Aptitude - Number System Online Test, Number System Questions and Answers updated

Solution: Let the numbers be a, b and c.
Then, a2 + b2 + c2 = 138 and (ab + bc + ca) = 131.
WKT, (a + b + c) 2 = a2 + b2 + c2 + 2(ab + bc + ca)
Substitutinga2 + b2 + c2 = 138,(ab + bc + ca) = 131.
(a + b + c)2= 138 + (2 x 131)
(a + b + c)2= 138 + 262
(a + b + c)2= 400
(a + b + c) = 20.

Solution: Let the ten's digit be x and unit's digit be y.
Then, x + y = 15 and x - y = 3 or y - x = 3.
Solving x + y = 15 and x - y = 3,
we get: x = 9, y = 6.
Solving x + y = 15 and y - x = 3, we get: x = 6, y = 9.
So, the number is either 96 or 69. Hence, the number cannot be determined

Solution: Let the ten's and unit's digit be x and 8 / x respectively.
Then, (10 x + 8 / x) + 18 = (10 x 8 / x) + x
=> 10x ^2 + 8 + 18x = 80 + x^2
=> 9x^2 + 18x - 72 = 0
=> x^2 + 2x - 8 = 0
=> (x + 4)(x - 2) = 0
=> x = 2 => ten's digit
=> 8 / x = 8/2 = 4 => unit's digit
Hence the number is 24

Solution: Since the number is greater than the number obtained on reversing the digits, so the ten's digit is greater than the unit's digit.
Let ten's and unit's digits be 2x and x respectively.
Then, (10 x 2x + x) - (10x + 2x) = 36
=> 9x = 36
=> x = 4
Required difference = (2x + x) - (2x - x) = 2x = 8

Solution: Let the number be x. Then, 1/3 of 1/4 of x = 15 <=> x = 15 x 12 = 180. So,
required number = ( 3 / 10 x 180 ) = 54.

Solution: Given Exp. = [(a + b)2 - 4ab] = (a-b)2,
where a = 476 and b = 424
[(476 + 424)2 - 4 x 476 x 424]
= (476 - 424)2
= 522
= 2704

Solution: Given Exp. = (1000)9 / 10^24 = (10^3)^9/10^24 = 10^(27-24) = 10^3 = 1000

Solution: The square of a natural number nerver ends in 2. 143642 is not the square of natural number.

Solution: 3 + 33 + 333 + 3.33 ------ 372.33 ------

Solution: Given Exp. = a^2 + b^2 - 2ab, where a = 287 and b = 269 = (a - b)^2 = (287 - 269)^2 = (18^2) = 324

Solution: Given Exp. = 8988 x 1/8 x 1/4 = 2247 / 8 = 280.875

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

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

Solution: 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.

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

Solution: (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.

Solution: Let 7589 -x = 3434 Then, x = 7589 - 3434 = 4155

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

Solution: Number = 269 x 68 + 0 = 18292
67) 18292 (273 134 ---- 489 469 ---- 202 201 --- 1 --- Therefore, Required remainder = 1

Solution: Required difference = (700000 - 70) = 699930