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Algebra
Level
2
What is the 4-digit number in which the first digit is one fifth of the last, and the second and third digits are the last digit multiplied by 3? (Hint: The sum of all digits is 12.)
The answer is 1155.
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1 solution
Let's say the number is 1000a+100b+10c+d. For a=1/5xd, since we are talking about digits, the only numbers that satisfy a and d are 1and 5, respectively. Also, a+b+c+d =12. Substituting for a and d, b+c = 6. Since 10b+c=3xd=15, solving simultaneous equations give b=1 and c=5. Thus the number is 1155.