Quantitative Aptitude: Quadratic Equations Questions Set 65

  1. I) m2 – 3m – 28 = 0
    II) n2 – n – 72 = 0
    m
    m<=n
    m>n
    m>=n
    Can’t be determined
    Option E
    I) m2 – 3m – 28 = 0
    (m + 4) (m – 7) = 0
    M = -4, 7
    II) n2 – n – 72 = 0
    (n + 8) (n – 9) = 0
    N = -8, 9
    Can’t be determined

     

  2. I) 3m2 + 19m + 28 = 0
    II) 2n2 + 13n + 21 = 0
    m
    m<=n
    m>n
    m>=n
    Can’t be determined
    Option E
    I) 3m2 + 19m + 28 = 0
    3m2 + 12m + 7m + 28 = 0
    3m (m + 4) + 7 (m + 4) = 0
    (3m + 7) (m + 4) = 0
    m = -7/3, -4 = -2.33, – 4
    II) 2n2 + 13n + 21 = 0
    2n2 + 6n + 7n + 21 = 0
    2n (n + 3) + 7 (n + 3) = 0
    (2n + 7) (n + 3) = 0
    n = -7/2, -3 = -3.5, -3
    I) 3m2 + 19m + 28 = 0
    3m2 + 12m + 7m + 28 = 0
    3m (m + 4) + 7 (m + 4) = 0
    (3m + 7) (m + 4) = 0
    m = -7/3, -4 = -2.33, – 4
    II) 2n2 + 13n + 21 = 0
    2n2 + 6n + 7n + 21 = 0
    2n (n + 3) + 7 (n + 3) = 0
    (2n + 7) (n + 3) = 0
    n = -7/2, -3 = -3.5, -3
    Can’t be determined

     

  3. I) 2m – 3n = -6
    II) 3m + 4n = 25
    m < n
    m<=n
    m>n
    m>=n
    can’t be determined
    Option A
    2m-3n = -6 –> (1)
    3m + 4n = 25 –> (2)
    Bn solving the equation (1) and (2),
    m = 3, n = 4
    m < n

     

  4. I) 12m2– 37m + 21 = 0
    II) 15n2 + 54n + 27 = 0
    m < n
    m<=n
    m > n
    m>=n
    can’t be determined
    Option C
    I) 12m2 – 37m + 21 = 0
    12m2 – 28m – 9m + 21 = 0
    4m (3m – 7) – 3 (3m – 7) = 0
    (4m – 3) (3m – 7) = 0
    m = ¾, 7/3 = 0.75, 2.33
    II) 15n2 + 54n + 27 = 0
    15n2 + 45n+ 9n + 27 = 0
    15n (n + 3) + 9 (n + 3) = 0
    (15n + 9) (n + 3) = 0
    n = -9/15, -3 = -3/5, -3

     

  5. I) m2 + 3√7 m – 70 = 0
    II) n2 + 2√3 n – 105 = 0
    m < n
    m<=n
    m>n
    m>=n
    Can’t be determined
    Option E
    I) m2 + 3√7 m – 70 = 0
    m2 + 5√7 m – 2√7 m – 70 = 0
    (m + 5√7) (m – 2√7) = 0
    m = 2√7, – 5√7
    II) n2 + 2√3 n – 105 = 0
    n2 + 7√3 n – 5√3 n – 105 = 0
    (n + 7√3) (n – 5√3) = 0
    n = 5√3, – 7√3
    Can’t be determined

     

  6. I) 14x² – 5√15 x – 90 = 0

    II) 6y² + √21 y – 21 = 0

    x < y
    x<=y
    x>y
    x>=y
    relationship between x and y cannot be determined
    Option E
    I) 14x²-5√15 x-90=0

    14x²-12√15 x+7√15 x – 90 = 0

    2x(7x – 6√15)+ √15(7x – 6√15) = 0

    (2x + √15)(7x – 6√15) = 0

    x = -√15/2, (6√15)/7

    II) 6y²+√21 y-21=0

    6y²+3√21 y-2√21 y -21=0

    3y(2y+√21)- √21(2y+√21)=0

    (3y- √21)(2y+√21)=0

    y =√21/3 ,-√21/2

    Hence, relationship between x and y cannot be determined

     

  7. I) 3×2– 13√2x + 24 = 0

    II) y2– 4√2y + 6 = 0

    x < y
    x<=y
    x>y
    x>=y
    relationship between x and y cannot be determined
    Option E
    I) 3×2– 13√2x + 24 = 0

    3x2 – 9√2x – 4√2x + 24 = 0

    3x(x – 3√2) – 4√2 (x – 3√2) = 0

    (3x – 4√2)(x – 3√2) = 0

    x = 4√2/3, 3√2

    II)y2– 4√2y + 6 = 0

    y2 – √2y – 3√2y + 6 = 0

    y(y – √2) – 3√2 (y – √2) = 0

    (y – √2) (y – 3√2) = 0

    y = √2, 3√2

    Hence, relationship between x and y cannot be determined

     

  8. I) 3×2– (6 + √5)x + 2√5 = 0

    II) 8y2– (16 + 3√5)y + 6√5 = 0

    x < y
    x<=y
    x>y
    x>=y
    relationship between x and y cannot be determined
    Option E
    I) 3×2– (6 + √5)x + 2√5 = 0

    3x2 – 6x – √5x + 2√5 = 0

    3x (x – 2) – √5 (x – 2) = 0

    (3x – √5) (x – 2) = 0

    x = √5/3,2

    II) 8y2– (16 + 3√5)y + 6√5 = 0

    8y2 – 16y – 3√5y + 6√5 = 0

    8y (y – 2) – 3√5 (y – 2) = 0

    (8y – 3√5) (y – 2) = 0

    y = (3√5)/8, 2

    Hence, relationship between x and y cannot be determined

     

  9. I) 18x² – 63x + 40 = 0

    II) 12y² + 47y + 45 = 0

    x < y
    x<=y
    x>y
    x>=y
    relationship between x and y cannot be determined
    Option C
    I) 18x² – 63x + 40 = 0

    18x²-15x-48x+40=0

    3x(6x-5)-8(6x-5)=0

    (3x-8)(6x-5)=0

    x=8/3,5/6

    II) 12y²+47y+45=0

    12y²+27y+20y+45=0

    3y(4y+9)+5(4y+9)=0

    (3y+5)(4y+9)=0

    Y =-5/3,-9/4

    Hence, x > y

     

  10. I) 20x²-119x+176=0

    II) 45y²+200y+155=0

    x < y
    x<=y
    x>y
    x>=y
    relationship between x and y cannot be determined
    Option C
    I) 20x²-119x+176=0

    20x²-64x-55x+176=0

    4x(5x-16)-11(5x-16)=0

    (4x-11)(5x-16)=0

    x=11/4,16/5

    II)

    45y²+200y+155=0

    45y²+45y+155y+155=0

    45y(y+1)+155(y+1)=0

    (45y+155)(y+1)=0

    y=-155/45,-1

    Hence, x > y

     

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