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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