Fraction Questions for SSC-CGL
Download SSC CGL Questions on Fraction PDF based on previous papers very useful for SSC CGL exams. Fraction Questions for SSC exams.
Download Fraction Questions for SSC CGL
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Question 1: If $2x – \frac{1}{2x} = 6$, then the value of $x^2 + \frac{1}{16x^2}$
a) $\frac{19}{2}$
b) $\frac{17}{2}$
c) $\frac{18}{3}$
d) $\frac{15}{2}$
Question 2: If x,y are positive acute angles, x + y < 90o and sin(2x -20o) = cos(2y + 20o), then the values of sec(x + y) is
a) $\sqrt{2}$
b) $\frac{1}{\sqrt{2}}$
c) $1$
d) $0$
Question 3: If $x^2=y + z, y^2=z + x, z^2=x+y$, then the value $\frac{1}{1+x} + \frac{1}{1+y} + \frac{1}{1+z}$
a) 1
b) 2
c) 0
d) -1
Question 4: The sum of a non-zero number and thrice its reciprocal is 13/2. Find the number.
a) 6
b) 7
c) 8
d) 9
Question 5: The reciprocal of the sum of the reciprocals of 8/7 and 5/6 is:
a) 83/40
b) 42/83
c) 83/42
d) 40/83
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Question 6: If $\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=0$ and x + y + z = 9, then what is the value of $x^3 + y^3 + z^3 – 3xyz$ ?
a) 81
b) 361
c) 729
d) 6561
Question 7: If A : B = 2 : 5, B : C = 4 : 3 and C : D = 2 : 1, then what is value of A : C : D?
a) 6 : 5 : 2
b) 7 : 20 : 10
c) 8 : 30 : 15
d) 16 : 30 : 15
Question 8: If $\frac{x}{y}=\frac{4}{9}$, then what is the value of $\frac{(7x^2-19xy+11y^2)}{y^2}$ ?
a) $\frac{59}{81}$
b) $\frac{100}{27}$
c) $\frac{319}{81}$
d) $\frac{913}{81}$
Question 9: If 27x + 27[x-(1/3)] = 99, then what is the value of x?
a) 2
b) 3
c) 4
d) 5
Question 10: If $a^{3} + b^{3}$ = 19 and a + b = 1, then what is the value of ab?
a) 5
b) -6
c) 7
d) -9
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Answers & Solutions:
1) Answer (A)
$2x – \frac{1}{2x} = 6$
or $x – \frac{1}{4x} = 3$
squaring on both sides:
$x^2 + \frac{1}{16x^2} – \frac{1}{2}$ = 9
or $x^2 + \frac{1}{16x^2}$ = 19/2
2) Answer (A)
Given sin(2x-20) = cos(2y+20)
as x and y are positive acute angles
hence cos(90-2x+20) = cos(2y+20)
or 90-2x+20 = 2y+20
or x+y = 45
or sec(x+y) = $\sqrt2$
3) Answer (A)
$x^2 = y+z$
$y^2 = z+x$
on substracting above two eq. we will get
$x^2 – y^2 = y – x$
So either $x=y$
or $x+y= -1$ (it is not possible as $z^2$ can not be negative)
So $x=y=z=2$
So given eq. will reduce to a value 1
4) Answer (A)
Let the number be $x$
According to ques, => $x + \frac{3}{x} = \frac{13}{2}$
=> $\frac{x^2 + 3}{x} = \frac{13}{2}$
=> $2x^2 + 6 = 13x$
=> $2x^2 – 13x + 6 = 0$
=> $2x^2 – x – 12x + 6 = 0$
=> $x(2x – 1) – 6(2x – 1) = 0$
=> $(2x – 1)(x – 6) = 0$
=> $x = 6 , \frac{1}{2}$
=> Ans – (A)
5) Answer (D)
Sum of the reciprocals of 8/7 and 5/6
= $\frac{7}{8} + \frac{6}{5}$
= $\frac{7(5)+6(8)}{40} = \frac{35+48}{40}$
= $\frac{83}{40}$
=> Reciprocal of 83/40 = $\frac{40}{83}$
=> Ans – (D)
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6) Answer (C)
Given : $\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=0$
=> $\frac{yz+zx+xy}{xyz}=0$
=> $xy+yz+zx=0$ ———–(i)
Also, $x+y+z=9$
Squaring both sides,
=> $(x+y+z)^2=(9)^2$
=> $x^2+y^2+z^2+2(xy+yz+zx)=81$
=> $x^2+y^2+z^2+2(0)=81$
=> $x^2+y^2+z^2=81$
To find : $x^3 + y^3 + z^3 – 3xyz$
= $(x+y+z)(x^2+y^2+z^2-xy-yz-zx)$
= $(9)(81-0)=729$
=> Ans – (C)
7) Answer (D)
Given : $\frac{A}{B}=\frac{2}{5}$ ———–(i)
$\frac{B}{C}=\frac{4}{3}$ ———–(ii)
and $\frac{C}{D}=\frac{2}{1}$ ———–(iii)
Multiplying equation (ii) by 10 and (iii) by 15 to make ‘C’ equal in both
=> $\frac{B}{C}=\frac{40}{30}$ and $\frac{C}{D}=\frac{30}{15}$
Now, multiplying equation (i) by 8 to make ‘B’ equal in both
=> $\frac{A}{B}=\frac{16}{40}$
Thus, we get = $A:B:C:D=16:40:30:15$
$\therefore$ A : C : D = 16 : 30 : 15
=> Ans – (D)
8) Answer (C)
Given : $\frac{x}{y}=\frac{4}{9}$
Let $x=4$ and $y=9$
To find : $\frac{(7x^2-19xy+11y^2)}{y^2}$
= $\frac{7(4)^2-19(4)(9)+11(9)^2}{(9)^2}$
= $\frac{112-684+891}{81}$
= $\frac{319}{81}$
=> Ans – (C)
9) Answer (A)
Expression : 27x + 27[x-(1/3)] = 99
=> $27x+27(\frac{3x-1}{3})=99$
=> $27x+9(3x-1)=99$
=> $27x+27x-9=99$
=> $54x=99+9=108$
=> $x=\frac{108}{54}=2$
=> Ans – (A)
10) Answer (B)
Given : $a^{3} + b^{3}$ = 19 ———–(i)
Also, $a+b=1$ ———–(ii)
Cubing both sides, we get :
=> $(a+b)^3=(1)^3$
=> $a^3+b^3+3ab(a+b)=1$
Substituting values from equation (i) and (ii)
=> $19+3ab(1)=1$
=> $3ab=1-19=-18$
=> $ab=\frac{-18}{3}=-6$
=> Ans – (B)
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