Classical

Numbers & Algebra - Numbers and Algebra MCQ

16:  

 A school has 5 divisions in a class IX having 60, 50, 55, 62 and 58 students. Mean marks obtained in a History test were 56, 64, 72, 63 and 50 by each division respectively. What is overall average of the marks per students?

A.

56.8

B.

58.2

C.

62.4

D.

60.8

 
 

Option: D

Explanation :

Average = (60x56+50x64+55x72+62x63+58x50)/ (60+50+55+60+58 ) = (3360+3200+3960+3906+2900)/285 = 60.8


17:  

What is the smallest number which when increased by 3 is divisible by 27, 35, 25 and 21?

A.

4722

B.

4725

C.

4728

D.

4731

 
 

Option: A

Explanation :

L.C.M. of 27, 35, 25 and 21 = 4725

∴ Number = 4725-3 = 4722.


18:  

Which of the following is true?

A.

Sum of four consecutive even numbers is always divisible by 8.

B.

Sum of four consecutive odd numbers is always divisible by 8.

C.

Product of any n consecutive natural numbers may not be divisible by n!.

D.

Product of 4 consecutive odd numbers is always divisible by 15.

 
 

Option: B

Explanation :

(A) Four consecutive even numbers can be written as 2n, 2n + 2, 2n + 4 and 2n + 6,where n is any natural number.
Sum = 2n +(2n + 2) + (2n + 4) + (2n +6) = 8n + 12
= 4(2n + 3) not always divisible by 8.
Thus, (A) is not true.
(B) Four consecutive odd numbers can be written as 2n-1, 2n+ 1, 2n + 3, 2n + 5 where n is a natural number
Sum = (2n-1) + (2n + 1) + (2n + 3) + (2n + 5)
= 8n + 8 = 8(n + 1) divisible by 8
Thus, (B) is true
(C) In product of n consecutive natural numbers atleast one is divisible by n, atleast one by n - 1 ... till 1.
Thus product is atleast divisible by
n * (n - 1) * (n - 2) *1  =  n!.
Thus, (C) is not true.
(D) Take four consecutive odd numbers as 7 x 9 x 11 x 13 which is not divisible by 15.
Thus, (D) is not true.


19:  

 Sum of all odd numbers up to 100 is

A.

5050

B.

2500

C.

2525

D.

5000

 
 

Option: B

Explanation :

Given numbers are 1, 3, 5.....99.
This is an A.P with a = 1, d = 2
Let it contain n terms
∴ 1 +(n-1)2 = 99
=> n = 50
Hence required sum = n/2 (first term +last term)
= 50/2(1 + 99) = 2500


20:  

If x+y+z=0,then x2/yx + y2/zx + z2/xy equal

A.

0

B.

1

C.

2

D.

3

 
 

Option: D

Explanation :

x2/yx + y2/zx + z2/xy
             ...(since, x+y+z=0  'x3+y3+z3=3xyz)
(x3+y3+z3) / xyz = 3xyz / xyz = 3.




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