CAT 1999 | Question: 161

Question

The question is followed by two statements I and II.

Mark

• A. if the question can be answered by any one of the statements alone, but cannot be answered by using the other statement alone.
• B. if the question can be answered by using either statement alone.
• C. if the question can be answered by using both the statements together, but cannot be answered by using either statement alone.
• D. if the question cannot be answered even by using both the statements together.

 

Find a pair of real numbers x and y that satisfy the following two equations simultaneously. It is known that the values of a, b, c, d, e and f are non-zero.

$ax + by = c$

$dx + ey = f$

1. a = kd and b = ke, c = kf, k $\neq$ 0
2. a = b = 1, d = e = 2, f $\neq$ 2c

Answer 1

$\text{ax+by=c}$

Here if we put $\text{a=kd, b=ke, c=kf}$

we get $\text{dx+ey=f}$

which is same as $\text{2nd}$ equation

So, thiese two are same line putting condition I

Now, By condition II putting $\text{a=b=1, d=e=2}$

we get two lines are parallel

So, Answer$: \text{(D)}$ if the question cannot be answered even by using both the statements together.

Comments

Using 1, we can get a point rt?