What is the sum of integers from 1 to 100 that are divisible by 2 or 5

Question

What is the sum of integers from 1 to 100 that are divisible by 2 or 5 ?

A. 550
B. 1050
C. 2550
D. 3050
E. 5050

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Ertucinar · Answer

Step 1: Identify numbers divisible by 2 or 5 in the range  .

- Numbers divisible by 2: 2, 4, 6, ..., 100 (Arithmetic sequence)
 First term (a) = 2, Common difference (d) = 2, Last term = 100
 Number of terms (n) =  \frac{100 - 2}{2} + 1 = 50 
 Sum =  \frac{50}{2} 	imes (2 + 100) = 2550

- Numbers divisible by 5: 5, 10, 15, ..., 100
 First term (a) = 5, Common difference (d) = 5, Last term = 100
 Number of terms (n) =  \frac{100 - 5}{5} + 1 = 20 
 Sum =  \frac{20}{2} 	imes (5 + 100) = 1050

Step 2: Avoid double-counting numbers divisible by both 2 and 5 (i.e., 10).
- Numbers divisible by 10: 10, 20, 30, ..., 100
 First term (a) = 10, Common difference (d) = 10, Last term = 100
 Number of terms (n) =  \frac{100 - 10}{10} + 1 = 10 
 Sum =  \frac{10}{2} 	imes (10 + 100) = 550

Step 3: Apply Inclusion-Exclusion Principle
Total sum = (Sum of multiples of 2) + (Sum of multiples of 5) - (Sum of multiples of 10)

2550 + 1050 - 550 = 3050

Final Answer: 3050

ManifestDreamMBA · Answer

Integers divisible by 2 = 2,4,...100
Sum = 2*50*51/2 = 2550

Integers divisible by 5 = 5,10,...100
Sum = 5*20*21/2 = 1050

Sum total = 2550+1050 = 3600

This however double counts integer divisible by both 2 and 5. We need to eliminate that
Integers divisible by 10 = 10,20,...100
Sum = 10*10*11/2 = 550
Total sum = 3600-550 = 3050

Dereno · Answer

Let S be the sum of integers from 1 to 100 that are divisible by 2 or 5.

Summation of first n terms is given by the formula :   / 2

The sum of integers divisible by 2 is:

S2 =2+4+6+⋯+100
 =2 (1+2+3+⋯+50)
 =2 *   / 2 
 = 50⋅51
 =  2550

The sum of integers divisible by 5 is:

S5 =5+10+15+⋯+100
 = 5 (1+2+3+⋯+20)
 =5 *  / 2
 =5 *10 * 21
 =  1050 
 
The sum of integers divisible by both 2 and 5 (i.e., divisible by 10) is:

S10 =10+20+30+⋯+100
 =10(1+2+3+⋯+10)
 =10 *  /2 
 =10 * 5 * 11
 =  550

We need to remove the error of   Double counting   ,

the sum of integers divisible by 2 or 5 is: 
S. = S2 +S5 −S10 
 = 2550+1050−550
 = 3600−550
 =  3050

Therefore, the sum of integers from 1 to 100 that are divisible by 2 or 5 is  3050 .  Option D

Ayeka · Answer

Integers divisible by 2= 2,4,6,8,10......,100
Sum= 2+4+6+8+10+......+98+100= 2(1+2+3+4+5+6+.....+50) 
 = 2 = 2 =2(25*51)=2,550

Integers divisible by 5= 5,10,15,20,25........,95,100
Sum= 5+10+15+20+25+........+95+100= 5(1+2+3+4+5+6+......+20)
 = 5 = 5 = 5(10*21)=1,050

Integers divisible by both 2 and 5= 10,20,30......90,100
Sum= 10(1+2+3+4+.....+9+10)=10(5*11)=550

sum of integers from 1 to 100 that are divisible by 2 or 5 = 2550+1050-550=3,050

Answer: D

What is the sum of integers from 1 to 100 that are divisible by 2 or 5

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GMAT Problem Solving (PS) Questions

What is the sum of integers from 1 to 100 that are divisible by 2 or 5

Prep Toolkit

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