if x = -29, then n = 10
- If x = -50, then n is different
- The probability that Ann picks a greater number than Bob can change
- Therefore, statement 2 is insufficient
- Since statement 1 alone is sufficient, statement 1 and 2 together are also sufficient
Answer: A, statement 1 alone is sufficient
Bunuel
