一题数學题，源于"30 DAYS TO THE GMAT CAT"

WISE123magi

理觧不出英文觧说，可以麻烦用中文觧说一下吗?

Susan has selected exactly three crayons, each a different color, from a crayon box. How many crayon colors were represented in th box before her selection?

ANS.
            C --BOTH statements 1and 2 TOGETHER are sufficient to answer the question asked; but NEITHER statement ALONE is sufficient.

1. Exactly four distinct three-crayon color combinations were represented in the box before Susan selected three crayons.
2. Just before Susan's selections, the box contained exactly five crayons.

EXPLANATION

Statement 1 alone is insufficient to answer the question. For example, letting lattes represent colors, the box could include four crayons and four different colors ----- A, B, C, and D -----offering four distinct three -crayon combinations: {ABC}, {ABD}, {ACD}, and {BCD}. As an alternative, the box could include five crayons but only three different colors ----- {A, A, A, B, C} ----- offering four distinct three-crayon combinations: {ABC}, {AAA}, {AAB}, and {AAC}.

Statement 2 alone is also insufficient to answer the question. Prior to Susan's selection, the box could have represented anywhere from three to five colors. Again, using letters to represent colors, possible combinations include {AAABC}, {AABCD}, and {ABCDE}, to judt a few.

Together, statement1 and 2 suffice to answer the question. Exactly three colors must be represented in a box of five crayons offering exactly four three-crayon combinations. Again, using lettere to represent colors, the configuration must be {AAABD}. All other five-crayon configurations of three or more colors offer too many thee-crayon color combinations. The closest is {AAB}, {AAC}, {ABC}, {ABB}, and {BBC}