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Is the cost of an Organ more than the cost of a Flute ? [#permalink]

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23 Nov 2011, 15:00

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

(1) Three times the cost of an organ is $15 more than twice the cost of a Flute. (2) Five times the cost of an organ is $12 more than six time the cost of a Flute.

Let me try: X: Cost of the organ Y: Cost of the flute

1) \(3X - 2Y = 15\) Two variables, one equation, not enough.

2) \(5X - 6Y = 12\) It seems the same as in 1) But, let's divide the equation by 6.

\(\frac{5X}{6} - Y = 2\)

So, if we had \(x - y\), the result would be greater than 2.

Answer: B

What do you think?

Thanks. Wasn't 100% clear before, since 2nd equation too got 2 variables. I took both the equations to solve and ended up in the trap answer C. Here the logic is 5/6 is less than 1 and still X possess a greater value as the answer is 2. Right?

Thanks metallicafan
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Let me try: X: Cost of the organ Y: Cost of the flute

1) \(3X - 2Y = 15\) Two variables, one equation, not enough.

2) \(5X - 6Y = 12\) It seems the same as in 1) But, let's divide the equation by 6.

\(\frac{5X}{6} - Y = 2\)

So, if we had \(x - y\), the result would be greater than 2.

Answer: B

What do you think?

Thanks. Wasn't 100% clear before, since 2nd equation too got 2 variables. I took both the equations to solve and ended up in the trap answer C. Here the logic is 5/6 is less than 1 and still X possess a greater value as the answer is 2. Right?

Thanks metallicafan

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

A) Three times the cost of an organ is $15 more than twice the cost of a Flute. B) Five times the cost of an organ is $12 more than six time the cost of a Flute.

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.

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

A) Three times the cost of an organ is $15 more than twice the cost of a Flute. B) Five times the cost of an organ is $12 more than six time the cost of a Flute.

Re: Is the cost of an Organ more than the cost of a Flute ? [#permalink]

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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

press kudos, if you like the question, appreciate the effort or encourage people to post.

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.

====

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.
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