Number System - Study Mode

[#206] If A = $$0.3overline {12} ,$$ xa0B = $$0.4overline {15} $$ xa0and C = $$0.30overline 9 ,$$ xa0then what is the value of A + B + C?
Correct Answer

(B) $$frac{{1141}}{{1100}}$$

Explanation

Solution: $$eqalign{
& A = 0.3overline {12} = frac{{312 - 3}}{{990}} = frac{{309}}{{990}} cr
& B = 0.4overline {15} = frac{{415 - 4}}{{990}} = frac{{414}}{{990}} cr
& C = 0.30overline 9 = frac{{309 - 30}}{{900}} = frac{{279}}{{900}} cr
& A + B + C = frac{{309}}{{990}} + frac{{414}}{{990}} + frac{{279}}{{900}} cr
& = frac{{3090 + 4140 + 3069}}{{9900}} cr
& = frac{{10269}}{{9900}} cr
& = frac{{1141}}{{1100}} cr} $$

[#207] How many numbers are there from 500 to 650 (including both) which are neither divisible by 3 nor 7?
Correct Answer

(C) 87

Explanation

Solution: Total number from 500 to 650 = 650 - 500 + 1 = 151 Total number from 500 to 650 which are divisible by 3 $$ = frac{{650}}{3} - frac{{500}}{3} = 216 - 166 = 50$$ Total number for 500 to 650 which are divisible by 7 $$ = frac{{650}}{7} - frac{{500}}{7} = 92 - 71 = 21$$ Total number from 500 to 650 which are divisible by 21 $$ = frac{{650}}{{21}} - frac{{500}}{{21}} = 30 - 23 = 7$$ Number neither divisible by 3 nor 7 = 151 - 50 - 21 + 7 = 151 - 71 + 7 = 80 + 7 = 87

[#208] 3 50 + 9 26 + 27 18 + 9 28 + 9 29 is divisible by which of the following integers?
Correct Answer

(A) 11

Explanation

Solution: 3 50 + 9 26 + 27 18 + 9 28 + 9 29 = 3 50 + 3 52 + 3 54 + 3 56 + 3 58 = 3 50 [1 + 3 2 + 3 4 + 3 6 + 3 8 ] = 3 50 [1 + 9 + 81 + 729 + 6561] = 3 50 × 7381 This no will be divided by 5, 7, 2, 50 it will be divisible by 11.

[#209] Convert decimal 101 to binary:
Correct Answer

(D) 1100101

Explanation

Solution:

[#210] When we reverse the digits of the number 13, the increases by 18. How many other two digit numbers increases by 18 when their digits are reversed?
Correct Answer

(B) 6

Explanation

Solution: Let the numbers are in the form of (10x + y), so when the digits of the number are reversed the number becomes (10y + x)
According to question, (10y + x) - (10x + y) = 18 Or, 9(y - x) = 18 → y - x = 2 So, the possible pairs of (x, y) are
(1, 3), (2, 4), (3, 5), (4, 6), (5, 7), (6, 8) and (7, 9) But, we need the number other than 13. Thus, there are 6 possible numbers i.e. 24, 35, 46, 57, 68, 79 So, total numbers of possible numbers are 6