Exercise: Numbers

Questions for: Numbers

If (64)2 - (36)2 = 20 x x, then x = ?
A:
70
B:
120
C:
180
D:
140
Answer: D

20 x x = (64 + 36)(64 - 36) = 100 x 28

     x = 100 x 28 = 140
20

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A number was divided successively in order by 4, 5 and 6. The remainders were respectively 2, 3 and 4. The number is:
A:
214
B:
476
C:
954
D:
1908
Answer: A 
 4 | x            z = 6 x 1 + 4  = 10
 -----------
 5 | y -2         y = 5 x z + 3  = 5 x 10 + 3  = 53
 -----------
 6 | z - 3        x = 4 x y + 2  = 4 x 53 + 2  = 214
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   | 1 - 4
   
Hence, required number = 214.
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587 x 999 = ?
A:
586413
B:
587523
C:
614823
D:
615173
Answer: A
587 x 999 = 587 x (1000 - 1)
= 587 x 1000 - 587 x 1
= 587000 - 587
= 586413.
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What is the unit digit in (4137)754?
A:
1
B:
3
C:
7
D:
9
Answer: D

Unit digit in (4137)754 = Unit digit in {[(4137)4]188 x (4137)2}

=Unit digit in { 292915317923361 x 17114769 }

= (1 x 9) = 9

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The difference of the squares of two consecutive odd integers is divisible by which of the following integers ?
A:
3
B:
6
C:
7
D:
8
Answer: D

Let the two consecutive odd integers be (2n + 1) and (2n + 3). Then,

(2n + 3)2 - (2n + 1)2 = (2n + 3 + 2n + 1) (2n + 3 - 2n - 1)

     = (4n + 4) x 2

     = 8(n + 1), which is divisible by 8.

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