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Bash, 3333 32 bytes

echop=%100\<60;echo $[$1%100<60&($1$[$1$p&$1/100)%100<60]100$p]

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Input is passed as an argument.

Output is 0 (falsey) or 1 (truthy).

(I've deleted an earlier 45-byte version that used egrep.]

Bash, 33 bytes

echo $[$1%100<60&($1/100)%100<60]

Try it online!

Input is passed as an argument.

Output is 0 (falsey) or 1 (truthy).

(I've deleted an earlier 45-byte version that used egrep.]

Bash, 33 32 bytes

p=%100\<60;echo $[$1$p&$1/100$p]

Try it online!

Input is passed as an argument.

Output is 0 (falsey) or 1 (truthy).

(I've deleted an earlier 45-byte version that used egrep.]

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Bash + Core utilities, 4533 bytes

egrepecho '$[$1%100<60&([01].|2[0-3]$1/100)[0-5].[0-5].$'<<<00000$1%100<60]

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Input is passed as an argument.

Output is in the exit code0 (0 = truthy,falsey) or 1 = falsy, as usual(truthy).

(I've deleted an earlier 45-byte version that used egrep.]

Bash + Core utilities, 45 bytes

egrep '([01].|2[0-3])[0-5].[0-5].$'<<<00000$1

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Input is passed as an argument.

Output is in the exit code (0 = truthy, 1 = falsy, as usual).

Bash, 33 bytes

echo $[$1%100<60&($1/100)%100<60]

Try it online!

Input is passed as an argument.

Output is 0 (falsey) or 1 (truthy).

(I've deleted an earlier 45-byte version that used egrep.]

Source Link

Bash + Core utilities, 45 bytes

egrep '([01].|2[0-3])[0-5].[0-5].$'<<<00000$1

Try it online!

Input is passed as an argument.

Output is in the exit code (0 = truthy, 1 = falsy, as usual).