Good algebra problem explanation required

[neuroticA]

1. If b,c and d are constants and x^2+bx+c=(x+d)^2 for all values of x, what is the value of c?
1)d=3
2)b=6

2. If a,b,k and m are positive integers, is a^k a factor of b^m?
1) a is a factor of b
2) k=m

3. Is Mod x-y>Mod x-z?
1) Mod x > Mod z
2) x<0

[vigngmat]

I got the below answers for the questions

1. D
2. A
3. E

Explanations are pretty hard to explain here..but I will try

1. if you expand the first question, you will get the below eqn

x^2+b*x+c=x^2+2dx+d^2;
If you match this eqn, you will get, b=2d; and c=d^2 or c=b^2/4
either of the answer choices would help to get the value of C, so D

2. b^m/a^k = integer;

1. a is a factor of b

b/a= integer; lets say b=10; a =2
then the main eqn, 10^m/2^k
lets say m=5, k=1; then 10^5/2^1 is an integer
try other values you will get the same so A/D

2. k=m;
lets say k=m=2; this wont help, as the values of b and a can be any and b/a can be integer or not. so B wrond.

So A

3. |x-y|>|x-z|

1. |x|>|z|
lets say x=-5, z=-3, this satisfies the above eqn. Substituet this in main eqn, then we get, |5+y|>2; here y can be any value, and may or might not satisfy the equation. So A is wrong
2. x<0; y , z can have any value so B wrong.

3. the values we have chose for x in choice 1, x=-5 and z=-3 didnt satisfy hence E

[CallMeDaOne]

Agree with Vigngmat on the answers for Q1 and Q3.


Regarding the Q2,

1. a is a factor of b.
Going by your approach, let a=2, b=10. Now if I reverse the values that you gave for k and m, so that k=5, m=1. Now here, 2^5 is not a factor of 10^1. So I cannot deduce that a^k is a factor of b^m just from the 1st statement given. So statement1 is NOT SUFFICIENT. So the answer cant be A.

2. k=m
Unless we know about a and b, we cannot deduce anything about a^k being a factor of b^m. So NOT SUFFICIENT.

Lets take 1 and 2 together, if a is a factor of b and k=m, then

a^k = a*a*a*....k times. -----------eq1
b^m = b*b*b*....k times (since k=m)----------eq2

now if a is a factor of b, then b/a = a positive integer, say X

divide eq2 by eq1 and we get
(b*b*b....k times)/(a*a*a....k times) = (b/a)^k = X^k

So, we deduce that a^k is a factor of b^m. So (1) and (2) taken together are SUFFICIENT.

So C should be the answer.

I got the below answers for the questions

1. D
2. A
3. E

Explanations are pretty hard to explain here..but I will try

1. if you expand the first question, you will get the below eqn

x^2+b*x+c=x^2+2dx+d^2;
If you match this eqn, you will get, b=2d; and c=d^2 or c=b^2/4
either of the answer choices would help to get the value of C, so D

2. b^m/a^k = integer;

1. a is a factor of b

b/a= integer; lets say b=10; a =2
then the main eqn, 10^m/2^k
lets say m=5, k=1; then 10^5/2^1 is an integer
try other values you will get the same so A/D

2. k=m;
lets say k=m=2; this wont help, as the values of b and a can be any and b/a can be integer or not. so B wrond.

So A

3. |x-y|>|x-z|

1. |x|>|z|
lets say x=-5, z=-3, this satisfies the above eqn. Substituet this in main eqn, then we get, |5+y|>2; here y can be any value, and may or might not satisfy the equation. So A is wrong
2. x<0; y , z can have any value so B wrong.

3. the values we have chose for x in choice 1, x=-5 and z=-3 didnt satisfy hence E

[vigngmat]

agree callmedaone..for question 2, answer is C.

[bose]

1 D as bx+c=2dx+d^2, so from 1 we know d and so know c as c=d^2, from 2 we know d, from d we know c.

2 C agree with callmedaone

3 E no info about y given

[amit_ace]

I think the answer of
1. A
x^2+bx+c=(x+d)^2 for all values of x
so if the equations is correct for all values of X we can input X =0
so
c=d^2
A says D=3
so C=9

Agree with answers for 2 and 3.

[NishantG]

My answer
D
C
E

[nikhilsikri]

hey guys could you explain the first one in little details..

my method seem little specious although ans i have got is D only ...

2. C
3. E

thanks in advance ...