Question

The sum of the numbers from 300 to 700 which are divisible by 3 or 5, is

a.13365
b.10000
c.94068
d.96785

Answer 1

Answer:

1000

Step-by-step explanation:

300+700= 1000 so, no one is the answer

Answer 2

‣ We have to find out the sum of the numbers from 300 to 700 which are divisible by 3 or 5.

‣ First we will find the numbers from 300 to 700 which are divisible by 3 or 5 :-

• LCM of 3 and 5 = 15

↦Now we will find difference between 300 and 700 :-

⟹ 700-300

⟹ 400

• Therefore , difference between 300 and 700 = 400

↦Number of terms = 400/15

⟹ 400/15

⟹ 80/3

⟹ 80/3

⟹ 26.66 [ check attachment for calculation]

⟹ 27 ( round off)

• Therefore number of terms = 27

↦We get A.P with common difference 15 and first term 300 :-

⟹ 300 , 300+15 , 300+30 ................ upto 27 terms

⟹ 300 , 315 , 330 ................ upto 27 terms

Now the above numbers which are in AP are divisible by 3 or 5.

Now find 27 th term :-

T27 = 300+(27-1)15

T27 = 300+(26×15)

T27 = 300+(26×15)

T27 = 300+390

T27 = 690

⟹ Sum = n/2 (a+l)

⟹ Sum = 27/2 (300+690)

⟹ Sum = 27/2 × (990)

⟹ Sum = 27 × 495

Sum = 13365

Therefore option a. 13365 is correct.

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Useful Formulae :-

1. Tn = a+(n-1)d

2. Sn = n/2[2a+(n-1)d]

3. Sn = n/2(a+l)

where :-

• a = first term
• n = number of terms
• d = common difference
• Tn = nth term

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