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 â‰¥ 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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