Q1.
Pratibha uses the digits ‘4’, ‘7’, ‘3’ and ‘2’, and makes the smallest and largest 4-digit numbers with them: 2347 and 7432. The difference between these two numbers is 7432 – 2347 = 5085. The sum of these two numbers is 9779. Choose 4-digits to make: a. the difference between the largest and smallest numbers greater than 5085. b. the difference between the largest and smallest numbers less than 5085. c. the sum of the largest and smallest numbers greater than 9779. d. the sum of the largest and smallest numbers less than 9779.
Answer
Pick four digits, arrange them in decreasing order for the largest number and in increasing order for the smallest.
a. Difference greater than 5085 → choose digits that are far apart, such as 9, 8, 1, 0.
Largest = 9810, Smallest = 1089
9810 − 1089 = 8721 and 8721 > 5085 ✓
9810 − 1089 = 8721 and 8721 > 5085 ✓
b. Difference less than 5085 → choose digits that are close together, such as 5, 4, 3, 2.
Largest = 5432, Smallest = 2345
5432 − 2345 = 3087 and 3087 < 5085 ✓
5432 − 2345 = 3087 and 3087 < 5085 ✓
c. Sum greater than 9779 → choose big digits, such as 9, 8, 7, 6.
Largest = 9876, Smallest = 6789
9876 + 6789 = 16,665 and 16,665 > 9779 ✓
9876 + 6789 = 16,665 and 16,665 > 9779 ✓
d. Sum less than 9779 → choose small digits, such as 4, 3, 2, 1.
Largest = 4321, Smallest = 1234
4321 + 1234 = 5555 and 5555 < 9779 ✓
4321 + 1234 = 5555 and 5555 < 9779 ✓
Why this works: the difference depends on how spread out the digits are — 9 and 0 together give a big difference. The sum depends on how big the digits themselves are — four large digits give a large sum.