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rxs0005
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What is the ratio of m to n? (1) If m is decreased by 3 21 Nov 2010, 03:34
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E
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75% (hard)

Question Stats:

45% (01:56) correct 55% (02:03) wrong based on 117 sessions

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Question:
What is the ratio of m to n?

(1) If m is decreased by 3 the ratio of m to n becomes 3 : 10.
(2) If m + n is increased by 3 the ratio of m to n becomes 7 to 12.
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What is the ratio of m to n? (1) If m is decreased by 3 21 Nov 2010, 11:36
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rxs0005
Question:
What is the ratio of m to n?

(1) If m is decreased by 3 the ratio of m to n becomes 3 : 10.
(2) If m + n is increased by 3 the ratio of m to n becomes 7 to 12.
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Statement 1: (m - 3)/n = 3/10. Not sufficient.

Statement 2: Let m' and n' be new values of m and n. Then, m' = 7x and n' = 12x since they are in the ratio 7:12.
7x + 12x = m + n + 3

Two equations, three variables. You cannot solve for m/n. You can get the ratios using fewer equations than the number of variables but here since constant terms are being added/subtracted, getting a ratio isn't possible.

If you would like to be sure, substitute for n from equation 1 into equation 2.
n = 10/3 (m - 3)
19x = m + 10/3 (m - 3) + 3
3/13 (19x + 7) = m
Similarly you will get n in terms of x and constants. You cannot cancel out x to get m/n.

e.g. this will work for m = 9 and n = 20
Also for m = 63, n = 200
Both statements are not sufficient. Answer (E).
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What is the ratio of m to n? (1) If m is decreased by 3 21 Nov 2010, 12:13
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rxs0005
Question:
What is the ratio of m to n?

(1) If m is decreased by 3 the ratio of m to n becomes 3 : 10.
(2) If m + n is increased by 3 the ratio of m to n becomes 7 to 12.
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1)If m is decreased by 3, then the ratio m:n results in 10 m - 3n = 30 ,one need either the value of m or n to find the ratio m:n
2)if m + n is increased by 3 , we dont know what m or n is increased and by what value 1, 2, 3?
If we combine both,
10 m - 3n =48 , again we need either the value of m or n , so E
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What is the ratio of m to n? (1) If m is decreased by 3 07 Aug 2025, 21:38
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1. Analyze the Question
The goal is to find a single, unique value for the ratio `m/n`. This is a Data Sufficiency question, so we need to know if it’s possible to find one, not what the value is.

2. Analyze Statement (1)
• “If m is decreased by 3 the ratio of m to n becomes 3 : 10.”
• This gives us a clear, unambiguous equation: `(m - 3) / n = 3 / 10`.
• This is a single equation with two variables (`10m - 3n = 30`). We cannot find a unique ratio from one equation.
• Conclusion: INSUFFICIENT.

3. Analyze Statement (2)
• “If m + n is increased by 3 the ratio of m to n becomes 7 to 12.”
• We must take this wording literally. The phrase “m + n is increased by 3” is the key. It tells us that the sum of the two variables changes, but it does not specify how that change is distributed between `m` and `n`.
• For example, does this mean:
• `m` increases by 3 and `n` is unchanged? The equation would be `(m + 3) / n = 7 / 12`.
• `n` increases by 3 and `m` is unchanged? The equation would be `m / (n + 3) = 7 / 12`.
• `m` increases by 1 and `n` increases by 2? The equation would be `(m + 1) / (n + 2) = 7 / 12`.
• Since there are infinite ways to change `m` and `n` so that their sum increases by 3, this statement does not provide a single, unique equation.
• Conclusion: INSUFFICIENT.

4. Combine Both Statements
• We have one clear equation from Statement (1): `10m - 3n = 30`.
• However, Statement (2) is ambiguous and does not provide a second clear equation.
• Since we cannot form a consistent system of two equations, we cannot find a unique solution for `m` and `n`. Depending on how we interpret the ambiguous second statement, we would get a different answer for the ratio `m/n`.
• Because we cannot find a single, unique ratio, the combination is not sufficient.
• Conclusion: INSUFFICIENT.

The final answer is E.
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