Quantitative Aptitude: Quadratic Equations Questions Set 67

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