Number System - Study Mode
[#371] If m and n are positive integers, then the digit in the unit's place of 5 n + 6 m is always :
Correct Answer
(A) 1
Explanation
Solution: In 5 n we have 5 as unit digit and in 6 m we have 6 as unit digit. ∴ 5 + 6 = 11(i.e unit digit always be 1)
[#372] 0.1 and $$frac{5}{8}$$ of a bamboo are in mud and water respectively and the rest length 2.75 m is above water. What is the length of the bamboo ?
Correct Answer
(A) 10 m
Explanation
Solution: $${ ext{0}}{ ext{.1 = }}frac{1}{{10}}left( {{ ext{mud}}}
ight),,,,,frac{5}{8}left( {{ ext{water}}}
ight)$$ Let total length of bamboo = 40x ( LCM of 8, 10 ) $$eqalign{
& { ext{Mud part :}} cr
& { ext{ = }}frac{1}{{10}} imes 40x = 4x cr
& { ext{Water part :}} cr
& { ext{ = }}frac{5}{8} imes 40x = 25x cr
& { ext{Remaining part :}} cr
& = (40x - 25x - 4x) cr
& = 11x cr
& 11x{ ext{ }} o { ext{ }}2.75m cr
& { ext{ }}x{ ext{ }} o { ext{ }}0.25m cr
& 40x{ ext{ }} o { ext{ }}10m cr} $$
[#373] The last digit of (1001) 2008 + (1002) = ?
Correct Answer
(B) 3
Explanation
Solution: $$eqalign{
& ,,,,,,,,,,,,,,,,,,,{(1001)^{2008}} + (1002) cr
& ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, downarrow cr
& { ext{unit digit}} o { ext{ }}{{ ext{1}}^{2008}} + 1002 cr} $$ Unit digit will be 1 in case of 1 respective of power ⇒ 1 + 1002 = 1003 ⇒ 3 unit digit (last digit)
[#374] The number 0.121212 . . . . . in the form $$frac{p}{q}$$ is equal to -
Correct Answer
(C) $$frac{4}{33}$$
Explanation
Solution: $$eqalign{
& { ext{0}}{ ext{.121212}}........ cr
& Rightarrow 0.overline {12} = frac{{12}}{{99}} = frac{4}{{33}} cr} $$
[#375] By how much does $$frac{6}{{frac{7}{8}}}$$ exceed $$frac{{frac{6}{7}}}{8}$$ ?
Correct Answer
(B) $$6frac{3}{4}$$
Explanation
Solution: $$eqalign{
& frac{6}{{frac{7}{8}}} = frac{{6 imes 8}}{7} = frac{{48}}{7} cr
& frac{{frac{6}{7}}}{8} = frac{6}{{7 imes 8}} = frac{6}{{56}} = frac{3}{{28}} cr
& { ext{Difference - }} cr
& = frac{{48}}{7} - frac{3}{{28}} cr
& = frac{{192 - 3}}{{28}} cr
& = frac{{189}}{{28}} cr
& = frac{{27}}{4} cr
& = 6frac{3}{4} cr} $$