If y (u-c) = 0 and j (u-k) = 0, Which of the Following Must be True, Assuming c < kc < k?

Question: If y (u-c) = 0 and j (u-k) = 0, which of the following must be true, assuming c < kc < k?

1. yj < 0
2. yj > 0
3. yj = 0
4. j = 0
5. y = 0

This topic is a part of GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Quantitative Review". GMAT Quant section consists of a total of 31 questions. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT quant topics in the problem-solving part require calculative mathematical problems that should be solved with proper mathematical knowledge.

Answer:

We need to solve the original equation (1): y (u-c) = 0
This means either

y = 0
OR
u - c = 0, in which case u = c

Now we need to solve the original equation (2): j (u-k) = 0
This means either

j = 0
OR
u – k = 0, in which case u = k

From the above two steps, we can see that:
u = c and u = k

But this cannot be simultaneously correct for both the equations. Still if we consider that u=c and u=k is correct. This means that u=c=k which can’t be true because it is given that c < k.

So only one option can be correct so either y=0 or j=0 which means yj=0.

Hence this is always true. (yj = 0)

Correct Answer: C

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