Question

Given that X and Y are non-negative. What is the value of X?
I. $2X + 2Y \leq 40$
I II. $X - 2Y \geq 20$

• A. If the question can be answered with the help of statement I alone
• B. If the question can be answered with the help of statement II alone
• C. If both, statement I and statement II are needed to answer the question
• D. If the question cannot be answered even with the help of both the statements

Hint:

When two inequalities involve two variables, try solving them together to eliminate a variable and isolate the unknown.

Answer 1

The Correct Option is C

We are given two inequalities and are asked to find the exact value of \( X \). Let’s analyze: From I: $2X + 2Y \leq 40$ $X + Y \leq 20$
This gives a range of possible values for \( X \) and \( Y \), but no unique value for \( X \) alone.
From II: $X - 2Y \geq 20$
This also represents a region or range in terms of both \( X \) and \( Y \), not a unique value for \( X \).
Combining I and II:
From I: $X + Y \leq 20$
From II: $X \geq 2Y + 20$
Substitute $X$ from II into I:
$(2Y + 20) + Y \leq 20$ $3Y + 20 \leq 20$ $3Y \leq 0$ $Y = 0$
Substitute $Y = 0$ into either inequality to get $X$:
From II: $X - 0 \geq 20$ $X \geq 20$
From I: $X + 0 \leq 20$ $X \leq 20$
So, combining both: $X = 20$ Thus, the unique value of \( X \) can be found only by using both statements together.