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Directions

This data sufficiency problem consists of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements, plus your knowledge of mathematics and everyday facts (such as the number of days in a leap year or the meaning of the word counterclockwise), you must indicate whether -

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
3. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
4. EACH statement ALONE is sufficient to answer the question asked.
5. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

Numbers
All numbers used are real numbers.

Figures
A figure accompanying a data sufficiency question will conform to the information given in the question but will not necessarily conform to the additional information given in statements (1) and (2).

Lines shown as straight can be assumed to be straight and lines that appear jagged can also be assumed to be straight.

You may assume that the positions of points, angles, regions, etc. exist in the order shown and that angle measures are greater than zero.

All figures lie in a plane unless otherwise indicated.

Note
In data sufficiency problems that ask for the value of a quantity, the data given in the statement are sufficient only when it is possible to determine exactly one numerical value for the quantity.

Is triangle ABC with sides a, b and c acute angled?
1. Triangle with sides a², b², c² has an area of 140 sq cms.>
2. Median AD to side BC is equal to altitude AE to side BC.

The correct choice is (A). Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.

The given question is an "Is" question. So, the answer has to be a definite YES or a definite NO. It cannot be a MAYBE.

The question stem states that a, b, and c are the measures of the sides of a triangle. If a, b and c measure the sides of a triangle, and let us say 'a' is the longest side of the triangle, then

1. the triangle is acute angled if a² < b² + c²
   
2. right angled if a² = b² + c² and
   
3. obtuse angled if a² > b² + c²
   

Now let us evaluate the statements given to us

Statement 1

Triangle with sides a², b², c²   has an area of 140 sq cms.

wThe statement provides us with one valuable information - we can form a triangle with sides a², b², c².

For any triangle we know that sum of two sides is greater than the third side.

So, a² < b² + c²

That is the condition to be satisfied for a triangle with sides a, b and c to be an acute angled triangle.
Statement 1 answers in the positive and the information is SUFFICIENT.

Statement 2

Median AD to side BC is equal to altitude AE to side BC

We can infer that the triangle is either equilateral or isosceles.

An equilateral triangle is definitely an acute angled triangle. However, an isosceles triangle need not be an acute angled triangle.

So, statement 2 is NOT SUFFICIENT.

Statement 1 is sufficient, while statement 2 is not sufficient.

Choice A is the correct answer.

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