4-Digit Locker Key Combination
XAT 2023 · Quantitative Ability & Data Interpretation · Medium · Numbers
Amit has forgotten his 4-digit locker key. He remembers that all the digits are positive integers and are different from each other. Moreover, the fourth digit is the smallest and the maximum value of the first digit is 3. Also, he recalls that if he divides the second digit by the third digit, he gets the first digit.
How many different combinations does Amit have to try for unlocking the locker?
- A.
2
- B.
1
- C.
4
- D.
5
- E.
3
E
Explanation
Let digits be . All positive (), distinct, , , and . Since and , cannot be 1. Thus or . Case 1: . . If , code is . If , code is . Case 2: or . . If , code is . If , no integer works with distinct non-repeating digits. Total combinations = 3.
Related Numbers questions
- #1334Delta Key Calculator PatternXATQADIMCQEasy
- #1335Averages and Extremes in MarksXATQADIMCQEasy
- #1336Grid Board Adjacent Squares ProbabilityXATQADIMCQMedium
- #1337Largest Possible GCD of 7 Distinct IntegersXATQADIMCQMedium
- #1489Simultaneous Order MondaysXATQADIMCQEasy
- #1500Circumference and Diameter RatioXATQADIMCQMedium
- #1505Three-Digit Profit DigitsXATQADIMCQMedium
- #1507Minimum Fruit Packing BoxesXATQADIMCQEasy
Practise this under exam conditions
Sign in to solve it with a live timer, the on-screen CAT calculator, and streak and accuracy tracking across every question you attempt.
Solve in the workspace