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

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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.

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Sakshi singh said: (5:38am on Saturday 22nd July 2017)
but sir remainder 17 are also come .if we calculate it well, some quick arithmetic as followed by using multiples of 23 like 230,2300 etc. 2300-230=2070 is clearly a multiple of 23.(2070-2050)*(2070-2071)*(2070-2095)=20*(-1)*(-25) by 23500/23remainder is come 17.

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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).

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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

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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

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