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by jainrahul1985 » Mon Feb 28, 2011 3:43 am
Is area of triangle ABC greater than area of triangle DEF ?
1. The value of area of ABC is less than that of perimeter of DEF.
2. Angles of ABC = Angles of DEF

OA E
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Source: — Data Sufficiency |

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by Anurag@Gurome » Mon Feb 28, 2011 4:24 am
(1) If ABC has dimensions 4-5-6, Area of ABC = 10 and DEF has dimensions 8-9-10; Perimeter of DEF= 27. Here Area of ABC < area of DEF.
If ABC and DEF have the same dimensions, say 4-6-8, then area of ABC = 12 and perimeter of DEF = 18. Here both the triangles will have same area.
Since we don't get a unique answer, so (1) is NOT SUFFICIENT.

(2) Angles of ABC = Angles of DEF implies that ABC and DEF are similar triangles. But here the area of ABC may or may not be greater than area of DEF.
So, (2) is also NOT SUFFICIENT.

Combining (1) and (2), consider the same examples as we did in statement 1, then again we we don't get a unique answer.

The correct answer is E.
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by maihuna » Mon Feb 28, 2011 6:12 am
I think solve using example is *difficult* technique as coming with right contrast in exam timing is tough.

here is an interpretation of mine w/o contrast :

1. We only know area of abc < perimeter of def but there is no fix relation between area and perimeter for 345 triangle , perimeter 12, area 6, for 300400500 triangle perimeter 1200, area 60000.

The difference from anurag approach is we *do not* need an counter ex, just an understanding, basic understanding that area and perimeter are not correlated in any way.

2. Weonly knew the sides will be proportional, similar triangle, above exapmlesays it doesnhave any bearing on final outcome

combining too doesnt help.
Anurag@Gurome wrote:(1) If ABC has dimensions 4-5-6, Area of ABC = 10 and DEF has dimensions 8-9-10; Perimeter of DEF= 27. Here Area of ABC < area of DEF.
If ABC and DEF have the same dimensions, say 4-6-8, then area of ABC = 12 and perimeter of DEF = 18. Here both the triangles will have same area.
Since we don't get a unique answer, so (1) is NOT SUFFICIENT.

(2) Angles of ABC = Angles of DEF implies that ABC and DEF are similar triangles. But here the area of ABC may or may not be greater than area of DEF.
So, (2) is also NOT SUFFICIENT.

Combining (1) and (2), consider the same examples as we did in statement 1, then again we we don't get a unique answer.

The correct answer is E.
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by GMATGuruNY » Mon Feb 28, 2011 7:10 am
jainrahul1985 wrote:Is area of triangle ABC greater than area of triangle DEF ?
1. The value of area of ABC is less than that of perimeter of DEF.
2. Angles of ABC = Angles of DEF

OA E
I received a PM asking me to comment.
Let's plug in familiar triangles that satisfy both statements. The sides of a 45-45-90 triangle are proportioned 1:1:√2.

Statement 1: The value of the area of ABC is less than that of the perimeter of DEF
If ABC = 1:1:√2 (area = 1/2) and DEF = 1:1:√2 (perimeter ≈ 3.4), then the areas are equal.
If ABC = 2:2:2√2 (area = 2) and DEF = 1:1:√2 (perimeter ≈ 3.4), then ABC has a greater area.
Insufficient.

Statement 2: Angles of ABC = Angles of DEF
Since the scenarios used in Statement 1 also satisfy statement 2, and in the first case ABC and DEF have equal areas and in the second case ABC has a greater area, insufficient.

Statements 1 and 2 combined:
Since the scenarios used in Statement 1 satisfy both statements, and in the first case ABC and DEF have equal areas and in the second case ABC has a greater area, insufficient.

The correct answer is E.
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