How many integers between 100 and 1,000 have a hundreds digit that is

Question

How many integers between 100 and 1,000 have a hundreds digit that is even, a tens digit that is odd, and a non-zero units digit that is divisible by 3?

A. 15
B. 30
C. 45
D. 60
E. 75

SaquibHGMATWhiz · Answer

Solution:      
  We are looking for integers between 100 and 100 such that
  Hundred digit is even. This means 200s, 400s, 600s and 800s.  4 options for the hundredth-digit place   
 Tens digit is odd. This means (210s, 230s, 250s, 270s, 290s), (410s, 430s, 450s, 470s, 490s), (610s, 630s,...), .....870s and 890s.  5 options for the tenth-digit place  
 Unit digit is non zero and the integer is divisible by 3. This means (213, 216, 219), (231, 234, 237), (252, 255, 258).  3 options for the unit digit       So, total number of such integers  =4	imes 5	imes 3=60

Hence the right answer is    Option D

Rabab36 · Answer

total 3 digit starting with even number between 100 and 1000 = 400

now with ten digit as odd

we will be left with 200

now 3 rd digit is non zero so it cannot
 be (210,230,250,270,290)

total 20

subtracting we get  180 numbers left

now unit digit divisible by 3 means it can be 3,6,9

213,216,219
233,236,239
253,256,259
273,276,279
293,296,299

total 15 *4 =60 is right ans

luisdicampo · Answer

Deconstructing the Question

We need to find the number of 3-digit integers (between 100 and 1,000) that satisfy three specific conditions for each digit.

1. Hundreds Digit (Must be Even)  
The hundreds digit of a 3-digit number cannot be 0.
Possible even digits:  {2, 4, 6, 8} 
Total options =  4

2. Tens Digit (Must be Odd)  
Possible odd digits:  {1, 3, 5, 7, 9} 
Total options =  5

3. Units Digit (Non-zero and divisible by 3)  
Digits divisible by 3 are {0, 3, 6, 9}. 
Since it must be "non-zero", the possible digits are:  {3, 6, 9} 
Total options =  3

4. Total Combination  
Using the Fundamental Counting Principle, we multiply the number of options for each position:
 Total = 4 * 5 * 3 =    60

The correct answer is D.

How many integers between 100 and 1,000 have a hundreds digit that is

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How many integers between 100 and 1,000 have a hundreds digit that is

Prep Toolkit

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