PROBLEM 2: How many three-digit numbers are there that have the property that on
ID: 3032293 • Letter: P
Question
PROBLEM 2: How many three-digit numbers are there that have the property that one digit is repeated? Let m be the SMALLEST DIGIT REPEATED 0) n00: There are 9 such acceptable numbers. For each digit, m, from rn = 1 to 9, the acceptable numbers are: mm0, mml, mm2, mm3., ...mm9 One of these numbers, mmO, has 2 permutations; one of these numbers, mmm, has 1 permutation; 8 of these numbers has 3 permutations Therefore, for each m = 1 to 9 there are 2 + 1 + 8x3-27 permutations. Thus there are 9 + 9x27 = 9 + 243 = 252 acceptable numbers. The test question will be taken from these questions: 1. How many three-digit numbers are there that have the property that the product of two of the digits is equal to the third digit? (A) 52 (B) 126 (C) 252 (D) 1024 2. How many three-digit numbers are there that have the property that one digit is the sum of the other two digits? (A) 52 (B) 126 (C) 252 (D) 1024 3. How many three-digit numbers are there that have the property that one digit is repeated? (A) 52 (B) 126 (C) 252 (D) 1024Explanation / Answer
2 Three digit number in which one digit is multiplication of other two.
first digit of a no. cannot be zero
100,111,122,133,144,155,166,177,188,199
200,212,221,224,236,242,248,263,284
300,313,331,326,362,339,393
400,414,441,428,482,
500,515,551
600,616,661,700,717,771,800,818,881,900,919,991
2.
three digit no. in which one digit is the sum of other two
no starting with 1
two digits will be 01,10,12,21,23,32,34,43,45,54,56,65,67,76,78,87,89,98=18
no starts with2
two digit will be 02,20,13,31,24,42,35,53,46,64,57,75,68,86,79,97=16
no starts with 3
no will be 03,30,14,41,25,52,36,63,47,74,58,85,69,96=14
no. starts with 4 ,no will be 12 ,similarly for 5 no count will be 10.....
no starts with 9 ,possible three digit no are 909,990=2
total three digit no. =18+16+14+12+10+8+6+4+2=
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.