Quantitative Aptitude: Quadratic Equations Questions Set 67

Shubhra
  1. 35m2+16m-3=0
    10n2+136n-56=0
    m<n
    m<=n
    m>n
    m>=n
    the relation cannot be determined
    Option E
    35m2+16m-3=0
    35m2 -5m+ 21m-3=0
    5m(7m -1) + 3(7m -1)=0
    (7m-1) ( 5m+3)=0
    m= 1/7 , -3/5
    10n2+136n-56=0
    10n2 -4n+ 140n -56=0
    n( 10n-4) + 14(10n-4)=0
    (10n-4) ( n+14)=0
    n= 4/10,- 14
    Hence the relation cannot be determined

     

  2. 10m2-136m-14=0
    25n2-10n-8=0
    m<n
    m<=n
    m>n
    m>=n
    the relation cannot be determined
    Option C
    10m2-136m-14=0
    10m2 -140m+m-14=0
    10m(m -14) + 1(m -14)=0
    (m-14) ( 10m+1)=0
    m= +14 , -1/10
    25n2-10n-8=0
    25n2 -20n+ 10n -8=0
    5n( 5n-4) + 2(5n-4)=0
    (5n-4) ( 5n+2)=0
    n= 5/4, -2/5
    Hence m>n

     

  3. 11m2+120m= 11
    8n2+74n+143=0
    m<n
    m<=n
    m>n
    m>=n
    the relation cannot be determined
    Option E
    11m2+120m= 11
    11m2 +121m-m-11=0
    11m(m +11) -1(m +11)=0
    (m+11) ( 11m-1)=0
    m=- 11 , 1/11
    8n2+74n+143=0
    8n2 +22n+52n+143 =
    2n( 4n+11) +13(4n+11)=0
    (4n+11) ( 2n+13)=0
    n= -11/4, -13/2
    Hence the relation cannot be determined

     

  4. 8m2+51m+18=0
    49n2-1=0
    m<n
    m<=n
    m>n
    m>=n
    the relation cannot be determined
    Option A
    8m2+51m+18=0
    8m2 +48m+3m+18=0
    8m(m +6) + 3(m +6)=0
    (m+6) ( 8m+3)=0
    m= -6 , -3/8
    49n2-1=0
    (7n-1) ( 7n+1)=0
    n= 1/7, -1/7
    Hence n>m

     

  5. 40m2-13m+1=0
    18n2+77n-18=0
    m<n
    m<=n
    m>n
    m>=n
    the relation cannot be determined
    Option D
    40m2-13m+1=0
    40m2 -8m-5m+1=0
    8m(5m -1) -1(5m -1)=0
    (5m-1) ( 8m-1)=0
    m= 1/5 , 1/8
    18n2+77n-18=0
    18n2 +81n- 4n -18=0
    9n( 2n+9) – 2(2n+9)=0
    (2n+9) ( 9n-2)=0
    n= -9/2, 2/9
    Hence m ≥ n

     

  6. 16m2+60m+14=0
    8n2– 77n-30=0
    m<n
    m<=n
    m>n
    m>=n
    the relation cannot be determined
    Option A
    16m2+60m+14=0
    16m2 + 56m+ 4m+14=0
    8m(2m +7) + 2(2m +7)=0
    (2m+7) ( 8m+2)=0
    m= -7/2 , -2/8
    8n2– 77n-30=0
    8n2 -80n+ 3n -30=0
    8n( n-10) + 3(n-10)=0
    (n-10) ( 8n+3)=0
    n= 10, -3/8
    Hence n>m

     

  7. 35m2+32m+5=0
    9n2– 36n+32=0
    m<n
    m<=n
    m>n
    m>=n
    the relation cannot be determined
    Option A
    35m2+32m+5=0
    35m2 + 25m+ 7m+5=0
    5m(7m +5) + 1(7m +5)=0
    (7m+5) ( 5m+1)=0
    m= -5/7 , -1/5
    9n2– 36n+32=0
    9n2 -12n-24n +32=0
    3n( 3n-4) -8(3n-4)=0
    (3n-4) ( 3n-8)=0
    n= 4/3, 8/3
    Hence n>m

     

  8. 35m2-18m-81=0
    10n2+184n-114=0
    m<n
    m<=n
    m>n
    m>=n
    the relation cannot be determined
    Option C
    35m2-18m-81=0
    35m2 – 45m+ 63m-81=0
    5m(7m -9) + 9(7m -9)=0
    (7m-9) ( 5m+9)=0
    m= 9/7 , -9/5
    10n2+184n-114=0
    10n2 -6n+ 190n -114=0
    n( 10n-6) + 19(10n-6)=0
    (10n-6) ( n+19)=0
    n= 6/10,- 19
    Hence m>n

     

  9. 10m2+79m+63=0
    48n2+10n-2=0
    m<n
    m<=n
    m>n
    m>=n
    the relation cannot be determined
    Option A
    10m2+79m+63=0
    10m2 +70m+9m+63=0
    10m(m +7) + 9(m +7)=0
    (m+7) ( 10m+9)=0
    m= -7 , -9/10
    48n2+10n-2=0
    48n2 -6n+ 16n -2=0
    6n( 8n-1) + 2(8n-1)=0
    (8n-1) ( 6n+2)=0
    n= 1/8, -2/6
    Hence n>m

     

  10. 2m2-35m= -17
    2n2+35n= +17
    m<n
    m<=n
    m>n
    m>=n
    the relation cannot be determined
    Option D
    2m2-35m= -17
    2m2 -34m-1m+17=0
    2m(m -17) -1(m -17)=0
    (m-17) ( 2m-1)=0
    m= 17 , 1/2
    2m2-35m= -17
    2m2 -34m-1m+17=0
    2m(m -17) -1(m -17)=0
    (m-17) ( 2m-1)=0
    m= 17 , 1/2
    2n2+35n= +17
    2n2 +34n+1n+17=0
    2n(n +17) +1(n +17)=0
    (n+17) ( 2n+1)=0
    n= -17 , -1/2
    m>n

     

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