Number System - Questions & Discussions

MBA CAT 2022
2976
11's euler number is 10, E(11) = 10.
and E(9) = 6.

Read the post on this link and you will understand. :)

http://www.pagalguy.com/forum/quantitative-questions-and-answers/55747-cat-2010-concepts-fundas-tips-13.html#post2629058


Are these kinds of advanced theorums required for CAT?
2977
AimIIMAC Says
Are these kinds of advanced theorums required for CAT?


Euler's Theorem is required to solve different remainder CAT problems in less time. It's not mandatory to learn but using these formulas you can solve qstns easily.

Remember CAT is not about solving problems, time is also a big constraint
2978
AimIIMAC Says
Are these kinds of advanced theorums required for CAT?


Required? No.
Needed? Yes.

Answers your query I guess. 😃
2979

Two pipes A and B can fill a tank in 6hr and 9hr respectively. when working alone. A third pipe C can empty same tank in 8hr. Pipes operated such that A and C work for the first 2 hr, then again B & C for next 2hr, again a and c and so. operating in such manner, if 68 litre filled in 30 hr, find volume of the tank.



what will be the answer???
its explained by few ppl but m nt getting dat approach

2980
Two pipes A and B can fill a tank in 6hr and 9hr respectively. when working alone. A third pipe C can empty same tank in 8hr. Pipes operated such that A and C work for the first 2 hr, then again B & C for next 2hr, again a and c and so. operating in such manner, if 68 litre filled in 30 hr, find volume of the tank.



what will be the answer???
its explained by few ppl but m nt getting dat approach


See I'll explain the question in terms of efficiency.

Efficiency of A= 100%/6 hr= 16.66% (i.e it does 16.66% work in each hour taking 6 hours to complete the 100% work)

B= 100/9= 11.11

c= 100/8 = -12.5 (It's doing negative work)

now, when A and C work together total efficiency = 16.66-12.5 =4.16
and efficiency in 2 hours = 4.16*2= 8.32


when B and C work together = 11.11-12.5= -1.39
efficiency in 2 hours= -1.39*2= -2.78

work done in 15 hours = 8.32*7+ (-2.7 *7 + 4.16 =42.94= 43% approx

now 43% of work = 68 litres

so 100% = 144 liters approx.

This solution is to make your concepts clear about efficiency and work. With time you'll improve.. ATB
2981

plzz help...

A function f is defined as f(n) = 6^n + 8^n for all integers n. Find the remainder when f(83) is divided by 49.
1)7 2)42 3)35 4)14

2982
plzz help...

A function f is defined as f(n) = 6^n + 8^n for all integers n. Find the remainder when f(83) is divided by 49.
1)7 2)42 3)35 4)14

E 49 =42

now, 6^84 mod 49 = (6^42)^2 mod 49 =1

=> 6^83 * 6 mod 49 =1

let remainder of 6^83 mod 49 be k

=> k* 6 mod 49 =1

=> k=41; (hit and trial)

again, similarly

8^83 md 49 =p

=>p* 8 mod 49 =1

=>p=43

total remainder = (41+43 ) mod 49 =84 mod 49 =35
2983
plzz help...

A function f is defined as f(n) = 6^n + 8^n for all integers n. Find the remainder when f(83) is divided by 49.
1)7 2)42 3)35 4)14


My take 35

Approach:

f(83) = 6^83 + 8^83 = (7-1)^83 + (7+1)^83

Using binomial expansion,it can be written as

C(83,0)(7)^0*(-1)^83 + C(83,1)(7)^1*(-1)^82 + ... + C(83,82)*(7)^82*(-1)^1 + C(83,83)*(7)^83*(-1)^0

+ C(83,0)(7)^0*(1)^83 + C(83,1)(7)^1*(1)^82 + ... + C(83,82)*(7)^82*(1)^1 + C(83,83)*(7)^83*(1)^0

Then the remaining terms in the expression is 2*( C(83,1)(7)^1*(1)^82 + C(83,3)*(7)^3*(1)^80 + ... + C(83,83)*7^83*(1)^0)

so,except 2*C(83,1)(7)^1*(1)^82,all other terms are divided by 49

and 2*C(83,1)(7)^1*(1)^82 = 2*83*7 leaves remainder 35 when divided by 49
2984
plzz help...

A function f is defined as f(n) = 6^n + 8^n for all integers n. Find the remainder when f(83) is divided by 49.
1)7 2)42 3)35 4)14


Should be 35.

