Official Quant thread for CAT 2013

MBA CAT 2024
21026
@mailtoankit said:
haan bhai....meine bhi pehele kiya hua tha!!
arey yaar..all old PGs here..sab ne liye hua hi hai..
21027


2222 mod 7=3
5555 mod 7 = 4
so prob reduces to 3^5555 +4^2222 remainder 7

now this can b written as 243^1111 + 16^1111 remainder 7

now use direct formula tht x^n + y^n is divisible by x+y if n is odd

given expression is divisible by 243+16=259
so it is also divisible by 7
and hence remainder=0
21028
@saurav205 said:
N is a 1001 digit number consisting of 1001 sevens. What is the remainder when N is divided by 1001?Options:7,777,700, 707
OA : 700
21029
@saurav205 said:
N is a 1001 digit number consisting of 1001 sevens. What is the remainder when N is divided by 1001?Options:7,777,700, 707
should be 700...
1001 = 13*7*11
7k
1001%6 = 5
77777%13 = 11
13p+11
11z+7

so remainder -> 7k=13p+11=11z+7
or 77x+7 = 13p+11
or 700...
21030
@saurav205 said:
N is a 1001 digit number consisting of 1001 sevens. What is the remainder when N is divided by 1001?Options:7,777,700, 707
should be 700...
1001 = 13*7*11
7k
1001%6 = 5
77777%13 = 11
13p+11
11z+7
so remainder -> 7k=13p+11=11z+7
or 77x+7 = 13p+11
or 700...
21031

Find all 2 digit numbers such that the sum of the digits consisting the number is not less than 7; the sum of the squares of the digits is not greater than 30; the number consisting of the same digits written in reverse order is not larger than half the given number.
1) 52
2) 51
3) 49
4) 53

Plz give answer along with explanation.

21032
@saurav205 said:
N is a 1001 digit number consisting of 1001 sevens. What is the remainder when N is divided by 1001?Options:7,777,700, 707
should be 700...
1001 = 13*7*11
7k
1001%6 = 5
77777%13 = 11
13p+11
11z+7

so remainder -> 7k=13p+11=11z+7
or 77x+7 = 13p+11
or 700...
21033
@Exodia said:
Find all 2 digit numbers such that the sum of the digits consisting the number is not less than 7; the sum of the squares of the digits is not greater than 30; the number consisting of the same digits written in reverse order is not larger than half the given number.1) 522) 513) 494) 53Plz give answer along with explanation.
52
21034
@viewpt
@viewpt said:
52
Could you explain a bit.
21035
@saurav205 said:
N is a 1001 digit number consisting of 1001 sevens. What is the remainder when N is divided by 1001?Options:7,777,700, 707
700

777777 mod 1001 = 0
so 77777 will be left
77777 mod 1001 = 700


21036
@Exodia said:
Find all 2 digit numbers such that the sum of the digits consisting the number is not less than 7; the sum of the squares of the digits is not greater than 30; the number consisting of the same digits written in reverse order is not larger than half the given number.1) 522) 513) 494) 53Plz give answer along with explanation.
the numbers can be 43, 34, 52, 25

but 52 is the only no satisfying the last condition

so 1) 52
21037
@joyjitpal said:
the numbers can be 43, 34, 52, 25but 52 is the only no satisfying the last conditionso 1) 52
Oop sorry seeing your soln. now I realized that the question had asked the number and not the number of numbers.
21038
@joyjitpal said:
the numbers can be 43, 34, 52, 25but 52 is the only no satisfying the last conditionso 1) 52
Bhai, I think 43 does not satisfy the last condition.
reverse of 43 is 34. this should not be greater than half of 43/2=21.5??
21039

What is the remainder when 128^1000 is divided by 153?
1) 103
2) 145
3) 118
4) 52

21040
@Exodia said:
What is the remainder when 128^1000 is divided by 153?1) 1032) 1453) 1184) 52
52
By CRT

17x+1=9y+7
21041
@Exodia said:
What is the remainder when 128^1000 is divided by 153?1) 1032) 1453) 1184) 52
153 = 9*17

128^1000%9 = (2^3)^333*2 = (-1)^odd*2 = -2 or 7
128^1000%17 = 9^8%17 = 1..

9p+7=17x+1

so 52...
21042
@Exodia said:
What is the remainder when 128^1000 is divided by 153?1) 1032) 1453) 1184) 52
52.
128^1000/17*9
128^1000/17
E(17) = 16
128^8/17 gives remainder 1
so 17K+1
128^1000/9
E(9) = 6
2^1000/9
2^4/9 gives remainder 7
so 9M+7
52 satisfies it..
21043

Find the remainder wen 21^3 + 23^3 + 25^3 + 27^3 is divided by 96 ?


ans-> 0 .
need soln plz
21044
@Abir1103 said:
Find the remainder wen 21^3 + 23^3 + 25^3 + 27^3 is divided by 96 ?ans-> 0 . need soln plz
combine 1st and last and the other two left in the middle then apply (a+b) funda we'll get 0
21045
@Abir1103 said:
Find the remainder wen 21^3 + 23^3 + 25^3 + 27^3 is divided by 96 ?ans-> 0 . need soln plz
combine the terms
:
21^3 + 27^3 and 23^3 + 25^3...use the a^3 + b^3 formula.....
try this out...you should be able to get it...
and please do not post the OA along with the question....