Number System - Study Mode
[#431] How many numbers less than 1000 are multiples of both 10 and 13 ?
Correct Answer
(D) 7
Explanation
Solution: Take LCM of 10 and 13 = 130 Any number divisible by 130 will be divisible by 13 and 10 i.e., 130, 260, 390, 520, 650, 780 & 910 ⇒ total numbers are 7
[#432] Which of the following is the smallest fraction ? $$frac{8}{{25}},$$ $$frac{7}{{23}},$$ $$frac{{11}}{{23}},$$ $$frac{{14}}{{53}}$$
Correct Answer
(D) $$frac{{14}}{{53}}$$
Explanation
Solution: $$frac{8}{{25}},frac{7}{{23}},frac{{11}}{{23}},frac{{14}}{{53}}$$ (184) , (175) ↑ ↑ $$frac{{8}}{{25}}$$ ⤩ $$frac{{7}}{{23}}$$ = $$frac{{8}}{{25}}$$ > $$frac{{7}}{{23}}$$ (371) , (322) ↑ ↑ $$frac{{7}}{{23}}$$ ⤩ $$frac{{14}}{{53}}$$ = $$frac{{7}}{{23}}$$ > $$frac{{14}}{{53}}$$ $${ ext{So}}frac{{14}}{{53}},{ ext{is smallest}}$$
[#433] How many digit required to write numbers from 1 to 50 ?
Correct Answer
(C) 91
Explanation
Solution: $$eqalign{
& { ext{No}}{ ext{. of digits}} cr
& { ext{0 - 9 }} o { ext{ 1}} imes { ext{9 = 9}} cr
& { ext{10 - 19 }} o { ext{ 2}} imes { ext{10 = 20}} cr
& { ext{20 - 29 }} o { ext{ 2}} imes { ext{10 = 20}} cr
& { ext{30 - 39 }} o { ext{ 2}} imes { ext{10 = 20}} cr
& 40{ ext{ - 49 }} o { ext{ 2}} imes { ext{10 = 20}} cr
& 50, o ,2 imes { ext{1 = 2 = 91}} cr} $$
[#434] $$left( {{2^{71}} + {2^{72}} + {2^{73}} + {2^{74}}}
ight)$$ xa0 xa0 is divided by :
Correct Answer
(B) 10
Explanation
Solution: $$eqalign{
& Leftrightarrow left( {{2^{71}} + {2^{72}} + {2^{73}} + {2^{74}}}
ight), cr
& = {2^{71}}left( {{2^0} + {2^1} + {2^2} + {2^3}}
ight), cr
& = {2^{71}}(1 + 2 + 4 + 8) cr
& = {2^{71}} imes 15 cr
& = {2^{70}} imes 30 cr
& { ext{It is divisible by 10}} cr} $$
[#435] $$999frac{{98}}{{99}} imes 99$$ xa0 is equal to :
Correct Answer
(A) 98999
Explanation
Solution: $$eqalign{
& = 999frac{{98}}{{99}} imes 99 cr
& = (1000 - 1)frac{{98}}{{99}} imes 99 cr
& = left[ {left( {1000 - 1}
ight) + frac{{98}}{{99}}}
ight] imes 99 cr
& = 99000 - 99 + 98 cr
& = 99000 - 1 cr
& = 98999 cr} $$