Olympiad Maths Prep

Track / Stage 4 / 164 of 340 #424 of 2000

Problem 424

AMC 12 late, AIME early
Combinatorics Difficulty 4.9 Find the answer

4. A group has 48 members, but only half of them

have uniforms. During a certain inspection ceremony, they formed a 6×86 \times 8 rectangular array, which exactly hid the members without uniforms inside the array. Later, more members joined, but the total still had half without uniforms. During the next inspection ceremony, they formed a different rectangular array, which again exactly hid the members without uniforms inside the array. Then the number of new members is \qquad people.

Official solution

4.124.12

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.