Classical

Numbers & Algebra - Numbers and Algebra MCQ

11:  

A number when divided by sum of 555 and 445 gives two times their diference as quotient and 30 as remainder. The number is

A.

1220

B.

1250

C.

22030

D.

220030

 
 

Option: D

Explanation :

Number = (555+445)*(555-445)*2+30
= (555+445)*2*110+30
= 220000+30 = 220030


12:  

 What is the remainder when 2050 x 2071 x 2095 is divided by 23?

A.

17

B.

12

C.

6

D.

3

 
 

Option: C

Explanation :

2050 x 2071 x 2095
=(23x89+3)x(23x90+1)x(23x91+2)
=(23[89 x 90+ 89 + 90 x 3]+ 3)x(23 x 91+2)
=(23 *K+ 3)* (23 * 91 + 2) )
=(23 *[K* 91 + K*  2 + 91 * 3]+ 6)
= 23 * L + 6 (where K and L are constants).
Hence remainder is 6.


13:  

 HCF of y3 - 4y and 4y (y3 + 8) is

A.

y(y + 2)

B.

y - 2

C.

2 (y + 2)

D.

(y + 2)(y2- 2y + 4)

 
 

Option: A

Explanation :

y3-4y = y(y2-4)
= y(y-2)(y+2)
4y(y3+8)
=4y(y+2)(y2-2y+4)
∴ HCF = y(y + 2).


14:  

A ball is dropped from a height of 12 m and it rebounds 1/2 of the distance it falls. If it continues to fall and rebound in this way, how far will it travel before coming to rest?

A.

36 m

B.

30 m

C.

48 m

D.

60 m

 
 

Option: A

Explanation :

Total distance travelled by the ball before coming to rest
= 12 + 2 (6 + 3 + 1.5 +...to?)
= 12 + 2. ( 6/ (1-1/2))
= 12 + 2(12)
= 36m


15:  

Sum of three prime numbers is 100. If one of them exceeds another by 36, then one of the numbers is

A.

7

B.

29

C.

41

D.

67

 
 

Option: D

Explanation :

x + (x + 36) + y = 100
⇒2x + y = 64
Therefore y must be even prime which is 2 
2x + 2 = 64
⇒x = 31.
∴ Third prime number = x + 36 = 31+ 36 = 67




Suggest an improvement