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DS problem

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by phoenix9801 » Fri May 25, 2012 2:25 am
Hi, I see before with a friend of mine and was wondering if any one knew how to solve? Looked similar to gmat question they might ask as Data Sufficiency. Can anyone please explain using plugging in numbers as simple as possible. Thanks.




Item F costs three times as much as item G, and item H cost $4 more than one-third the price of item G.


....Quantity A..................Quantity B

The Cost of Item F..........The Cost of item H


a) Quantity A is greater
b) Quantity B is Greater
c) the two quantity are equal
d) the relationship cannot be determined from the information given
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by eagleeye » Fri May 25, 2012 4:11 am
Hey Phoenix9801:

Let the price of Item G be G, then we are given:
A = 3G;
B = 4+G/3;

Now I can tell from just this that the relationship can't be determined from this info, but let me show you using numbers. Let's equate the two (A and B) first.
A=B => 3G = 4+G/3 => 3G-G/3 = 4 => 8G/3 = 4 => G = 3/2 = 1.5

Let me know if this helps :)

Now if G = 1.5 ; A=3G = 4.5; B = 4+G/3= 4.5 ; then A and B are equal.
If G < 1.5; let G = 0; then A=0; B = 4; then B is greater than A.
If G > 1.5[/i]; let G = 3; A=9; B = 4+3/3 = 5; then A is greater than B.

So clearly as G ranges from 0 to 1.5 to 4; we get three different answers. Hence correct answer is D

Let me know if this helps :)
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by aneesh.kg » Fri May 25, 2012 8:30 am
phoenix9801 wrote:Hi, I see before with a friend of mine and was wondering if any one knew how to solve? Looked similar to gmat question they might ask as Data Sufficiency. Can anyone please explain using plugging in numbers as simple as possible. Thanks.

Item F costs three times as much as item G, and item H cost $4 more than one-third the price of item G.

....Quantity A..................Quantity B

The Cost of Item F..........The Cost of item H


a) Quantity A is greater
b) Quantity B is Greater
c) the two quantity are equal
d) the relationship cannot be determined from the information given
This looks like a GRE problem.
Let the cost of G be $1.
Cost of F = 3*1 = $3
Cost of H = 4 + (1/3)*1 = $4.33

H > F

Let the cost of G be $100.
Cost of F = 3*100 = $300.
Cost of H = 4 + (1/3)*(100) = 33.33 + 4 = 37.33

F > H

Relationship depends of the magnitude of quantity G.

[spoiler](D)[/spoiler] is the correct answer.

This can be understood better by plotting F and H, which are straight lines w.r.t. G, using co-ordinate geometry as shown below:

Image
Last edited by aneesh.kg on Fri May 25, 2012 8:48 am, edited 2 times in total.
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by GMATGuruNY » Fri May 25, 2012 8:30 am
phoenix9801 wrote:Hi, I see before with a friend of mine and was wondering if any one knew how to solve? Looked similar to gmat question they might ask as Data Sufficiency. Can anyone please explain using plugging in numbers as simple as possible. Thanks.




Item F costs three times as much as item G, and item H cost $4 more than one-third the price of item G.


....Quantity A..................Quantity B

The Cost of Item F..........The Cost of item H


a) Quantity A is greater
b) Quantity B is Greater
c) the two quantity are equal
d) the relationship cannot be determined from the information given
Let G=3.
Then H = 4 + (1/3)G = 4 + (1/3)3 = 5.
F = 3G = 3*3 = 9.
F > H.

Let G=1.
Then H = 4 + (1/3)G = 4 + (1/3)1 = 4 1/3.
F = 3G = 3*1 = 3.
F < H.

The correct answer is D.
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by ronnie1985 » Fri May 25, 2012 9:59 am
Put G = 3 then G = 1/3 onr can find that the relationship cannot be established from the given info

(D)
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