How many 4 -digit positive integers are there in w... | Free GMAT Practice Question | GMAT Panda

👋 Hi! I'm GMAT Panda. Ask me anything about this question, or click a button below to get started!

How many 4 -digit positive integers are there in which all 4 digits are even?

Explanation	Calculations	Help
$We first define each digit of the 4-digit number with a variable.$	$a = thousands digit b = hundreds digit c = tens digit d = units digit$
$We then count the possible values for the thousands digit, which cannot be zero for a 4-digit number.$	$a \in {2, 4, 6, 8} (4 options)$
$We next count the possible values for the hundreds, tens, and units digits, which can include zero.$	$b, c, d \in {0, 2, 4, 6, 8} (5 options each)$
$We multiply the counts for each digit since each choice is independent.$	$4 \times 5 \times 5 \times 5 = 500$	Theory & Tactics Method Card PC2-A Click to view full details

Scroll horizontally to view all columns

500

How many 4 -digit positive integers are there in which all 4 digits are even?

Explanation	Calculations	Help
$We first define each digit of the 4-digit number with a variable.$	$a = thousands digit b = hundreds digit c = tens digit d = units digit$
$We then count the possible values for the thousands digit, which cannot be zero for a 4-digit number.$	$a \in {2, 4, 6, 8} (4 options)$
$We next count the possible values for the hundreds, tens, and units digits, which can include zero.$	$b, c, d \in {0, 2, 4, 6, 8} (5 options each)$
$We multiply the counts for each digit since each choice is independent.$	$4 \times 5 \times 5 \times 5 = 500$	Theory & Tactics Method Card PC2-A Click to view full details

Scroll horizontally to view all columns

500