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Arithmetic Aptitude | Numbers III - with Explanation


1. 
217 x 217 + 183 x 183 = ?
A.79698
B.80578
C.80698
D.81268
Answer: Option B
Explanation:
(217)2 + (183)2= (200 + 17)2 + (200 - 17)2
= 2 x [(200)2 + (17)2]       [Ref: (a + b)2 + (a - b)2 = 2(a2 + b2)]
= 2[40000 + 289]
= 2 x 40289
= 80578


2. 
The unit digit in the product (784 x 618 x 917 x 463) is:
A.2
B.3
C.4
D.5
Answer: Option A
Explanation:
Unit digit in the given product = Unit digit in (4 x 8 x 7 x 3) = (672) = 2

3. 
If the number 653 xy is divisible by 90, then (x + y) = ?
A.2
B.3
C.4
D.6
Answer: Option C
Explanation:
90 = 10 x 9
Clearly, 653xy is divisible by 10, so y = 0
Now, 653x0 is divisible by 9.
So, (6 + 5 + 3 + x + 0) = (14 + x) is divisible by 9. So, x = 4.
Hence, (x + y) = (4 + 0) = 4.


4. 
3897 x 999 = ?
A.3883203
B.3893103
C.3639403
D.3791203
E.None of these
Answer: Option B
Explanation:
3897 x 999= 3897 x (1000 - 1)
= 3897 x 1000 - 3897 x 1
= 3897000 - 3897
= 3893103.


5. 
What is the unit digit in 7105 ?
A.1
B.5
C.7
D.9
Answer: Option C
Explanation:
Unit digit in 7105 = Unit digit in [ (74)26 x 7 ]
But, unit digit in (74)26 = 1
 Unit digit in 7105 = (1 x 7) = 7


6. 
Which of the following numbers will completely divide (461 + 462 + 463 + 464) ?
A.3
B.10
C.11
D.13
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.

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