gmatcracker2010 wrote:

How many three-digit integers are not divisible by 3 ?

A. 599

B. 600

C. 601

D. 602

E. 603

Three-digit numbers range from 100 to 999

How many 3-digit numbers total?

Inclusive: (Greatest-Least) + 1

(999 - 100) = 899 + 1 = 900 numbers altogether

1)

Find a pattern - divisible by 3? (digits must sum to 3 or a multiple of 3)

100: no

101: no

102: yes

103: no

104: no

105: yes

2 out of 3, \(\frac{2}{3}\), are NOT divisible by 3

\(\frac{2}{3}*900 = 600\)Answer B

2) Use

evenly spaced set's properties* to find how many numbers ARE divisible by 3, i.e. find how many are multiples of 3

Subtract those multiples of 3 from the total of 3-digit numbers

First and last multiples of 3 in this range?

The first multiple of 3 is 102

The last multiple of 3 is 999

Number of terms (multiples of 3) =

\(\frac{(Last Term-FirstTerm)}{Increment} + 1\)

\((\frac{999-102}{3}+1)=(\frac{897}{3}+1)=(299+1)=300\)There are 900 numbers from 100 to 999

300 ARE divisible by 3

(900-300) = 600 are NOT divisible by 3

Answer B

*

See benjiboo ,

PART 2:Find number of integers that are a multiple of a certain number in a set

The whole Guide to Series and Sequences is excellent
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