This set of Aptitude Questions and Answers (MCQs) focuses on “Factors and Sum of Factors – Set 3”.
1. Find the sum of all factors of 800 which are divisible by 40.
a) 1720
b) 1460
c) 1860
d) 1680
View Answer
Explanation: 40 = 23*5 and 800 = 25*52.
Therefore, the sum of all factors of 800 which are divisible by 40 = (23 + 24 + 25)(51 + 52) = 56*30 = 1680.
2. Find the sum of divisors of 10800 which are perfect squares.
a) 5460
b) 5420
c) 4460
d) 4440
View Answer
Explanation: 10800 = 24*33*52.
Therefore, the sum of divisors of 10800 which are perfect squares = (20 + 22 + 24)(30 + 32)(50 + 52) = 5460.
3. Find the sum of the sum of even divisors of 80 and the sum of odd divisors of 90.
a) 248
b) 288
c) 258
d) 238
View Answer
Explanation: 80 = 24*5 and 90 = 2*32*5.
Sum of even divisors of 80 = (21 + 22 + 23 + 24)(50 + 51) = 30*6 = 180.
Sum of odd divisors of 90 = (20)(30 + 31 + 32)(50 + 51) = 1*13*6 =78.
Hence, the sum of the sum of even divisors of 80 and the sum of odd divisors of 90 = 180+78 = 258.
4. Find the number of factors of 2400 which are not divisible by 24.
a) 18
b) 36
c) 27
d) 9
View Answer
Explanation: 2400 = 25*3*52 and 24 = 23*3.
Total number of factors of 2400 = (5+1)(1+1)(2+1) = 36.
Number of factors which are divisible by 24 = 3*1*(2+1) = 9.
Therefore, the number of factors of 2400 which are not divisible by 24 = 36-9 = 27.
5. Find the sum of all factors of 1500 which are not divisible by 75.
a) 2498
b) 4368
c) 3150
d) 1218
View Answer
Explanation: 1500 = 22*3*53 and 75 = 3*52.
Sum of all factors of 1500 = (20 + 21 + 22)(30 + 31)(50 + 51 + 52 + 53) = 7*4*156 = 4368.
Sum of all factors of 1500 which are divisible by 75 = (20 + 21 + 22)(31)(52 + 53) = 7*3*150 = 3150.
Therefore, the sum of all factors of 1500 which are not divisible by 75 = 4368-3150 = 1218.
6. If n is a number and if 2n has 18 factors and 3n has 20 factors, then how many factors does 6n have?
a) 24
b) 28
c) 32
d) 21
View Answer
Explanation: Let n = 2p*3q, then number of factors of n = (p+1)(q+1).
Then, 2n = 2p+1*3q. The number of factors of 2n = (p+2)(q+1) = 18. The possible values are 2*9 and 6*3.
Also, 3n = 2p*3q+1. The number of factors of 3n = (p+1)(q+2) = 20. The possible values are 5*4 and 10*2.
From above values(6*3 and 5*4), we can infer that p=4 and q=2 i.e., n = 24*32.
Therefore, 6n = 25*33. The number of factors of 6n is 6*4 = 24.
7. Find the sum of the sum of divisors of 72 and 80.
a) 371
b) 381
c) 379
d) 383
View Answer
Explanation: 72 = 23*32 and 80 = 24*5.
Sum of divisors of 72 = (20 + 21 + 22 + 23)(30 + 31 + 32) = 15*13 = 195.
Sum of divisors of 80 = (20 + 21 + 22 + 23 + 24)(50 + 51) = 31*6 = 186.
Therefore, the sum of the sum of divisors of 72 and 80 = 195+186 = 381.
8. What is the total number of divisors of the number 612*159*1414?
a) 89100
b) 81900
c) 89900
d) 88900
View Answer
Explanation: 612*159*1414 = 226*321*59*714.
Therefore, the total number of divisors of the number 612*159*1414 = 27*22*10*15 = 89100.
9. How many factors of 216 are not perfect cubes?
a) 12
b) 16
c) 14
d) 10
View Answer
Explanation: 216 = 23*33 = 81*271.
Total number of factors = (3+1)(3+1) = 16.
The number of perfect cube factors of 216 = (1+1)(1+1) = 4.
Therefore, the total number of factors which are not perfect cubes are 16-4 = 12.
10. Find the sum of all 2-digit and 3-digit divisors of 400.
a) 941
b) 940
c) 943
d) 942
View Answer
Explanation: 400 = 24*52.
Sum of all divisors of 400 = (20 + 21 + 22 + 23 + 24)(50 + 51 + 52) = 31*31 = 961.
Sum of 1-digit divisor = 1+2+4+5+8 = 20.
Therefore, the sum of all 2-digit and 3-digit divisors of 400 = 961-20 = 941.
To practice all aptitude questions, please visit “1000+ Quantitative Aptitude Questions”, “1000+ Logical Reasoning Questions”, and “Data Interpretation Questions”.
If you find a mistake in question / option / answer, kindly take a screenshot and email to [email protected]
