What is the ratio of c to d?
1. The ratio of 3c to 3d is 3 to 4
2. The ratio c+3 to d+3 is 4 to 5
So I definitely fell for the trap answer D
My question is if stmt 2 said c+3 to d+3 is 5 to 5 does the answer change?
Ratio problem checking my logic
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 ceilidh.erickson
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There are 2 ways we can think about this: algebraically or conceptually.
Algebraically:
Target question: c/d = ?
We will only get a sufficient answer if we can get a value for that fraction.
1) The ratio of 3c to 3d is 3 to 4 > (3c)/(3d) = 3/4
Simplify 3/3 to 1/1 > c/d = 3/4
Sufficient.
2) The ratio c+3 to d+3 is 4 to 5 > (c + 3)/(d + 3) = 4/5
We can't simplify the 3's because we have sums in the numerator and denominator. Instead, crossmultiply:
5(c + 3) = 4(d + 3)
5c + 15 = 4d + 12
5c + 3 = 4d
There is no way to manipulate this equation to simply get c/d.
Insufficient.
The answer must be A.
To your question, changing the ratio to 5/5 would change our answer, because a 1:1 ratio means that the terms must be the same:
(c + 3)/(d + 3) = 5/5
Simplify > (c + 3)/(d + 3) = 1
c + 3 = d + 3
c = d
If the variables are equal, then the ratio c/d = 1
That would have been sufficient.
Algebraically:
Target question: c/d = ?
We will only get a sufficient answer if we can get a value for that fraction.
1) The ratio of 3c to 3d is 3 to 4 > (3c)/(3d) = 3/4
Simplify 3/3 to 1/1 > c/d = 3/4
Sufficient.
2) The ratio c+3 to d+3 is 4 to 5 > (c + 3)/(d + 3) = 4/5
We can't simplify the 3's because we have sums in the numerator and denominator. Instead, crossmultiply:
5(c + 3) = 4(d + 3)
5c + 15 = 4d + 12
5c + 3 = 4d
There is no way to manipulate this equation to simply get c/d.
Insufficient.
The answer must be A.
To your question, changing the ratio to 5/5 would change our answer, because a 1:1 ratio means that the terms must be the same:
(c + 3)/(d + 3) = 5/5
Simplify > (c + 3)/(d + 3) = 1
c + 3 = d + 3
c = d
If the variables are equal, then the ratio c/d = 1
That would have been sufficient.
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
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 ceilidh.erickson
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Conceptually: With ratio problems, it's often faster to think conceptually than to do the algebra.
Target question: What is the ratio of c to d?
If we get a proportional relationship between the two, we'll have sufficient information.
Proportional relationships are always multiplicative (involving multiplication or division):
"one half of something" > (1/2)n
"5 times something" > 5y
"25% of something" > 0.25x
"the ratio of c to d" > c/d
Additive relationships, on the other hand, give us information about real values, but not about proportions.
"4 more than x" > x + 4
"10 less than y" > y  10
1) The ratio of 3c to 3d is 3 to 4
Multiplying each term by 3 will not change the proportion between them. The ratio of c/d will be the same as the ratio of 3c/3d.
2) The ratio c+3 to d+3 is 4 to 5
Knowing the proportional relationship after we've added real values to c and d wouldn't help. We don't know how much difference the +3 made proportionally.
Try testing numbers:
c + 3 = 4 and d + 3 = 5
c = 1, d = 2
c/d = 1/2
or...
c + 3 = 400 and d + 3 = 500
c = 397, d = 497
c/d = 397/497
That gives us a different ratio, and one that's really close to 4/5. The bigger the numbers get, the less of a difference the +3 made to the overall ratio.
To your question:
Does that help?
Target question: What is the ratio of c to d?
If we get a proportional relationship between the two, we'll have sufficient information.
Proportional relationships are always multiplicative (involving multiplication or division):
"one half of something" > (1/2)n
"5 times something" > 5y
"25% of something" > 0.25x
"the ratio of c to d" > c/d
Additive relationships, on the other hand, give us information about real values, but not about proportions.
"4 more than x" > x + 4
"10 less than y" > y  10
1) The ratio of 3c to 3d is 3 to 4
Multiplying each term by 3 will not change the proportion between them. The ratio of c/d will be the same as the ratio of 3c/3d.
2) The ratio c+3 to d+3 is 4 to 5
Knowing the proportional relationship after we've added real values to c and d wouldn't help. We don't know how much difference the +3 made proportionally.
Try testing numbers:
c + 3 = 4 and d + 3 = 5
c = 1, d = 2
c/d = 1/2
or...
c + 3 = 400 and d + 3 = 500
c = 397, d = 497
c/d = 397/497
That gives us a different ratio, and one that's really close to 4/5. The bigger the numbers get, the less of a difference the +3 made to the overall ratio.
To your question:
We can see conceptually that that would work. No matter what numbers we might test, we'll get that c and d are equal, so the ratio must be 1/1.My question is if stmt 2 said c+3 to d+3 is 5 to 5 does the answer change?
Does that help?
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
 OptimusPrep
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Required: c:d = ?kdn508 wrote:What is the ratio of c to d?
1. The ratio of 3c to 3d is 3 to 4
2. The ratio c+3 to d+3 is 4 to 5
So I definitely fell for the trap answer D
My question is if stmt 2 said c+3 to d+3 is 5 to 5 does the answer change?
Statement 1: 3c:3d = 3:4
Or c:d = 3:4
SUFFICIENT
Statement 2: c+3/d+3 = 4/5
4c + 12 = 5d + 15
4c  5d = 3
We cannot find the ratio of c:d
INSUFFICIENT
Correct Option: A
If Statement 2 were: c+3/d+3 = 5/5 = 1
Hence c+3 = d+3
c/d = 1
In this case, we can find the ratio of c:d
So the answer would have been D
Always remember, in the ratio questions, try to bring all the terms in the form of the required ratio.
If there is a constant, then you might not be able to get the desired ratio in that term.

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S1
3c/3d = 3/4
c/d = 3/4; SUFFICIENT
S2
(c + 3)/(d + 3) = 4/5
5(c + 3) = 4(d + 3)
5c + 15 = 4d + 12
5c + 3 = 4d
But we can't isolate c/d! We're stuck with that +3 that we can't eliminate, so this is NOT SUFFICIENT.
3c/3d = 3/4
c/d = 3/4; SUFFICIENT
S2
(c + 3)/(d + 3) = 4/5
5(c + 3) = 4(d + 3)
5c + 15 = 4d + 12
5c + 3 = 4d
But we can't isolate c/d! We're stuck with that +3 that we can't eliminate, so this is NOT SUFFICIENT.
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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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