DS problem

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phoenix9801: Master | Next Rank: 500 Posts; Posts: 190; Joined: Thu Jan 14, 2010 8:29 pm; Thanked: 2 times

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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Source: Beat The GMAT — Problem Solving | Fri May 25, 2012 2:25 am

eagleeye: Legendary Member; Posts: 520; Joined: Sat Apr 28, 2012 9:12 pmFollowed by: 49 members; Thanked: 339 times; GMAT Score:770

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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aneesh.kg: Master | Next Rank: 500 Posts; Posts: 385; Joined: Mon Apr 16, 2012 8:40 amFollowed by: 29 members; Location: Pune, India; Thanked: 186 times

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:

Last edited by aneesh.kg on Fri May 25, 2012 8:48 am, edited 2 times in total.

Aneesh Bangia
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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

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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ronnie1985: Legendary Member; Posts: 626; Joined: Fri Dec 23, 2011 2:50 amFollowed by: 10 members; Location: Ahmedabad; Thanked: 31 times

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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