Official Quant thread for CAT 2013

Find the 100th digit after the decimal point of
(root5 +2) ^500

OPTIONS

1) 5
2) 1
3) 9
4) 0



Understanding the nature of color, however, has proved ……………. task, despite the numerous fields that ……………… the project. Even knowing how to start can be difficult. Is color to be understood as an ……………….. part of reality, a property of objects with a …………….. similar to shape and size? Or is color more like pain, to be found only in …………….. and so somehow subjective?
OPTIONS

1) a daunting, form part of, objective, dimension, experience
2) an impossible, form part of, integral, dimension, suffering
3) a daunting, contribute to, objective, status, experience
4) an impossible, contribute to, integral, status, suffering

Prince Siddhartha enjoyed all types of luxuries and sensual pleasures during his youth. ………..….. with this type of life, he had a crisis when he realized that everything was …………….. and that his existence was subject to old age, sickness, and death. After seeing the ……………. joy of a monk and out of compassion for all living beings, he ………….. his promising future as prince in order to start a long quest for a higher purpose, which entails the ……………….. of old age, sickness and death.
OPTIONS

1) Dissatisfied, meaningless, extreme, embraced, culmination
2) Unsatisfied, ephemeral, extreme, embraced, end
3) Dissatisfied, empty, tranquil, renounced, cessation
4) Unsatisfied, ephemeral, serene, renounced, cessation

@rkshtsurana said:
[x]^3 + {x}^2 = -7.91by options x = -2.03{x} = 0.03[x] = -2so -8 + 0.9x = -7.9so option A
but [-2.03] = -3 and not -2
coreect me if i am wrong..
@padmanabhan1989 said:
I didnt get this step buddy " for -ve values [-4.23] = -3 (note the diff)" why -3?
i made the correction bro...sorry for the confusion..it should be -5...evryone do check n verify for evryone's benefit

@pankaj1988 said:
Sun Life Insurance Company issues standard, preferred, and ultra-preferred policies. Among the company €™s policy holders of a certain age, 50% are standard with a probability of 0.01 of dying in the next year, 30% are preferred with a probability of 0.008 of dying in the next year, and 20% are ultra-preferred with a probability of 0.007 of dying in the next year. If a policy holder of that age dies in the next year, what is the probability of the deceased being a preferred policy holder?A. 0.1591 B. 0.2727C. 0.375 D. None of theseSoln also plz
0.2727?
30*.008/((50*.01)+(30*.008)+(20*.007)
On being asked how many ripe mangoes his tree had, a farmer excitedly told his wife, “Had there been 10 more, I would have been able to pack them in two boxes, each containing a perfect square number of mangoes. Oh, and one of them would also have a perfect cube number of mangoes and the other a perfect fourth power!” He then added wistfully, “But now I will just pack them in five boxes, each containing an equal number of mangoes, and the number of mangoes in each box is a perfect cube.” The wife only knew that the number of ripe mangoes was a three-digit number.

What is the sum of digits of the number of ripe mangoes on the tree?
OPTIONS

1) 13
2) 5
3) 9
4) Cannot be determined
@surajmenonv said:
i made the correction bro...sorry for the confusion..it should be -5...evryone do check n verify for evryone's benefit
Boss [-4.23] should be -4 right. why it is -5? Correct me If I am wrong!
@padmanabhan1989 said:
Boss [-4.23] should be -4 right. why it is -5? Correct me If I am wrong!
its not...the definition of greatest integer function says its the next lowest integer...-5 is lower than -4yy whereas -4 is greater than -4.yy
hope it helps :)
@padmanabhan1989 said:
[x] denotes the greatest integer value just below x and {x} its fractional value. The sum of [x]^3 and {x}^2 is -7.91. Find x.a) -2.03 b) -1.97 c) -2.97 d) -1.7 I can't understand the Question also. Please explain the Qestion and answer.
-1.7 is the answer
[-1.7] = -2
{-.7} =1-.7 =.3
integral part -2
fractional part .3
@krum said:
greatest integer function - [4.2]=4, [5.0]=5, [-2.3]=-2 hope u get the picture{x}, should be clear[-2.03]^3+{-2.03}^2=>-2^3+.03^2=>-8+.0009=>-7.9991only this one comes closest, if i'm not making any mistake@padmanabhan1989 above is wrong, [-2.3]=-3are u sure about the value -7.91?
An intelligence agency wants to develop a new code containing 1050 distinct critical words for its sleuths. It intends to use just three symbols - α, β and γ – for each letter in the code. If all the words are designed to have exactly p number of characters, what is the minimum required value of p?
OPTIONS

