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soni_pallavi: Master | Next Rank: 500 Posts; Posts: 107; Joined: Tue Jun 05, 2012 3:25 amFollowed by: 13 members; Thanked: 1 times

by soni_pallavi » Fri Nov 23, 2012 11:53 pm

Q1) The cost of a square slab is proportional to its thickness and also proportional to the square of its length.What is the cost of a square slab that is 3 meters long and 0.1 meter thick?

1)The cost of a square slab that is 2 meters long and 0.2 meter thick is 160$ more than the cost of a square slab that is 2 meters long and 0.1 meter thick.

2)The cost of a square slab that is 3 meters long and 0.1 meter thick is 200$ more than the cost of a square slab that is 2 meters long and 0.1 meter thick.

Thanks

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Source: Beat The GMAT — Data Sufficiency | Fri Nov 23, 2012 11:53 pm

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Sat Nov 24, 2012 3:57 am

soni_pallavi wrote:Q1) The cost of a square slab is proportional to its thickness and also proportional to the square of its length.What is the cost of a square slab that is 3 meters long and 0.1 meter thick?

1)The cost of a square slab that is 2 meters long and 0.2 meter thick is 160$ more than the cost of a square slab that is 2 meters long and 0.1 meter thick.

2)The cost of a square slab that is 3 meters long and 0.1 meter thick is 200$ more than the cost of a square slab that is 2 meters long and 0.1 meter thick.

Thanks

Let us assume that C = Cost, T = thickness, L = Length, k = constant of proportionality
C = k * L * TÂ²

(1) The cost of a square slab that is 2 meters long and 0.2 meter thick is $160 more than the cost of a square slab that is 2 meters long and 0.1 meter thick.
C = k * 2 * (0.2)Â² = 0.08k
C = k * 2 * (0.1)Â² = 0.02k

0.08k = 160 + 0.02k
0.06k = 160
k = 160/0.06 = 1000
Substitute this value of k in C = k * L * TÂ²; SUFFICIENT.

(2) The cost of a square slab that is 3 meters long and 0.1 meter thick is 200$ more than the cost of a square slab that is 2 meters long and 0.1 meter thick, which is the same as statement but with different values; SUFFICIENT.

The correct answer is D.

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