HURDLE-02 : PYTHAGORAS THEOREM
(Solve this Hurdle by 27th Jan.)
In any given exam there are about 1 or 2 questions based on pythagoras theorem.
Wouldn't it be nice that you remember some of the Pythagoras triplets thus saving up to 30 seconds in each question.
This saved time may be used to attempt other questions.
Remember one more right question may make a lot of difference in UrPERCENTILE score.
The unique set of pythagoras triplets with the Hypotenuse less than 100 or one of the side less than 20 are as follows :
(3,4,5), (5, 12, 13), (8, 15, 17), (7, 24, 25), (20, 21, 29), (12,35,37), (9,40, 41), (28, 45, 53), (11, 60, 61), (33, 56, 65), (16, 63, 65), (48, 55, 73), (36, 77, 85), (13, 84, 85), (39, 80, 89), (65, 72, 97), (UrPercentile.com) (15,112,113), (17,144,145), (19,180,181) and (20,99,101)
If you multiply the digits of the above mentioned sets by any constant you will again get a pythagoras triplet .
Example : Take the set (3,4,5).
Multiply it by 2 you get (6,8,10) which is also a pythagoras triplet.
Multiply it by 3 you get ( 9,12,15) which is also a pythagoras triplet. (UrPercentile.com)
Multiply it by 4 you get (12,16,20) which is also a pythagoras triplet.
You may multiply by any constant you will get a pythagoras triplet
Take another example (5,12,13) Multiply it by 5,6 and 7 and check if you get a pythagoras triplet.
TIPS FOR SMART GUESSING :
You will notice that in any case, whether it is a unique triplet or it is a derived triplet (derived by multiplying a constant to a unique triplet), all the three numbers cannot be odd.
In case of unique triplet , the hypotenuse is always odd and one of the remaining side is odd the other one is even.
Below are the first few unique triplets with first number as Odd.
3 4 5
5 12 13
7 24 25
9 40 41
11 60 61
You will notice following trend for unique triplets with first side as odd.
Hypotenuse = (Sq(first side) +1) / 2
Other side = Hypotenuse -1
Example : First side = 3 ,
so hypotenuse = (3*3+1)/2= 5 and other side = 5-1=4
Example 2: First side = 11
so hypotenuse = (9*9+1)/2= 41 and other side = 41-1=40
Please note that the above is not true for a derived triplet for example 9,12 and 15, which has been obtained by multiplying 3 to the triplet of 3,4,5. You may check for other derived triplets.
Below are the first few unique triplets with first number as Even .
4 3 5
8 15 17
12 35 37
16 63 65
20 99 101
You will notice following trend for unique triplets with first side as Even.
Hypotenuse = Sq( first side/ 2)+1
Other side = Hypotenuse-2
Example 1. First side =8
So hypotenuse = sq(8/2) +1= 17
Other side = 17-2=15
Example 2. First side = 16
So hypotenuse = Sq(16/2) +1 =65
Other side = 65-2= 63
SOLVE THE FOLLOWING:
Q1. There is a park with corners B,G,F,A,E,D,C,I and H such that (ABGF),(ACDE) and (CBHI) are squares of different sizes such that the area of the bigger square is equal to total area of the two smaller squares. (UrPercentile.com) The perimeter of the park is 72 units. What is the area of the smallest square ?
A) Cannot be determined. B) Figure not possible C) 36 D) 25 E) 16
Q2. Due to heavy rains and wind a electric pole leaned against a wall of the nearby house. The tops most portion of the pole was 5 m above the ground when it leaned against the wall. The pole was dragged from the bottom, and when it was moved 1 m away from the wall, the top of the pole fell down to the ground and touched the bottom of the wall. How far was the pole originally from the wall?
A) 12 m B) 5 m C) 13 m D) 17m E) None of these
Q3. A pole of 36 m length is divided into 3 unequal parts and the three are welded to each other to form a right angle triangle. The length of one of the part is equal to the half of the sum of the remaining two . What is the length of the longest part ?
A) 12 m B) 21 m C) 12 m D) 15m E) None of these
Q4. A man puts a rope along the sides of a rectangular park . He needs 46 m of rope to cover all the 4 sides. When he puts the rope along the two diagonals of the park he needs 12 m less rope. What is the area of the park.
A) 120 Sq m B) 60 Sq m C) 136 Sq m D) 240 Sqm E) None ofthese
Read the article below and answer the question 5
mentioned after the passage :
"STOCK price volatility, manipulation and corporate mismanagement are the biggest worries for retail investors, says a study.
According to a study on "India Household Investors Survey" by Society for Capital Market Research and Development for Ministry of Company Affairs, "These problems get manifested in the erratic behaviour of the secondary market. Such market behaviour has the effect of discouraging or even driving away the genuine investors from the market."
The study was based on a sample of 5,900 investors spread over 90 cities and towns in 24 States.
The concern about price volatility and manipulation rose suddenly due to the wild gyrations of the Indian share index on May 17, 2004. Details of the study say that price volatility and manipulation taken together are the cause of worry for as many as 50 per cent of the respondents.
On corporate governance, around 50 per cent of the respondents had a negative opinion on company management and a little over 30 per cent had a positive opinion while around 20 per cent had no opinion.
The finding of the study says that majority of retail investors do not regard mutual fund equity schemes as a superior investment alternative to direct holding of equity shares. "The percentage of households who owned equity shares directly is more than 2.5 times the percentage of those who owned any mutual fund schemes," it said.
The boom since 2003 has also made investors more cautious and they are net sellers than buyers, the study pointed out.
"Having become wiser from the mistakes of the past, the retail investors have become less gullible," the study said.
"A rise in the average price-earning ratio to just 17-18 based on the BSE Sensex and the NSE Nifty companies, begins to ring alarm bell for investors and the market authorities, whereas average P/E ratio of 30-40 in early 1990s was simplistically accepted because not many market participants understood the ratio"." - Source: Hindu Business Line
Q5. What can be said about the current retail investor ?
A) They prefer to invest in mutual fund equity schemes over the
B) They are skeptical.
C) A unnatural rise in price-earning ratio makes them
D) Both B and C
E) All, A, B and C
Jejune adj : lacking interest, barren, lacking maturity or sophistication, lacking or not providing proper nourishment
Levity n : Lack of seriousness especially during a serious occasion.
Nonchalance n : Indifference, lack of interest , appearing calm.
Paucity n. Lack of something, inadequate, scarcity
Stupor n : lack of awareness, lack of alertness due to lack of sleep, shock,use of alcohol or drugs
Feckless n. Lacking purpose or lacking interest
Impiety n. Lack of respect to religion or lack of respect ordutifulness