Official Quant thread for CAT 2013

MBA CAT 2024
11721
@sujamait said:
Let ABCD be a cyclic quadrilateral such that one of its diagonals is a diameter of the circle. If AB = 72cm,find the measure of the diagonal which is not the diameter of the circle.I. Radius of the circle is 45 cm.II. Side opposite to AB is of length 45 rt 2 cm.
Hi can u pls explain this sum. i am gettin the ANS as E. side opp to AB is DC so we have DC=45 root 2 .. and in the end we dono the value of one side and the diagonal.. so i marked E . pls throw some light on this..
11722
@GaHaVeBa

Since one of the diagonals is the diameter, visualize the entire quadrilateral as 2 distinct right angle triangles joined together. Now, with statement 1 alone get the diameter and hence the hypotenuse and the side of one of the right angle triangles. not suffficient
2.with statement 2alone with just get one of the sides of both the right angle triangles, not sufficient,

3. using both the statements together we get all the sides of both the triangles. Now we can use Ptolemy's theorem and which says Ab* CD + AD* BC = diagonal1*diagonal2. and since we know one of the diagonals, the second can be found.


so answer is "we need both statements to answer"
11723
A person buys some apples and mangoes from the market at a rate such that a mango is two times costlier than an apple and he sells them such that a mango is thrice the price of an apple. By selling the apple at twice its cost price, he makes the total of 150% profit. Find the proportion of mangoes to the apples.
11724
@jain4444 said:
A person buys some apples and mangoes from the market at a rate such that a mango is two times costlier than an apple and he sells them such that a mango is thrice the price of an apple. By selling the apple at twice its cost price, he makes the total of 150% profit. Find the proportion of mangoes to the apples.
1/2
11725

four digits of the number 29138576 are omitted so that the result is as large as possible.The largest omitted digit is: 5/6/7/8/9??

Question is saying the number is after omission or to be omitted??

11726
@jain4444 said:
A person buys some apples and mangoes from the market at a rate such that a mango is two times costlier than an apple and he sells them such that a mango is thrice the price of an apple. By selling the apple at twice its cost price, he makes the total of 150% profit. Find the proportion of mangoes to the apples.
1:2
11727
@CBZ123 said:
four digits of the number 29138576 are omitted so that the result is as large as possible.The largest omitted digit is: 5/6/7/8/9??Question is saying the number is after omission or to be omitted??
The number after omission of the digits must be as large as possible
11728
@CBZ123 said:
four digits of the number 29138576 are omitted so that the result is as large as possible.The largest omitted digit is: 5/6/7/8/9??Question is saying the number is after omission or to be omitted??
omit 2,1,3 and 5. so remaining 9876 will be largest possible. and largest omitted digit is 5
11729
the perimeter of a traingular field is 80m.If two of its sides are 16m and 30m .Find the approximate length of the altitude on to the longest side.
11730
@CBZ123 said:
@tiwarishiva@soumitrabengeri or is it 2(8)9138576xxx and after omission of 8,x,x,x i hv got the largest possible number as 29138576?? getting confused in language
It is the same as @tiwarishiva said..omit 2,3,1,5 and the largest number you will get is 9876
11731
@CBZ123 said:
@tiwarishiva@soumitrabengeri or is it 2(8)9138576xxx and after omission of 8,x,x,x i hv got the largest possible number as 29138576?? getting confused in language
Don't get confused out of given 8 digits u need to omit 4 digits such that remaining 4 digit form largest possible number. so u will be picking out four least valued digits out of which 5 is largest.
11732

@nole said:
the perimeter of a traingular field is 80m.If two of its sides are 16m and 30m .Find the approximate length of the altitude on to the longest side.

240/17?
11733
@CBZ123 yeah,can u write the solution please.
11734
@nole three sides 16,30,34 make a right angled triangle.Hence 1/2(16*30)=1/2(34*X) area ..X=240/17
11735
@soumitrabengeri @CBZ123 so to solve questions like these we will have to remember triplets(that form right angled triangle)? Also is there any other way to solve it,if we don't know the triplets?One more doubt is if i drop a altitude from a vertex to other side, will it divide any triangle into two right angled traingles ?
11736
@nole said:
the perimeter of a traingular field is 80m.If two of its sides are 16m and 30m .Find the approximate length of the altitude on to the longest side.
It is a right angled triangle..16,30,34
Equate the areas :
1/2*16*30 = 1/2*34*altitude

altitude = 240/17
11737
@nole said:
@soumitrabengeri@CBZ123so to solve questions like these we will have to remember triplets(that form right angled triangle)? Also is there any other way to solve it,if we don't know the triplets?One more doubt is if i drop a altitude from a vertex to other side, will it divide any triangle into two right angled traingles ?
I don't know of any other way to solve these questions..i tried for a pythagoras triplet since only the sides values were known
You don't have to remember the triplets. Just check if it is a triplet while solving
11738
@soumitrabengeri also one more doubt is we took two different sides as base first 16 then 34 as base.I wanted to know the meaning of base.anything on which perpendicular line is dropped is base ?
11739
@nole said:
@soumitrabengeri also one more doubt is we took two different sides as base first 16 then 34 as base.I wanted to know the meaning of base.anything on which perpendicular line is dropped is base ?
Yes..in this case..the sides 16 and 30 are perpendicular to each other..so 1/2*base*height
Any of the two sides- 16 or 30 can be the base
And then since we dropped a perpendicular on the side whose value was 34..again the same formula..1/2*base*height
11740
@soumitrabengeri nice explaination man...great job..thanks