General Mathematics

Question: The length of a rectangle is increased by `60%` and the width is decreased by `20%`. The area decreases by :
A
`37 1/2%`

B
`60%`

C
`75%`

D
None

Note: Let length = l and breadth = b Let the required decrease in breadth be x%. Then,`160/100 l xx ((100 - x))/100 xx b` `= lb => 160 (100 - x)` `= 100 xx 100` `or 100 - x` `= 10000/160` `= 125/2 => x` `= (100 - 125/2)` `= 37 1/2.`
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Question: If the radius of a circle is decreased by `50%`, its area is reduced by :
A
`25%`

B
`50%`

C
`75%`

D
None

Note: Let original radius be R. Then, area` = π R^2` New radius `= 50% of R = 50/100 R = R/2.` New area`= π xx (R/2)^2` `= (πR^2)/4` decrease`= (πR^2 - (π R^2)/4)` `= (3 π R^2)/4` :. Decrease `% = ((3 πR^2)/(4) xx 1/(π R^2) xx 100)%` `= 75%`.
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Question: For a sphere of a radius `10` cm, the numerical value of surface area is what percent of the numerical value of its volume ?
A
`24%`

B
`26.5%`

C
`30%`

D
`45%`

Note: surface area `= 4 πR^2` `= 3/R (4/3 π R^3)` `= 3/4 xx Volume When `R = 10.` we have `S = 3/10 V` `= (3/10 xx 100)% of V` `= 30% of V.`
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Question: The radius of a sphere is increased by `50%`. The increase in surface area of the sphere is :
A
`100%`

B
`125%`

C
`150%`

D
`200%`

Note: Let original radius`= R, New radius `= 150/100 R` `= 3/2 R.` Original Surface area `= 4 π R^2` New surface area `= 4 π (3/2 R)^2` `= 9 π R^2` :. Increase`= ((5 π R^2)/(4 π R^2) xx 100)%` `= 125%.`
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Question: A cricket team won `40%` of the total number of matches it played during a year. If it lost `50%` of the matches played and `20` matches were drawn , the total number of matches played by the team during the year was :
A
`200`

B
`100`

C
`50`

D
`40`

Note: `40% of x + 50% of x + 20 = x` `=> 40/100 x + 50/100 x + 20 = x` `or x = 200.`
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Question: Arun gave a portion of the money he had to Gopal. Gopal in turn gave `40%` of what he got from Arun to Dinesh. How much money did Dinesh get ? To find out the answer, which of the following informations given in statements (p) and (Q) is∕are sufficient ? P: Arun had Rs.`4,000` with him. Q: The difference between the amounts of Gopal and Dinesh was `Rs. 500`
A
Only Q is sufficient

B
Only P is sufficient

C
Either P or Q is sufficient

D
Both P and Q together are needed

Note: P:A`= 4000 & Q : G - D = 500` Clearly, `D = 40% of G or G = 100/40 D` `= 5/2 D.` `:. D - G = 500 => 5/2 D - D` `= 500 or D = 1000/3` Thus, only Q is sufficient
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Question: `3, 5, 7, 12, 17, 19.`
A
`19`

B
`17`

C
`13`

D
`12`

Note: Each of the numbers except `12,` is a prime number.
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Question: `10, 14, 16, 18, 21, 24, 26.`
A
`26`

B
`24`

C
`21`

D
`18`

Note: Each of the numbers except `21,` is an prime number.
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Question: `3, 5, 9, 11, 14, 17, 21,`
A
`21`

B
`17`

C
`14`

D
`9`

Note: Each of the number except `14,`is an odd number.
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Question: `1, 4, 9, 16, 23, 25, 36,`
A
`9`

B
`23`

C
`25`

D
`36`

Note: Each of the given numbers except`23,` is a perfect square.
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Question: The length of a rectangle is increased by `60%` and the width is decreased by `20%`. The area decreases by :

Question: If the radius of a circle is decreased by `50%`, its area is reduced by :

Question: For a sphere of a radius `10` cm, the numerical value of surface area is what percent of the numerical value of its volume ?

Question: The radius of a sphere is increased by `50%`. The increase in surface area of the sphere is :

Question: A cricket team won `40%` of the total number of matches it played during a year. If it lost `50%` of the matches played and `20` matches were drawn , the total number of matches played by the team during the year was :

Question: `3, 5, 7, 12, 17, 19.`

Question: `10, 14, 16, 18, 21, 24, 26.`

Question: `3, 5, 9, 11, 14, 17, 21,`

Question: `1, 4, 9, 16, 23, 25, 36,`