This set of Aptitude Questions and Answers (MCQs) focuses on “Number System – Set 2”.
1. The value of x in \(\frac{36}{11}*\frac{36}{11}-\frac{x}{11}*\frac{12}{11}+\frac{25}{11}*\frac{25}{11}\)=1
a) 150
b) 50
c) 100
d) 125
View Answer
Explanation: The above expression is of the form, a2-2ab+b2 = (a-b)2
Hence, x = 2*25*3 = 150.
2. When a certain number is multiplied by 21, the product consists entirely of 3’s. What is the minimum number of 3’s in the product?
a) 6
b) 7
c) 5
d) 8
View Answer
Explanation: Let the product be 33333……
When we divide the product by 21, we get the number which is multiplied and exact number of 3’s in the product.
\(\frac{333333}{21}\)=15873
Hence, the minimum number of 3’s in the product is 6.
3. Find the sum of cubes of first 50 natural numbers.
a) 1625625
b) 1525625
c) 1556625
d) 1575625
View Answer
Explanation: We know that, sum of cubes of n natural numbers is given by \(\frac{n^2 (n+1)^2}{4} \)
Therefore, the sum of cubes of first 50 natural number is \(\frac{50^2(50+1)^2}{4} \)=1625625.
4. Find the sum of squares of number from 101 to 200.
a) 2348350
b) 3383350
c) 2338350
d) 3385350
View Answer
Explanation: We know that, sum of square of first n natural number is given by \(\frac{n(n+1)(2n+1)}{6}\)
Hence, the sum of squares of number from 101 to 200 = \(\frac{200(200+1)(2*200+1)}{6}-\frac{100(100+1)(2*100+1)}{6}\)=2348350.
5. Find the sum of first 75 odd natural numbers.
a) 5625
b) 6425
c) 6525
d) 7225
View Answer
Explanation: We know that, sum of first n odd natural number is given by n2.
Therefore, the sum of first 75 odd natural numbers = 752 = 5625.
6. Find the sum of first 90 even natural numbers.
a) 8110
b) 8100
c) 8190
d) 8180
View Answer
Explanation: We know that, sum of first n even natural number is given by n2+n.
Therefore, the sum of first 90 even natural numbers = 902+90 = 8190.
7. Find the total number of three-digit numbers with unit digit 7 and divisible by 11.
a) 9
b) 8
c) 7
d) 6
View Answer
Explanation: Three-digit numbers with unit digit 7 and divisible by 11 are 187, 297, 407, 517, 627, 737, 847 and 957.
Hence, the total number of three-digit numbers with unit digit 7 and divisible by 11 is 8.
8. If B is the set of squares of natural numbers and m & n are any two elements of B, then which of the following statement is correct?
a) m+n belongs to B
b) m-n belongs to B
c) m/n belongs to B
d) m*n belongs to B
View Answer
Explanation: We know that product of two square numbers is also a square number.
For example, 25*36=90 and 81*100=8100 which are also square numbers.
Hence, m*n belongs to B.
9. If 2p+3q=25 and 2p+2-3q+1=37, then find the value of p and q?
a) 4,3
b) 4,2
c) 3,3
d) 3,5
View Answer
Explanation: 2p+3q=25 …… (i)
2p+2-3q+1=37 = 4*2p – 3*3q …… (ii)
On multiplying equation (i) by 3 and adding with equation (2), we get,
7*2p = 112
2p = 16, hence, p=4.
Therefore, q = 2.
10. If m<0<n, then which of the following relation correct?
a) \(\frac{1}{m}>\frac{1}{n}\)
b) \(\frac{1}{m}<\frac{1}{n}\)
c) \(\frac{1}{m}^3 >\frac{1}{n^3}\)
d) \(\frac{1}{m} > \frac{1}{n}\)
View Answer
Explanation: As m<0<n, m<0 and n>0.
\(\frac{1}{m}\) < 0 and \(\frac{1}{n}\) > 0.
\(\frac{1}{m}\) < 0 < \(\frac{1}{n}\) i.e.,\(\frac{1}{m}\) < \(\frac{1}{n}\).
To practice all aptitude questions, please visit “1000+ Quantitative Aptitude Questions”, “1000+ Logical Reasoning Questions”, and “Data Interpretation Questions”.
