Is y = 7?

Hi


the Q is JUST - Is y=7?--NOTHING about roots

I. tells you x=3, we do not know anything about y.. Insuff

II. tells us (x-3)(y-7)=0..
so different cases..
x=3, y can be 7, 0, 1,2 .. so 7 is possible but not MUST--
y=7, x could be anything But suff for us..
so different CASES .. Insuff

combined we know for sure x=3, BUT y can be 7 or any other number..
so Insuff


IF statement I was y=2..
ans will be A..
since y=2, it cannot be =7..
so our answer for IS x=7? would be NO

Is y = 7?

(1) (x - 4) = 0
(2) (x - 3)(y - 7) = 0

statement 1 gives x=4 clearly not sufficient as we dont know anything about y

statement 2 (x-3)(y-7)=0 clearly not sufficient as it gives relation in form of x and y

together 1 + 2 we get
y=7 so answer should be C

(1) (x - 3) = 0
=> x =3
We have no information about value of y
Not sufficient
(2) (x - 3)(y - 7) = 0
=> x=3 or y = 7
Not sufficient
Combining 1 and 2 , we get
Not sufficient as y may or may not be equal to 7
Answer E

Sorry I noted down the question wrong first time so a new attempt

Is y = 7?

(1) (x - 3) = 0
(2) (x - 3)(y - 7) = 0

1) Not Sufficient as it onky gives x = 3 no value for y
2) we get x=3 and y=7
So Answer must be B as we get y=7

Is y = 7?

(1) (x - 3) = 0
(2) (x - 3)(y - 7) = 0

Only statement 2, gives the exact value of y, hence Answer is B.

ans is E, although i also think it should be B. Can't seem to figure that out.

Im sorry but I am unable to understand your answer. Why is that for every quadratic root, if one is equal to 0, the other is not equal to 0? I thought every quadratic had two roots thus two factors and that would be it. Could you please explain further?

Thank you.

Yes every quadratic equation has TWO roots.

so if (x-a)(x-b) = 0..
when can that be possible..
1)when x=a, this means one root is a, other can be anything, which can not be ascertained with the given info..
2)when x=b, this means one root is b, other can be anything, which can not be ascertained with the given info....
3)OR when BOTH x=b=0, here the roots are a and b[/quote]

Did you mean a=b=0 on the 3rd point?

So is it correct to say that - in this question, combining both AC, we only get one root of y and hence it is insufficient? (but if the question is considered 'must be true', the y=7 should be sufficient and B could be an answer)?; and if the answer choice A was (y-2)=0, then the answer to the question would have been C?

Thank you

Thank you Chetan

(x - 3)(y - 7) = 0 you know that the following 3 cases are possible:

1. x-3 =0 and y-7 not equal to 0
2. x-3 not equal to and y-7 = 0
3. x-3 = 0 and y-7 = 0.

Statement-1: X=3 Gives no clue of what exactly Y would be Hence Insufficient.

Statement-2: (X-3) (X-7) = 0 as discussed above Y may or may not be equal to 7.

Combining both statements still, Y may or may not be zero.

Hence E

it is clear x=3 in first statement
second statement says y is equal or not equal to 7, because x=3
so the answer is E

Statement 1 is insufficient because it does provide any info on y
Statement 2 is insufficient because y could be anything as long a x=3

when we combine the two we get x = 3 so x-3 =0 and y could be anything

Target question: Is y = 7?

Statement 1: x - 3 = 0
In other words, x = 3
Since we have no information about y, statement 1 is NOT SUFFICIENT

Statement 2: (x - 3)(y - 7) = 0
This tells us that EITHER x = 3 OR y = 7
So, y COULD equal 7, or y might not equal 7

For example, consider these two possible cases:
Case a: x = 2 and y = 7. Notice that these values satisfy the equation (x - 3)(y - 7) = 0. In this case, the answer to the target question is YES. y DOES equal 7
Case b: x = 3 and y = 2. Notice that these values satisfy the equation (x - 3)(y - 7) = 0. In this case, the answer to the target question is NO. y does NOT equal 7
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
There are several values of x and y that satisfy BOTH statements. Here are two:
Case a: x = 3 and y = 7. In this case, the answer to the target question is YES. y DOES equal 7
Case b: x = 3 and y = 6. In this case, the answer to the target question is NO. y does NOT equal 7


Answer: E

Cheers,
Brent

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