What is the ratio of c to d?

OptimusPrepJanielle

In your answer you arrive to the step:

4c+12=5d+15

Can you please explain why these steps are not valid:

4c+12=5d+15 (/-12)

4c=5d+3 (/5d)

4c/5d=3/1 (which would be a ratio)

Did I do an illegal move within the operations with ratio?

Any help appreciated,
Thanks,
Aron.

jozsaron

yes, when you divided by 5d the right-hand side, make sure you divide the whole expression

krashan

So does that mean the answer is (D) Each statement alone is sufficient?

No, the correct answer is A.

(c + 3)/(d +3) = 4/5.
4d - 5c = 3.

From that we cannot get the ratio of c to d. For example, d = 7 and c = 5, then c/d = 5/7 but if d = 12 and c = 9, then c/d = 9/12 = 3/4.

In problems on ratios, it’s always important to know the fundamental properties and use them in solving questions.
If both the terms of a ratio are multiplied by the same constant, the ratio does not change.

For example, if ratio a:b = 5:6 and we assume that a=5 and b=6, then multiplying both the numbers by 2 will give us 10 and 12, which are also in the ratio of 5:6.

However, we cannot say the same thing about addition or subtraction. Adding the same number to both the terms of the ratio will change the ratio in a certain way, depending on what type of ratio is given. And will subtracting the same number from both the terms of the ratio.

With this information, it is now easy to see that statement I alone is sufficient.
\(\frac{3c}{3d}\)= ¾ only means that \(\frac{c}{d}\) = ¾. This is a unique answer to the question which asked us to find out the ratio of c and d.

Statement I being sufficient, the possible answer options are A or D. Answer options B, C and E can be eliminated.

From statement II, we can say \(\frac{c+3}{d+3}\) = \(\frac{4}{5}\). But this is not sufficient to find unique values for c and d and hence a unique value for c:d.

For example, if c = 1 and d = 2, then, \(\frac{c+3}{d+3}\)= \(\frac{4}{5}\). In this case, c:d = 1:2.

On the other hand, if c = 5 and d = 7, \(\frac{c+3}{d+3}\) = \(\frac{4}{5}\). But, in this case, c:d = 5:7.

Therefore, statement II is insufficient. Answer option D can be eliminated.
The correct answer option is A.

Hope this helps!

What is the ratio of c to d?

(1) The ratio of 3c to 3d is 3 to 4.

\(\frac{3c}{3d} = \frac{3}{4}\)
\(\frac{c}{d} = \frac{3}{4}\)

SUFFICIENT.

(2) The ratio of c + 3 to d +3 is 4 to 5.

\(\frac{c + 3}{d + 3} = \frac{4}{5}\)

We can get different values in this situation. INSUFFICIENT.

(1) \(\frac{3c}{3d}=\frac{3}{4}\)

\(=\frac{c}{d}=\frac{3}{4} Sufficient. \)

(2)\( \frac{c+3}{d+3}=\frac{4}{5}\)

\(=5c+15=4d+12\)

\(=5c-4d=-3\); We don't get the ratio of \(c:d\); Insufficient.

The answer is A

Solution:

Question Stem Analysis:

We need to determine the ratio of c to d, i.e., the value of c/d.

Statement One Alone:

We are given that (3c) / (3d) = 3/4. Cancelling the 3s on the left hand side, we have c/d = 3/4. Statement one alone is sufficient.

Statement Two Alone:

We are given that (c + 3) / (d + 3) = 4/5. This does not allow us to determine the value of c/d. For example, c could be 1 and d could be 2 so that (c + 3) / (d + 3) = 4/5. However, c could be 5 and d could be 7 so that (c + 3) / (d + 3) = 8/10 = 4/5. In the former case, c/d = 1/2, but in the later case, c/d = 5/7. Statement two alone is not sufficient.

Answer: A

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