Combination of Sequence | B.Stat Objective | TOMATO 79
Try this TOMATO problem from I.S.I. B.Stat Entrance Objective Problem based on Combination of Sequence.
Logic and combination of sequence (B.Stat Objective)
The two sequence of numbers {1,4,16,64,.....} and {3,12,48,192,.....} are mixed as follows {1,3,4,12,16,48,64,192,....}. One of the numbers in the mixed series is 1048576. Then the number immediately preceeding it is
262144
786432
814572
786516
Key Concepts
Logic
Sequence
Integers
Check the Answer
Answer: 786432.
B.Stat Objective Question 79
Challenges and Thrills of Pre-College Mathematics by University Press
Try with Hints
The first series is of form \(4^{r}\) for \(r \geq 0\) \(r \in\) set of natural numbers the second series is of form \(3 \times 4^{r}\) for \(r \geq 0\) \(r \in\) set of natural numbers and the third series is of \(4^{r}\),\(3 \times 4^{r}\) in alternate element form for \(r \geq 0\) \(r \in\) set of natural numbers
given that 1048576=\(4^{r}\)=\(4^{10}\)
then preceeding term \(3 \times 4^{9}\)=(3)(262144)=786432.
Logic and Group | TOMATO B.Stat Objective Question
Try this problem from I.S.I. B.Stat Entrance Objective Problem based on Logic and Group.
Logic and Group ( B.Stat Objective Question )
Four passengers in a compartment of the Delhi-Howrah Rajdhani Express discover that they form an interesting group. Two are lawyers and two are doctors. Two of them speak Bengali and the other two Hindi and no two of the same profession speak the same language . They also discover that two of them are Christians and two Muslims, no two of the same religion are of the same profession and no two of the same religion speak the same language. The Hindi speaking doctor is a christian.Then which one holds
BLM
CLB
BDC
BDH
Key Concepts
number Series
Logic
Integers
Check the Answer
Answer: CLB
B.Stat Objective Problem
Challenges and Thrills of Pre-College Mathematics by University Press
Try with Hints
one doctor HDC then other doctors by given conditions is BDM
then other two LM and LC and for DMB then LM is H that is HLM
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 2008 based on Logic and Speed.
Logic and Speed - AIME I, 2008
Ed and Sue bike at equal and constant rates and they swim at equal and constant rates. The same way they jog at equal and constant rates. ed covers 74 kms after biking for 2 hrs, jogging for 3 hrs and swimming for 4 hrs while sue covers 91 kms after jogging for 2 hrs swimming for 3 hrs and biking for 4 hrs. Their biking jogging and swimming rates are whole numbers of km/hr, find the sum of the squares of Ed's biking jogging and swimming rates.
is 107
is 314
is 840
cannot be determined from the given information
Key Concepts
Logic
Speed
Integers
Check the Answer
Answer: is 314.
AIME I, 2008, Question 3
Elementary Number Theory by David Burton
Try with Hints
Let a,b, c be biking jogging and swimming rates then 2a+3b+4c=74 first eqn and 4a+2b+3c=91 second eqn subtracting second from first eqn gives 2a-b-c=17 third eqn
third eqn multiplied by 3 + first eqn gives 8a+c=125 gives \(a \leq 15\) third eqn multiplied by 4 +first eqn gives 10a-b=142 gives \(a \gt 14\)
then a=15 and b=8, c=5 and \(a^{2} +b^{2} + c^{2}\)=225+64+25=314.
P,Q, R are statements such that if P is true then at least one of the following is correct (i) Q is true (ii) R is not true then
if both Q and R are true then P is true
if both P and Q are true then R is true
if both P and R are true then Q is true
none of these
Key Concepts
Logic
Relations
True-False
Check the Answer
Answer: if both P and Q are true then R is true
B.Stat Objective Question 67
Challenges and Thrills of Pre-College Mathematics by University Press
Try with Hints
P true gives (i) holds and (ii) do not hold that is Q true and R true
P true gives (i) do not hold and (ii) holds that is Q non true and R non true
then from given conditions when P true and first condition holds that is Q true then second condition do not hold that is R is true that is if both P and Q are true then R is true.
Logic and True-False | B.Stat Objective | TOMATO 65
Try this TOMATO problem from I.S.I. B.Stat Entrance Objective Problem based on Logic and True-False.
Logic and True-False (B.Stat Objective problems)
Let P,Q,R,S be four statements such that if P is true then Q is true, if Q is true then R is true and if S is true then at least one of Q and R is false then it follows that
if S is false then both Q and R are true
if at least one of Q and R is true then S is false
if P is true then S is false
if Q is true then S is true
Key Concepts
Logic
Relations
True-False
Check the Answer
Answer: if at least one of Q and R is true then S is false
B.Stat Objective Question 65
Challenges and Thrills of Pre-College Mathematics by University Press
Try with Hints
P true implies Q true and Q true imples R true
S true implies Q false with R false
then R true implies Q true implies P true with S false then if at least one of Q and R is true then S is false.
Relations and Numbers | B.Stat Objective | TOMATO 63
Try this TOMATO problem from I.S.I. B.Stat Objective based on Relations and Numbers.
Relations and Numbers (B.Stat Objective problems)
We consider the relation , "a person x shakes hand with a person y".Obviously if x shakes hand with y, then y shakes hand with x. In a gathering of 99 persons , one of the following statements is always true, considering 0 to be an even number, find which one is it.
there is at least one person who shakes hand with an odd number of persons
there is at least one person who shakes hand with an even number of persons
there are even number of persons who shake hand exactly with an even number of persons
none of these
Key Concepts
Logic
Relations
Numbers
Check the Answer
Answer: there is at least one person who shakes hand with an even number of persons
B.Stat Objective Question 63
Challenges and Thrills of Pre-College Mathematics by University Press
Try with Hints
Let R be handshakes among 99 persons holds
first person may handshake with at most 98(even) other persons, for second person similar arguments hold and this holds with similar arguments for all persons
then there exists at least one person who shakes hand with an even number of persons.
Box and ball Probability | B.Stat Objective TOMATO Problem 59
Try this problem from I.S.I. B.Stat TOMATO Objective Problem based on Box and ball Probability.
Box and ball Probability ( B.Stat Objective Problem )
A box contains 100 balls of different colours 28 red 17 blue 21 green 10 white 12 yellow 12 black. The smallest number n such that any n balls drawn from the box will contain at least 15 balls of the same colour is
8
77
11
10
Key Concepts
number Series
Logic
Integers
Check the Answer
Answer: 77
B.Stat Objective Problem
Challenges and Thrills of Pre-College Mathematics by University Press
Try with Hints
28 -15 gives 13 and 17-15 gives 2 and 21 -15 gives 6 rest are less than 15
