Number System - Study Mode

[#441] The value of $$frac{1}{{15}} + $$ $$frac{1}{{35}} + $$ $$frac{1}{{63}} + $$ $$frac{1}{{99}} + $$ $$frac{1}{{143}}$$ is :
Correct Answer

(A) $$frac{5}{{39}}$$

Explanation

Solution: $$ = frac{1}{{15}} + frac{1}{{35}} + frac{1}{{63}} + frac{1}{{99}} + frac{1}{{143}}$$ $$ = frac{1}{{3 imes 5}} + frac{1}{{5 imes 7}} + frac{1}{{7 imes 9}} + frac{1}{{9 imes 11}} + frac{1}{{11 imes 13}}$$ $$ = frac{1}{2}left[ {frac{1}{3} - frac{1}{5} + frac{1}{5} - frac{1}{7} + frac{1}{7} - frac{1}{9} + frac{1}{9} - frac{1}{{11}} + frac{1}{{11}} - frac{1}{13}}
ight]$$ $$ = frac{1}{2}left[ {frac{1}{3} - frac{1}{{13}}}
ight]$$ $$ = frac{1}{2} imes frac{{10}}{{39}}$$ $$ = frac{5}{{39}}$$

[#442] In a class, there are 'z' students. Out of them 'x' are boys. What part of the class is composed of girls ?
Correct Answer

(C) 1 - $$frac{{x}}{{z}}$$

Explanation

Solution: Total students = z Total boys = x Total girls = z - x ⇒ $$frac{{{ ext{Number of girls}}}}{{{ ext{Total students}}}}$$ = $$frac{z - x}{{z}}$$ = 1 - $$frac{x}{{z}}$$

[#443] A person gives $$frac{1}{4}$$ of his property to his daughter, $$frac{1}{2}$$ to his sons and $$frac{1}{5}$$ for charity. How much has he given away ?
Correct Answer

(B) $$frac{19}{20}$$

Explanation

Solution: Let the property is 'P' units According to the question, Given part, $$eqalign{
& = frac{1}{4}P + frac{1}{2}P + frac{1}{5}P cr
& = frac{{5P + 10P + 4P}}{{20}} cr
& = frac{{19}}{{20}}P cr} $$ Part of property given away $$frac{19}{{20}}$$

[#444] Symbiosis runs a Corporate Training Programme. At the end of running the first programme, its total takings were Rs. 38950. There were more than 45 but less than 100 participants. What was the participant fee for the programme ?
Correct Answer

(A) Rs. 410

Explanation

Solution: 38950 is completely divisible by 410 only. Hence, Rs. 410 is the correct answer.

[#445] The least number more than 5000 which is divisible by 73 is -
Correct Answer

(B) 5037

Explanation

Solution: On dividing 5000 by 73, we get 36 remainder Required number = 5000 + (73 - 36) = 5037