E(49) = 42.
So had it been f(84), then we would have got the remainder as 2.
=> 6*6^83 mod 49 = 1.
=> 6X m0d 49 = 1.
=> 6*41 mod 49 = 1.
Similarly, 8Y mod 49 = 1.
=> 8*43 mod 49 = 1.
Hence, we get (41 + 43) mod 49 = (-8 - 6) mod 49 = -14 or 35.
2985

Q. A positive whole number M less than 100 is represented in base 2 notation, base 3 notation, and base 5 notation. It is found that in all three cases the last digit is 1, while in exactly two out of the three cases the leading digit is 1. The M equals?

2986
DJ Harry Says
Q. A positive whole number M less than 100 is represented in base 2 notation, base 3 notation, and base 5 notation. It is found that in all three cases the last digit is 1, while in exactly two out of the three cases the leading digit is 1. The M equals?

Hi,
M in the form (30K +1)
So ans. 91satisfying all conditions...
Regards
Never Back Down
2987

1) A is a set of 7 consecutive two digit numbers, none of these numbers being a multiple of 10. Reversing the numbers in set A forms numbers in set B. The difference between the sum of the elements in Set A and those in set B is 63.The smallest number in set A can be ? A)64 B)13 C)31 D)75

2) How many single digit even natural number solutions are there for the equation A+B+C+D = 24 such that A+B > C+D

A)20 B)11 C)16 D)24

3) three positive real numbers x,y,z are such that x+y+Z = 1. which of the following inequalities best discribe the relation between XY YZ ZX.

A) xy+yz+zx > 1/3
B)xy+yz+zx C)xy+yz+zx D)xy+yz+zx

2988

1) C
2) B
3) B ( not sure about 3)

2989

thnx yaar but
now 43% of work = 68 litres

so 100% = 144 liters approx. so fr 100% its cmin more then 144 Litres....

hey n can u plz solve this question:-(6^83+8^83)/49 remainder will be???
i solved n gt the answer as 14 but my answer is wrong....can u plz solve

2990
1) C
2) B
3) B ( not sure about 3)





Hi Suresh , Thanks for your reply. May you please give the explanation here for above two. Thanks in advance.
2991

hi puys ,

pls help me out in this question :

2^1002 / 1003 what will b d remainder ???

please explain with solution !!!

2992
1) A is a set of 7 consecutive two digit numbers, none of these numbers being a multiple of 10. Reversing the numbers in set A forms numbers in set B. The difference between the sum of the elements in Set A and those in set B is 63.The smallest number in set A can be ? A)64 B)13 C)31 D)75

2) How many single digit even natural number solutions are there for the equation A+B+C+D = 24 such that A+B > C+D

A)20 B)11 C)16 D)24

3) three positive real numbers x,y,z are such that x+y+Z = 1. which of the following inequalities best discribe the relation between XY YZ ZX.

A) xy+yz+zx > 1/3
B)xy+yz+zx C)xy+yz+zx D)xy+yz+zx


1) C (go by options)
2) I am not sure about that !!!!
3) C (go by options)
2993
hi puys ,

pls help me out in this question :

2^1002 / 1003 what will b d remainder ???

please explain with solution !!!


1003 = 59 * 17

so 2^58 leaves remainder 1 when divided by 59 and 2^16 leaves remainder 1 when divided by 17 .. (by fermat theorem).. check definition of fermat theorem . you will understand easily

1002 mod 58 = 16 and 1002 mod 16 = 10

2^(58k + 16) mod 59 = 1* (2^8 )^2 mod 59 = 1*400 mod 59 = -13

2^(16k + 10) mod 17 = 1* (2^4)^2 * 2^2 mod 17 = 1*1*4 mod 17 = 4

so final remainder will be of form 59a - 13 = 17b + 4

now you can choose the answer from the options
2994

can anyone solve d following question:-
(6^83+8^83)/49 remainder will be???
i solved n gt the answer as 14 but my answer is wrong....can u plz solve

2995
can anyone solve d following question:-
(6^83+8^83)/49 remainder will be???
i solved n gt the answer as 14 but my answer is wrong....can u plz solve

Hi,
( (7-1)^83 + (7+1)^83 )/49
On Exp. Numerator 1s are getting cancelled so are all the powers of 7 >=2, only 7^1 is left so 7 + 7 = 14,
Had there been 7 instead of 49 ans. would have been 0 ,
Had there been 7^3 in denominator ans would have been 2(7 + 49) coz all the powers of 7 >= 3 would have been cancelled..
____________________________________________________________

Regards,
Never Back Down