Ultimate Quant Marathon Blog For IIM CAT

The perimeter of a right triangle is 60. The height to the hypotenuse is 12 what is the area?
(A) 75 (B) 144 (C) 150 (D) 300 (E) none of these

Find the area of right angle triangle whose inradius is 4 and circumradius
is 10?
a) 28                   b) 56                    c) 96                     d) 192                   e) none of these

On a circle 26 equidistant points are marked. these points are joined to form a triangles. Of the triangles formed, how many of them will have their circumcenter on one of their sides.?

A) 318 B) 312 C) 288 d) 624 e) None of these

In a triangle ABC, perpendiculars BD and CE are drawn to the sides AC and AB. Points  D and E are joined, then the ratio of the area of ADE to the area of ABC is:

1) Cos²A 2) Sin²A 3) Cot²A 4) Tan²A  5) None of these

Two triangles are considered distinct if they cannot be superimposed on each other by rotation. How many distinct triangles, with integer sides,  exist, such that there perimeter is 30?

A) 19    B) 57    C) 114    d) 38    E) 36

Find the maximum area that can be bound by four line segments of length 1, 2, 3 and 4. (you are not allowed to break a segment, you may join two )

1) 6√2

2) 2√6

3) 4√6

4) 3√2

5) None of these

Find the largest value for for pairs of real numbers which satisfy

Four Equilateral triangles are formed taking one of their sides as the sides of the square, the third vertices of equilateral triangles being inside the square. The ratio of the area of fig formed by the third vertices of the triangles to that of the square is nearly

A golden rectangle is a rectangle in which the ratio of the width to length is the same as that of the length to the sum of the length and width. Which of the following is also true about a golden rectangle?
I. The ratio of the length to width is the same as the ratio of the width to the difference of the length and width.
II. The product of the length and width is equal to the product of the sum of the two sides and the difference of the two sides.
III. The length has to be greater than two times the width.

(1) Only I and II (2) Only II and III
(3) Only I and III (4) All the three statements
(5) None of these

New Problem: A fresh one, I created it this morning, trying to find the most adequate data!

In a triangle ABC, altitude AD=6 is drawn to cut BC at D. From D, altitude DE=3 is drawn to cut AC at E. If it is know that AB =12. Find the ratio of the area of ABC to area of DEC?

A) 4:1 B) 16:1 C) 25:1 D) 5:1 E) Cannot be determined