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09 Jun 2025, 10:07
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
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Question Stats:
100% (00:27) correct
0% (00:00) wrong based on 3 sessions
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A basketball league assigns every player a two-digit number for the back of their jersey. If the league uses only the digits 1–5, what is the maximum number of players that can join the league such that no player has a number with a repeated digit (e.g., 22), and no two players have the same number?
11 Jun 2025, 00:37
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Given:
To find: Maximum number of players that can join the league.
This is nothing but the total number of such valid two-digit numbers that can be formed.
Solution:
Therefore, the league can assign such numbers to a maximum of 20 players.
Correct Answer: 20
Shweta Koshija
GMAT, GRE, SAT Coach for 10+ years
- Each jersey number = two-digit number
- Digits allowed = 1, 2, 3, 4, 5
- No digit repeats (e.g., 22 is not allowed)
- No two players have the same number
To find: Maximum number of players that can join the league.
This is nothing but the total number of such valid two-digit numbers that can be formed.
Solution:
- For a two-digit number:
- First digit (tens place): Cannot be 0 (but 0 is not among allowed digits anyway).
- So first digit choices: 1, 2, 3, 4, 5 — 5 options.
- Second digit (units place): Can be any of the 4 remaining digits (cannot be the same as the first digit).
- First digit (tens place): Cannot be 0 (but 0 is not among allowed digits anyway).
- Thus, total number of possible distinct numbers:
- 5 choices for the first digit × 4 choices for the second digit
- = 20 numbers.
Therefore, the league can assign such numbers to a maximum of 20 players.
Correct Answer: 20
Shweta Koshija
GMAT, GRE, SAT Coach for 10+ years
14 Jun 2025, 06:54
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OE
In this problem, each of the digits 1–5 can be either the tens digit, the units digit, or not a digit in the jersey number. What you’re really counting is the number of unique jersey numbers.
Make two slots, one for the tens digit and one for the units digit. You have 5 choices for the tens digit and 4 choices for the units digit (since you cannot use the same digit again), resulting in 5 × 4 = 20 possibilities. The slot labels are different (Tens and Units), so don’t divide 20 by anything. You could also list out the jersey numbers, since the number of possibilities is relatively limited.
There are 5 groups of 4 each for 20 total possibilities. If you notice partway through your list that each of the 5 possible tens digits will have 4 possibilities (any of the available units digits other than the same), use the pattern to solve more quickly.
GMAT-Club-Forum-0tk5xx0p.png [ 24.53 KiB | Viewed 171 times ]
In this problem, each of the digits 1–5 can be either the tens digit, the units digit, or not a digit in the jersey number. What you’re really counting is the number of unique jersey numbers.
Make two slots, one for the tens digit and one for the units digit. You have 5 choices for the tens digit and 4 choices for the units digit (since you cannot use the same digit again), resulting in 5 × 4 = 20 possibilities. The slot labels are different (Tens and Units), so don’t divide 20 by anything. You could also list out the jersey numbers, since the number of possibilities is relatively limited.
There are 5 groups of 4 each for 20 total possibilities. If you notice partway through your list that each of the 5 possible tens digits will have 4 possibilities (any of the available units digits other than the same), use the pattern to solve more quickly.
Attachment:
GMAT-Club-Forum-0tk5xx0p.png [ 24.53 KiB | Viewed 171 times ]
