Number System - Study Mode

[#496] The greatest value among the fractions :$$frac{2}{7},$$ $$frac{1}{3},$$ $$frac{5}{6},$$ $$frac{3}{4}$$
Correct Answer

(B) $$frac{5}{6}$$

Explanation

Solution: $$frac{{2}}{{7}}$$ $$frac{{1}}{{3}}$$ $$frac{{5}}{{6}}$$ $$frac{{3}}{{4}}$$ ↓ ↓ ↓ ↓ 0.2857 0.333 0.83 0.75 $$frac{5}{6},{ ext{is the greatest value}}$$

[#497] The sum of three consecutive odd natural numbers each divisible by 3 is 63. What is the largest among them ?
Correct Answer

(C) 27

Explanation

Solution: $$eqalign{
& left( x
ight) + left( {x + 6}
ight) + left( {x + 12}
ight) = 63 cr
& 3x + 18 = 63 cr
& 3x = 45 cr
& x = 15 cr
& { ext{So,the largest number is}} cr
& { ext{ = }}15 + 12 cr
& = 27 cr} $$

[#498] If the some of a number and its reciprocal be 2 then number is = ?
Correct Answer

(B) 1

Explanation

Solution: $$eqalign{
& x + frac{1}{x} = 2 cr
& {x^2} + 1 = 2x cr
& {x^2} - 2x + 1 = 0 cr
& {left( {x - 1}
ight)^2} = 0 cr
& { ext{Then, }}x{ ext{ = 1}} cr} $$

[#499] If two numbers are each divided by the same divisor, the remainder are respectively 3 and 4. If the sum of two numbers be divided by the same divisor, the remainder is 2. The divisor is -
Correct Answer

(C) 5

Explanation

Solution: Shortcut Method : Divisor = 1st remainder + 2nd remainder - 3rd remainder $$eqalign{
& = 3 + 4 - 2{ ext{ }} cr
& = 7 - 2 cr
& = 5 cr} $$

[#500] The numerator and denominator of a fraction are in the ratio 3 : 4. If 9 is subtracted from the numerator, the resulting fraction in $$frac{2}{3}$$ of the original fraction. The numerator of the original fraction is
Correct Answer

(A) 27

Explanation

Solution: $$eqalign{
& { ext{Let}},{ ext{the}},{ ext{fraction}},{ ext{be}},frac{{3k}}{{4k}} cr
& herefore frac{{ {3k - 9} }}{{4k}} = {frac{2}{3}} cr
& herefore 9k - 27 = 8k cr
& herefore k = 27 cr } $$