Number System - Study Mode

[#316] The value of $${ ext{0}}{ ext{.}}overline 2 + { ext{0}}{ ext{.}}overline 3 + { ext{0}}{ ext{.}}overline {32} $$ xa0 xa0 is :
Correct Answer

(A) $$0.overline {87} $$

Explanation

Solution: $$eqalign{
& 0.overline 2 + 0.overline 3 + 0.overline {32} cr
& = frac{2}{9} + frac{3}{9} + frac{{32}}{{99}} cr
& = frac{{22 + 33 + 32}}{{99}} cr
& = frac{{87}}{{99}} cr
& = 0.overline {87} cr} $$

[#317] $$0.overline {142857} div 0.overline {285714} ,$$ xa0 xa0is equal to :
Correct Answer

(C) $$frac{1}{2}$$

Explanation

Solution: $$eqalign{
& = 0.overline {142857} div 0.overline {285714} ,{ ext{ }} cr
& = frac{{142857}}{{999999}} div frac{{285714}}{{999999}} cr
& = frac{{142857}}{{285714}} cr
& = frac{1}{2} cr} $$

[#318] A man read $$frac{2}{5}$$ th of a book on the first day. He read $$frac{1}{3}$$ rd more on second day than he read in the first day. 15 pages were left for the third day. The number of pages in the book is -
Correct Answer

(C) 225

Explanation

Solution: $$eqalign{
& { ext{Accroding to question}} cr
& ({ ext{P are the pages)}} cr
& Rightarrow { ext{P}} - frac{2}{5}{ ext{P}} - frac{8}{{15}}{ ext{P}} = 15, cr
& x08ecause left[ {frac{8}{{15}} = frac{2}{5} imes frac{4}{3}}
ight] cr
& Rightarrow frac{{15{ ext{P}} - { ext{6P}} - 8{ ext{P}}}}{{15}} = 15 cr
& Rightarrow { ext{P}} = 225{ ext{ pages}} cr} $$

[#319] Unit digit of the number (22) 23 is :
Correct Answer

(D) 8

Explanation

Solution: $$eqalign{
& {left( {22}
ight)^{23}} cr
& { ext{ Result unit digit}} cr
& {2^1},,,,,,,,,,,,,,,,2,,,,,,,,,,,,,2, leftarrow | cr
& {2^2},,,,,,,,,,,,,,,4,,,,,,,,,,,,,4,,,,,,,,,,,|,,{ ext{Cycle}} cr
& {2^3},,,,,,,,,,,,,,,8,,,,,,,,,,,,,8,,,,,,,,,,,|,,,{ ext{Completes}} cr
& {2^4},,,,,,,,,,,,,,16,,,,,,,,,,,,6 leftarrow ,| cr
& {2^5},,,,,,,,,,,,,32,,,,,,,,,,,,2,,, cr
& { ext{So divided power of 22 by 4 }} cr
& frac{{23}}{4} = { ext{ remainder 3}} cr
& {2^3},,,, = ,,,,,8, cr
& { ext{unit digit = 8}} cr} $$

[#320] A number consists of two digits. If the number formed by interchange the digits is added to the original number, the resulting number (i.e., the sum) must be divisible by -
Correct Answer

(A) 11

Explanation

Solution: Let the unit digit of the number be x And ten's place number be y Number = 10y + x Interchange digit's = 10x + y Adding result = 10y + x + 10x + y = 11x + 11y = 11(x + y) So number is divisible by 11