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Arithmetic Aptitude :: Numbers
Which of the following numbers will completely divide (461 + 462 + 463 + 464 ) ?
Answer : Option B
Explanation :
(461 + 462 + 463 + 464 ) = 461 x (1 + 4 + 42 + 43 ) = 461 x 85
= 460 x (4 x 85)
= (460 x 340), which is divisible by 10.
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.
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
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.
8796 x 223 + 8796 x 77 = ?
Answer : Option B
Explanation :
8796 x 223 + 8796 x 77 = 8796 x (223 + 77) [Ref: By Distributive Law ]
= (8796 x 300)
= 2638800
Answer : Option D
Explanation :
Given Exp. = 8988 x1 8 × 1 4 = 2247 8 = 280.875
287 x 287 + 269 x 269 - 2 x 287 x 269 = ?
Answer : Option D
Explanation :
Given Exp.
= a 2 + b 2 - 2ab , where a = 287 and b = 269
= (a - b )2 = (287 - 269)2
= (182 )
= 324
Which one of the following can't be the square of natural number ?
Answer : Option D
Explanation :
The square of a natural number nerver ends in 2.
143642 is not the square of natural number.
Answer : Option B
Explanation :
Given Exp. =( 1000 ) 9 10 2 4 = ( 10 ) 3 9 10 2 4 =( 10 2 7 10 2 4 =10(27-24) = 103 = 1000
{(476 + 424)2 - 4 x 476 x 424} = ?
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.
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