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Arithmetic Progressions — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsArithmetic Progressions1 Mark
MCQ
How many two $-$ digit numbers are divisible by $3?$
  • A
    $25$
  • ✓
    $30$
  • C
    $32$
  • D
    $36$
✓

Answer

Correct option: B.
$30$
The two $-$ digit numbers divisible by $3$ start from
$\{12, 15, 18, 21, ......., 99\}$
Here,
$a = 12$
$d = 3$
$a_n= a + (n - 1)d$
$\Rightarrow 99 = 12 + (n - 1)(3)$
$\Rightarrow 99 = 12 + 3n - 3$
$\Rightarrow 90 = 3n$
$\Rightarrow n = 30$

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