Is the cost of an Organ more than the cost of a Flute ?

Right. Maybe it is not the most elegant solution, but it is what I would do.
I am sure that there is a better way to solve it.

IMO its B. This is how i solved it...

S1: 3M = 15+2F
=> M = 5+0.66F.. In this equation as we are getting the decreased value in terms of 0.66F. So insufficient.
For example F can be 100 so M = 71 or if F = 12, M becomes 23.

S2: 5M = 12+6F
=> M = 2.4+1.2F. Here for whatever may be the value of the flute is Organ price is always greater as 1.2F will always be greater than F. Sufficient.

Thanks for more clarity +1

Can't this be solved just by logic,

For 3x-2y = 12 or to have a +ve value, x can be less than y or x can be greater than y...so not sufficient.

For 5x-6y=15 or = to have a +ve value, x should be always greater than y...so sufficient.

Ans = B.

I know this is a crude method, but it helps when v have a crunch of time and in GMAT, v always do..

Yes this can be solved using logic. The above 2 explanation is just to illustrate how the logic works.
There are chances for beginners to go with the trap answer option C.
+1 to you.

Best approach is to do the following

Is Q>F?

Is 5Q>5F?

Statement 2

5Q = 6F+12

Replacing

6F+12>5F

F>-12? Of course

B

Is the cost of an orange more than the cost of an apple?

1) Three times the cost of an orange is 15 more than twice the cost of an apple

2) Five times the cost of an orange is 12 more than six times the cost of an apple


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I like this one! It's a good illustration of why you want to always translate GMAT DS word problems into DS algebra problems, before you start working through them. Here's my translation:

Q: Is o > a?

(1) 3o = 15 + 2a

(2) 5o = 12 + 6a

From here, you could either test numbers immediately, or simplify. I lean towards simplifying, myself - it makes it easier to see which numbers you can pick, if you decide to go that route. Simplify so that o is by itself:

(1) o = 5 + 2/3 a

(2) o = 2.4 + 6/5 a

At this point, you can either test numbers or use logic. To test numbers, try picking some extremes: a very small value for a, and a very large value for a.

Statement 1:

a = 3, o = 5 + 2 = 7. Answer is 'yes'
a = 300, o = 5 + 200 = 205. Answer is 'no'

Insufficient.

Statement 2:

a = 5, o = 2.4 + 6 = 8.4. Answer is 'yes'
a = 500, o = 2.4 + 600 = 602.4. Answer is 'yes'

Notice that the second term is always coming out bigger than a - so the answer should always be 'yes'. Sufficient.

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Or, use some reasoning: in (1), 2/3 a could be either very close to the value of a, or very far away. You don't know if the +5 will make it larger, or make it stay smaller. But in (2), 6/5 a will always be bigger than a, so the answer will always be 'yes' regardless of what you add to it.

Merging topics. Please refer to the discussion above.