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

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Is the cost of an Organ more than the cost of a Flute ? [#permalink] New post 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.
[Reveal] Spoiler: OA

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Last edited by Bunuel on 27 Jan 2014, 05:28, edited 1 time in total.
Renamed the topic and edited the question.
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Re: DS#1 [#permalink] New post 23 Nov 2011, 16:22
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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?
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Re: DS#1 [#permalink] New post 23 Nov 2011, 20:02
metallicafan wrote:
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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Re: DS#1 [#permalink] New post 24 Nov 2011, 05:54
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cleetus wrote:
metallicafan wrote:
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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Re: DS#1 [#permalink] New post 24 Nov 2011, 06:22
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cleetus wrote:
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.
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Re: DS#1 [#permalink] New post 24 Nov 2011, 08:02
Thanks for more clarity +1
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Re: DS#1 [#permalink] New post 24 Nov 2011, 08:58
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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..:)
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Re: DS#1 [#permalink] New post 24 Nov 2011, 10:05
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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Re: DS#1 [#permalink] New post 27 Jan 2014, 05:27
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cleetus wrote:
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.


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
Re: DS#1   [#permalink] 27 Jan 2014, 05:27
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