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**How many 2-digit positive integers are divisible by 4 or 9?**

A. 32
B. 22
C. 30
D. 34
**Answer: Option C**

## Show Answer

Solution(By Apex Team)

**Number of 2-digit positive integers divisible by 4**The smallest 2-digit positive integer divisible by 4 is 12. The largest 2-digit positive integer divisible by 4 is 96. All the 2-digit positive integers are terms of an Arithmetic progression with 12 being the first term and 96 being the last term. The common difference is 4. The nth term $a_{n}=a_{1}+(n-1) d$, where a1 is the first term, ‘n’ number of terms and ‘d’ the common difference. So, 96 = 12 + (n – 1) × 4 84 = (n – 1) × 4 Or (n – 1) = 21 Hence, n = 22 i.e., there are 22, 2-digit positive integers that are divisible by 4.

**Number of 2-digit positive integers divisible by 9**The smallest 2-digit positive integer divisible by 9 is 18. The largest 2-digit positive integer divisible by 9 is 99. All the 2-digit positive integers are terms of an Arithmetic progression with 18 being the first term and 99 being the last term. The common difference is 9 The nth term $a_{n}=a_{1}+(n-1) d$, where a1 is the first term, ‘n’ number of terms and ‘d’ the common difference. So, 99 = 18 + (n – 1) × 9 Or 81 = (n – 1) × 9 Or (n – 1) = 9 Hence, n = 10 i.e., there are 10 2-digit positive integers that are divisible by 9. Removing double count of numbers divisible by 4 and 9 Numbers such as 36 and 72 are multiples of both 4 and 9 and have therefore been counted in both the groups. There are 2 such numbers. Hence, number of 2-digit positive integers divisible by 4 or 9 = Number of 2-digit positive integers divisible by 4 + Number of 2-digit positive integers divisible by 4 – Number of 2-digit positive integers divisible by 4 and 9 = 22 + 10 – 2 = 30

## Related Questions On Progressions

### How many terms are there in 20, 25, 30 . . . . . . 140?

A. 22B. 25

C. 23

D. 24

### Find the first term of an AP whose 8th and 12th terms are respectively 39 and 59.

A. 5B. 6

C. 4

D. 3

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A. -45B. -55

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D. 0

### The sum of the first 16 terms of an AP whose first term and third term are 5 and 15 respectively is

A. 600B. 765

C. 640

D. 680