Aptitude - Equations

If e varies directly as n and e/d = 10, then what is the value of e when d = 30?

A.  25

B.  0.12

C.  200

D.  78

E.  300

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If a1=1 and an+1-3an+2 = 4n for every positive integer n, then a100 equals

A.  399-200

B.  399+200

C.  3100-200

D.  3100+200

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If 3x – 5y = 5 and x/x + y = 5/7, then what is the value of x – y ?

A.  3

B.  4

C.  6

D.  9

E.  None of these

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Solve the following equation 3s + 5 = s – 1

A.  63

B.  – 3

C.  -56

D.  62

E.  10

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The number of non-negative real roots of 2x – x – 1 = 0 equals

A.  0

B.  1

C.  2

D.  3

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If x = 3 –  √5 , then the value of x2+16/x2 is equal to

A.  10

B.  24

C.  26

D.  28

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If a - 4 = 4 (2- a), then what is the value of a?

A.  0.33

B.  9/14

C.  23.78

D.  567

E.  35

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If 2x + 3y -31, y – z - 4 and x + 2z – 11, then what is the value of x + y + z ?

A.  12

B.  13

C.  15

D.  16

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If a = log2, b = log 3 and c = log 7 then find the value of log67 in terms of a, b and c.

A.  b/(a+c)

B.  c/(a+b)

C.  a/(b+c)

D.  None of these

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If f (x+(y/8), x-(y/8)) = xy, then f (m, n) + f (n, m) = 0

A.  only when m = n

B.  only when m ≠ n

C.  only when m = -n

D.  for all m and n

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If  x *y=x2 + y2 – xy, then the value of 9*11 is:

A.  93

B.  103

C.  113

D.  121

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[{√196-√64}*-2.5]=(?)  

A.  -12

B.  15

C.  14

D.  12

E.  -15

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If 3x – 4y + z = 7; 2x – z + 3y = 19; x + 2y + 2z = 24, then what is the value of z ?

A.  4

B.  5

C.  6

D.  8

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The number of positive integers n in the range 12  ? n? 40 such that the product (n – 1) (n –2)…3.2.1 is not divisible by n is 

A.  5

B.  7

C.  13

D.  14

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If 4x + 5y = 83 and 3x/2y = 21/22 how much is y – x

A.  17

B.  8

C.  10

D.  6

E.  4

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Solve for real x: 6x2 + 5x - 6 ≥ 0

A.  x€ R

B.  x € R-(-3/2,2/3)

C.  x€R-(-2/3,3/2)

D.  x €(-3/2,2/3)

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If x=1+2a+3a2+4a2+……( -1 < a < 1 ) and y=1+3b+6b2+10b3+……( -1 < b < 1 )then find 1+ab+(ab)2+(ab)3+….. in terms of x and y.

A.  (x1/2y1/3)/( x1/2+y1/3-1)

B.  (xy)/(x+y-1)

C.  (x1/3y1/2)/( x1/3+y1/2-1)

D.  None of these

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The cost of 8 Sharpeners and 12 Pens is Rs. 76/- What is the cost of 20 Sharpeners and 30 Pens?  

A.  113. 172

B.  Rs.186

C.  Rs. 190

D.  cannot be determined

E.  None of these

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If n(x) = x2 - 10x, then n(-10) =

A.  0

B.  2.3

C.  9.0

D.  5.9

E.  20.0

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Let x and y be consecutive integers. Suppose m be the number of solutions of x3 − y3 = 3k2 and n be the number of solutions of x3 − y3 = 2t2,where k, t are integers. Then m + n equals:

A.  31

B.  13

C.  5

D.  6

E.  none of these

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If (x + 4) (x + 6) (x +1) 2> 0, then the solution set for the inequality is

A.  R

B.  (-6,-4)

C.  [-6,-4]

D.  R-[-6,-4]

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If 5x + 9 > 3x + 19, what is the range of values x can take?

A.  [5,∞)

B.  (-∞,5)

C.  (5,∞)

D.  (-∞,5]

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The g.c.d. of x3 + x2 – x – 1 and x2 – 1 is

A.  x + 1

B.  x2 – 1

C.  x – 1

D.  x3 – 1

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The total number of integer pairs (x, y) satisfying the equation x + y = xy is

A.  0

B.  1

C.  2

D.  None of the above

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If a, b and c are the sides of a triangle and a4 + b4 + 2a2b2 = c4, then the triangle is

A.  right-angled triangle

B.  acute-angled triangle

C.  equilateral triangle

D.  obtuse-angled triangle

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Which of the following is true?

A.  The second round issues have a higher maturity than the first round for all dates.

B.  The second round issue of any date has a lower maturity only when the first round notified amount exceeds that of the second round.

C.  On at least one occasion, the second round issue having lower maturity received a higher number of competitive bids.

D.  None of the above three statements is true

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If 9c + 2d = 11 and z – 3d = 5, then what is the value of g?

A.  0.78

B.  78g

C.  0.678

D.  76

E.  2.0

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Which family has the lowest average savings?

A.  Ahuja

B.  Bose

C.  Coomar

D.  Dubey

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If a sum of money at certain rate of interest doubles in 5 years and at a different rate of interest becomes 3 times in 12 years, the better rate of interest is

A.  20%

B.  10%

C.  162/3

D.  15%

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H.C.F. of two polynomials is a + 5 and their L.C.M. is (a + 5) (a + 4) (a – 1). If one of the polynomial is a2+ 4a – 5,then the other polynomial is

A.  a2+ 9a – 20

B.  a2– 9a + 20

C.  a2 + 9a + 20

D.  a2– 9a – 20

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