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If k = a c /b d = c e/d f = a e/b f when all quantities are positive, then which of the following must be true? (A) k = e/ f (C) k= a/b (B) k= c/d (D) All of the above?
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If k = a c /b d = c e/d f = a e/b f when all quantities are positiv...
**Given Information:**

k = a c / b d
c e / d f = a e / b f

**To determine:**

Which of the following must be true:

(A) k = e / f
(B) k = c / d
(C) k = a / b
(D) All of the above

**Approach:**

We need to determine the relationship between k, a, b, c, d, e, and f based on the given information.

**Solution:**

Let's break down the given equations and analyze them separately.

1. k = a c / b d

2. c e / d f = a e / b f

**Analyzing the first equation:**

k = a c / b d

We can rewrite this equation as:

k b d = a c

This equation implies that k is directly proportional to a c, and inversely proportional to b d.

**Analyzing the second equation:**

c e / d f = a e / b f

Cross-multiplying this equation, we get:

c e * b f = d f * a e

This equation implies that c e b f is equal to d f a e.

Now, let's analyze the options:

(A) k = e / f

From the given equations, we cannot directly determine the relationship between k, e, and f. Therefore, option A cannot be determined to be true.

(B) k = c / d

From the given equations, we cannot directly determine the relationship between k, c, and d. Therefore, option B cannot be determined to be true.

(C) k = a / b

From the given equations, we know that k is directly proportional to a c and inversely proportional to b d. However, we cannot determine the exact relationship between k and a / b. Therefore, option C cannot be determined to be true.

(D) All of the above

Since we cannot determine the exact relationships between k and e / f, k and c / d, and k and a / b based on the given equations, option (D) cannot be true.

**Conclusion:**

None of the options provided (A, B, C, D) must be true based on the given information.
Community Answer
If k = a c /b d = c e/d f = a e/b f when all quantities are positiv...
D. all of the above
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If k = a c /b d = c e/d f = a e/b f when all quantities are positive, then which of the following must be true? (A) k = e/ f (C) k= a/b (B) k= c/d (D) All of the above?
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If k = a c /b d = c e/d f = a e/b f when all quantities are positive, then which of the following must be true? (A) k = e/ f (C) k= a/b (B) k= c/d (D) All of the above? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about If k = a c /b d = c e/d f = a e/b f when all quantities are positive, then which of the following must be true? (A) k = e/ f (C) k= a/b (B) k= c/d (D) All of the above? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If k = a c /b d = c e/d f = a e/b f when all quantities are positive, then which of the following must be true? (A) k = e/ f (C) k= a/b (B) k= c/d (D) All of the above?.
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