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RE: Question Bank  100 Algebra Questions From Previous CAT Papers (Solved)

RE: Quant Boosters  Hemant Malhotra  Set 14
Q30) A teacher asks one of her students to divide a 30digit number by 11. The number consists of six consecutive 1’s, then six consecutive 2’s, and likewise six 3’s, six 4’s and six 7’s in that order from left to right. The student inserts a threedigit number between the last 4 and the first 7 by mistake and finds the resulting number to be divisible by 11. Find the number of possible values of the threedigit number.

RE: Quant Boosters  Hemant Malhotra  Set 14
let A,B,C,D
let A got a rs
B got a * b rupees
C got a * b * c rupees
D got a * b * c * d rupees
a(1+b+bc+bcd)=70
a * (1+b+bc+bcd) = 2 * 35
this will be minimum when all values are as close as possible
1+b+bc+bcd=35
b(1+c+cd)=34
so b=2
1+c+cd=17
so c(1+d)=16
so c=4 and d=3
so a=2,b=2,c=4,d=3
so 2,4,16,48 these are values 
RE: Quant Boosters  Hemant Malhotra  Set 14
Q29) In a group of four boys, each of them has a certain number of Re. 1 coins with him. Every boy has an amount that is an integral multiple of the amount possessed by every other boy who has an amount less than him. If the total amount with the four boys put together is Rs. 70, and no two boys have the same amount, what is the minimum possible amount (in Rs.) with the boy who has the maximum number of Rs. 1 coins with him?

RE: Quant Boosters  Hemant Malhotra  Set 14
Q28) How many arrangements can be made in a round table of 8 chairs if 2 of them like to sit opposite to each other ?

RE: Quant Boosters  Hemant Malhotra  Set 14
1step = 1 way =2^0
2 step = (1,1) , (2,0) = 2^1 way
3 step = (1,1,1) , (2,1) ,(1,2) ,(3)=2^2=4 way
4 step = 2^3= 8 way
5 step = 2^4 = 16 way
6 step = 2^5 = 32 way
now step 7th step will be sum of previous 6 steps= 63
8th step = sum of previous 6 step = 125 
RE: Quant Boosters  Hemant Malhotra  Set 14
Q27) In how many ways can you climb up 8 steps if the minimum and maximum steps you can take at a time are 1 and 6 respectively?

RE: Question Bank  100 CAT level questions on Time, Speed and Distance topic
t + t/12 = 9 (time taken in the return journey is 1/12th the time taken for the onward journey)
t = 108/13 = 8.30 hours
t + t/6 = 9.68 hours? 
RE: Quant Boosters  Hemant Malhotra  Set 14
Q26) A teacher asks one of her students to divide a 30digit number by 11. The number consists of six consecutive 1’s, then six consecutive 2’s, and likewise six 3’s, six 4’s and six 7’s in that order from left to right. The student inserts a threedigit number between the last 4 and the first 7 by mistake and finds the resulting number to be divisible by 11. Find the number of possible values of the threedigit number

RE: Quant Boosters  Hemant Malhotra  Set 14
Q25) Let S be the set of the first six natural numbers. If five numbers are picked randomly from S, what is the probability that the sum of the five numbers is divisible by 3?