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Answer for Question 3:


Triangle A has one side of length x. If (x^8) ^ 1/2 = 81 , what is the perimeter of Triangle A?

1) Triangle A has sides whose lengths are consecutive integers
2) Triangle A is NOT a right triangle

(A) Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
( Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.(D) Each statement ALONE is sufficient.
(E) Statements (1) and (2) TOGETHER are NOT sufficient.

Answer : C


Approach:

(x^8) ^ 1/2 = 81

x^4 = 81

x = 3


Thus, we know that one side of Triangle A has a length of 3.

Statement (1) tells us that Triangle A has sides whose lengths are consecutive integers. Given that one of the sides of Triangle A has a length of 3, this gives us the following possibilities: (1, 2, 3) OR (2, 3, 4) OR (3, 4, 5).

However, the first possibility is NOT a real triangle, since it does not meet the following condition, which is true for all triangles: The sum of the lengths of any two sides of a triangle must always be greater than the length of the third side. Since 1 + 2 is not greater than 3, it is impossible for a triangle to have side lengths of 1, 2 and 3.

Thus, Statement (1) leaves us with two possibilities. Either Triangle A has side lengths 2, 3, 4 and a perimeter of 9 OR Triangle A has side lengths 3, 4, 5 and a perimeter of 12. Since there are two possible answers, Statement (1) is not sufficient to answer the question.

Statement (2) tells us that Triangle A is NOT a right triangle. On its own, this is clearly not sufficient to answer the question, since there are many non-right triangles that can be constructed with a side of length 3.

Taking both statements together, we can determine the perimeter of Triangle A.

From Statement (1) we know that Triangle A must have side lengths of 2, 3, and 4 OR side lengths of 3, 4, and 5. Statement (2) tells us that Triangle A is not a right triangle; this eliminates the possibility that Triangle A has side lengths of 3, 4, and 5 since any triangle with these side lengths is a right triangle (this is one of the common Pythagorean triples). Thus, the only remaining possibility is that Triangle A has side lengths of 2, 3, and 4, which yields a perimeter of 9.

The correct answer is C: BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

I would like to correct my 4th answer from C to A

1) A

2) C

3) C

4) D
I will post the solution for the last one later . A bit confused over it .

Vijay wrote:
thakkarvijayrajiv wrote:
Sania has a circular garden in her backyard. She puts poles A,B and C on the circumference of her garden. Then she ties ropes between these poles. Is length of one of the ropes is equal to the diameter of her garden?

1. Slope of line joining pole A and B is 3/4 and slope of line joining poles B and C is -4/3
2. Length of line joining pole A and B is 12 and length of line joining B and C is 5



The area of a parallelogram is 100. What is the perimeter of the parallelogram ?
1) the _base_ of the parallelogram is 10
2) one of the angles of the parallelogram is 45 degree



Triangle A has one side of length x. If (x^8) ^ 1/2 = 81 , what is the perimeter of Triangle A?
1) Triangle A has sides whose lengths are consecutive integers
2) Triangle A is NOT a right triangle



In triangle ABC, AB has a length of 10 and D is the midpoint of AB. What is the length of line segment DC?

(1) Angle C= 90
(2) Angle B= 45



Answer For question 1:

Answer: A

From statement (1): Given that the slope of line AB is 3/4 and slope of line BC is -4/3. This implies that the product of slopes = -1. Hence AB perpendicular BC and B is a right angle. Thus AC is a diameter which implies ABC form a semi-circle.
Hence sufficient

From statement (2): Given that length of line AB is 12 and length of BC is 5. However this does not imply that ABC is a right angled triangle. We can draw number of different triangles with the same given two sides but with different third side.
Hence insufficient



Answer For question 2:

Answer: C

From (1) - For a parallelogram, Area = _base_*Height => Height = 10 - There are infinite ways to draw a parallelogram with 100 as area, as long as the height is 10 units.( parallelograms with varying slants from 1 to 179 degrees) -- insufficent

From (2) - one of the angles is 45 degrees - hence the opposite angle is 45 degrees too, and the two remaining angles wil be 135 degrees each. But this doesn't tell us the measure of the sides to determine the perimeter - insufficient

From(1) and (2) together

From (2) we know that there is only one of such parallelograms that has an angle 45 to the _base_.
_base_ = 10. One angle = 45 degrees

Answer For question 3:

Need to workout 3rd problem. Will post soon

Answer For question 4:

Answer: A

From statement (1): it is given that angle C = 90 degrees ...this implies that ABC is a right angle triangle with AB as the hypotenuse and DC as the median. We know that --- In all right triangles, the median on the hypotenuse is the half of the hypotenuse. Hence DC=5


Kudos Vijay ...Perfect answers ...and very well explained detailed answers !!

As explained by Vijay, correct answers are:
1) A
2) C
3) C
4) A

Keep up the good work !!