### 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

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

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

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

A.  63

B.  – 3

C.  -56

D.  62

E.  10

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

A.  0

B.  1

C.  2

D.  3

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

A.  10

B.  24

C.  26

D.  28

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

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

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

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

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

A.  93

B.  103

C.  113

D.  121

[{√196-√64}*-2.5]=(?)

A.  -12

B.  15

C.  14

D.  12

E.  -15

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

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

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

A.  17

B.  8

C.  10

D.  6

E.  4

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)

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

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

If n(x) = x2 - 10x, then n(-10) =

A.  0

B.  2.3

C.  9.0

D.  5.9

E.  20.0

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

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]

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

A.  [5,∞)

B.  (-∞,5)

C.  (5,∞)

D.  (-∞,5]

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

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

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

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

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

Which family has the lowest average savings?

A.  Ahuja

B.  Bose

C.  Coomar

D.  Dubey

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%

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