1) 6
2) 7
3) 8
4) This code is not possible
@surajmenonv said:
its not...the definition of greatest integer function says its the next lowest integer...-5 is lower than -4yy whereas -4 is greater than -4.yyhope it helps
Got it boss.. Thanks....
@sujamait said:
On being asked how many ripe mangoes his tree had, a farmer excitedly told his wife, “Had there been 10 more, I would have been able to pack them in two boxes, each containing a perfect square number of mangoes. Oh, and one of them would also have a perfect cube number of mangoes and the other a perfect fourth power!” He then added wistfully, “But now I will just pack them in five boxes, each containing an equal number of mangoes, and the number of mangoes in each box is a perfect cube.” The wife only knew that the number of ripe mangoes was a three-digit number.What is the sum of digits of the number of ripe mangoes on the tree?OPTIONS1) 13 2) 5 3) 9 4) Cannot be determined
Is it 9?
@sujamait said:
Find the 100th digit after the decimal point of (root5 +2) ^500OPTIONS1) 5 2) 1 3) 9 4) 0 Understanding the nature of color, however, has proved ……………. task, despite the numerous fields that ……………… the project. Even knowing how to start can be difficult. Is color to be understood as an ……………….. part of reality, a property of objects with a …………….. similar to shape and size? Or is color more like pain, to be found only in …………….. and so somehow subjective?OPTIONS1) a daunting, form part of, objective, dimension, experience2) an impossible, form part of, integral, dimension, suffering3) a daunting, contribute to, objective, status, experience4) an impossible, contribute to, integral, status, sufferingPrince Siddhartha enjoyed all types of luxuries and sensual pleasures during his youth. ………..….. with this type of life, he had a crisis when he realized that everything was …………….. and that his existence was subject to old age, sickness, and death. After seeing the ……………. joy of a monk and out of compassion for all living beings, he ………….. his promising future as prince in order to start a long quest for a higher purpose, which entails the ……………….. of old age, sickness and death.OPTIONS1) Dissatisfied, meaningless, extreme, embraced, culmination 2) Unsatisfied, ephemeral, extreme, embraced, end 3) Dissatisfied, empty, tranquil, renounced, cessation 4) Unsatisfied, ephemeral, serene, renounced, cessation
i think we shouldnt start posting verbal n di problems here...it will lead to a lot of confusion....wont it be better and more comprehensive if we just stick to quant problems in official quant thread buddy??
just my opinion ...
@sujamait said:
On being asked how many ripe mangoes his tree had, a farmer excitedly told his wife, “Had there been 10 more, I would have been able to pack them in two boxes, each containing a perfect square number of mangoes. Oh, and one of them would also have a perfect cube number of mangoes and the other a perfect fourth power!” He then added wistfully, “But now I will just pack them in five boxes, each containing an equal number of mangoes, and the number of mangoes in each box is a perfect cube.” The wife only knew that the number of ripe mangoes was a three-digit number.What is the sum of digits of the number of ripe mangoes on the tree?OPTIONS1) 13 2) 5 3) 9 4) Cannot be determined
number of ripe mangoes 135 aa rhe so 9 hi hoga
@sujamait said:
Find the 100th digit after the decimal point of (root5 +2) ^500OPTIONS1) 5 2) 1 3) 9 4) 0
root 5 = 2.23
so 4.43^500
since last digit is 3
3^4n = 1??
i know this is not the right method
@chandrakant.k said:
root 5 = 2.23so 4.43^500 since last digit is 3 3^4n = 1??i know this is not the right method
buddy root 5 is non terminating non repeating......thats d whole problem :P
@sujamait said:
An intelligence agency wants to develop a new code containing 1050 distinct critical words for its sleuths. It intends to use just three symbols - α, β and γ – for each letter in the code. If all the words are designed to have exactly p number of characters, what is the minimum required value of p?OPTIONS1) 6 2) 7 3) 8 4) This code is not possible
code impossible
@sujamait said:
On being asked how many ripe mangoes his tree had, a farmer excitedly told his wife, “Had there been 10 more, I would have been able to pack them in two boxes, each containing a perfect square number of mangoes. Oh, and one of them would also have a perfect cube number of mangoes and the other a perfect fourth power!” He then added wistfully, “But now I will just pack them in five boxes, each containing an equal number of mangoes, and the number of mangoes in each box is a perfect cube.” The wife only knew that the number of ripe mangoes was a three-digit number.What is the sum of digits of the number of ripe mangoes on the tree?OPTIONS1) 13 2) 5 3) 9 4) Cannot be determined
since the number of ripe mangoes is a 3 digit number
the maximum number = 200
the nearest cube = 125 in each box
so total 625 the first statement doesn't hold true here.
so check for 64
total mangoes = 64*5 = 320 other condition not satisifed
take 27
total mangoes == 27*5 = 135
now had there been 10 more total = 145
which can be divided as 64+81
so 135 is the number of mangoes
sum of digit = 9??

@surajmenonv : Yeah.. i think this problem should be solved by using log. may be @sujamait sir can guide us..

ALL : Please post the solution while posting your answer. There will be different ways of solving a particular problem. And different people will have different approach. so it would to learn how others think of solution and it will be a good experience 😃 😃
@catter2011 said:
code impossible


@sujamait
An intelligence agency wants to develop a new code containing 1050 distinct critical words for its sleuths. It intends to use just three symbols - α, β and γ – for each letter in the code. If all the words are designed to have exactly p number of characters, what is the minimum required value of p?
Bhai (3)^n>1050
min value of n=7
so option 2
@Torque024 said:
@sujamaitAn intelligence agency wants to develop a new code containing 1050 distinct critical words for its sleuths. It intends to use just three symbols - α, c and γ – for each letter in the code. If all the words are designed to have exactly p number of characters, what is the minimum required value of p?Bhai (3)^n>1050min value of n=7so option 2
3^n kasie ayaa ?

aint it p!/ α! β! γ! = 1050, given γ+ β+α = p
@sujamait said:
An intelligence agency wants to develop a new code containing 1050 distinct critical words for its sleuths. It intends to use just three symbols - α, β and γ – for each letter in the code. If all the words are designed to have exactly p number of characters, what is the minimum required value of p?OPTIONS1) 6 2) 7 3) 8 4) This code is not possible
is it 7?
my heart says not possible though :P