Numbers - General Questions

{(476 + 424)2 - 4 x 476 x 424} = ?

A.	2906
B.	3116
C.	2704
D.	2904
E.	None of these

Answer: Option C

Explanation:

Given Exp.	= [(a + b)² - 4ab], where a = 476 and b = 424
	= [(476 + 424)² - 4 x 476 x 424]
	= [(900)² - 807296]
	= 810000 - 807296
	= 2704.

(1000)⁹ � 10²⁴ = ?

A.	10000
B.	1000
C.	100
D.	10
E.	None of these

Answer: Option B

Explanation:

Given Exp. =(1000)⁹=(10³)⁹=(10)²⁷= 10^(27-24) = 10³ = 100010²⁴10²⁴10²⁴

3 + 33 + 333 + 3.33 = ?

A.	362.3
B.	372.33
C.	702.33
D.	702
E.	None of these

Answer: Option B

Explanation:

3
+  33
+ 333
+   3.33
  ------
  372.33
  ------

287 x 287 + 269 x 269 - 2 x 287 x 269 = ?

A.	534
B.	446
C.	354
D.	324
E.	None of these

Answer: Option D

Explanation:

Given Exp.	= a² + b² - 2ab, where a = 287 and b = 269
	= (a - b)² = (287 - 269)²
	= (18²)
	= 324

8988 � 8 � 4 = ?

A.	4494
B.	561.75
C.	2247
D.	280.875
E.	None of these

Answer: Option D

Explanation:

Given Exp. = 8988 x1/8x1/4=2247/8= 280.875

8796 x 223 + 8796 x 77 = ?

A.	2736900
B.	2638800
C.	2658560
D.	2716740
E.	None of these

Answer: Option B

Explanation:

8796 x 223 + 8796 x 77	= 8796 x (223 + 77) [Ref: By Distributive Law ]
	= (8796 x 300)
	= 2638800

A number when divided successively by 4 and 5 leaves remainders 1 and 4 respectively. When it is successively divided by 5 and 4, then the respective remainders will be

A.	1, 2
B.	2, 3
C.	3, 2
D.	4, 1

Answer: Option B

Explanation:

4 | x            y = (5 x 1 + 4) = 9
 --------
 5 | y -1         x = (4 x y + 1) = (4 x 9 + 1) = 37
 --------
   | 1 -4

 Now, 37 when divided successively by 5 and 4, we get

 5 | 37
 ---------
 4 | 7 - 2
 ---------
   | 1 - 3
 
 Respective remainders are 2 and 3.

106 x 106 - 94 x 94 = ?

A.	2400
B.	2000
C.	1904
D.	1906
E.	None of these

Answer: Option A

Explanation:

106 x 106 - 94 x 94	= (106)² - (94)²
	= (106 + 94)(106 - 94) [Ref: (a² - b²) = (a + b)(a - b)]
	= (200 x 12)
	= 2400.

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