Aptitude - Numbers

Answer: Option E

Explanation:

Unit digit in 3⁴ = 1 Unit digit in (3⁴)¹⁶ = 1

Unit digit in 3⁶⁵ = Unit digit in [ (3⁴)¹⁶ x 3 ] = (1 x 3) = 3

Unit digit in 6⁵⁹ = 6

Unit digit in 7⁴ Unit digit in (7⁴)¹⁷ is 1.

Unit digit in 7⁷¹ = Unit digit in [(7⁴)¹⁷ x 7³] = (1 x 3) = 3

Required digit = Unit digit in (3 x 6 x 3) = 4.

Answer: Option E

Explanation:

 3251          Let 4207 - x = 3007
+ 587          Then,  x = 4207 - 3007 = 1200
+ 369
 ----
 4207
 ----

Answer: Option D

Explanation:

Let 7589 -x = 3434

Then, x = 7589 - 3434 = 4155

Answer: Option E

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.

Answer: Option E

Explanation:

Unit digit in the given product = Unit digit in (4 x 8 x 7 x 3) = (672) = 2

Answer: Option D

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.

Answer: Option B

Explanation:

3897 x 999	= 3897 x (1000 - 1)
	= 3897 x 1000 - 3897 x 1
	= 3897000 - 3897
	= 3893103.

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

Answer: Option D

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 D

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.