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.
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RE: Quant Boosters  Hemant Malhotra  Set 14

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: 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?

RE: Quant Boosters  Hemant Malhotra  Set 14
Q24) Doodhnath, a milkman, has 100 litres of milk and water solution that contains 70% milk. What quantity of water (in litres) should he add to the solution to bring down the concentration of milk to 40%?
(a) 65
(b) 75
(c) 40
(d) 85 
RE: Quant Boosters  Hemant Malhotra  Set 14
Q23) What is the remainder when sum of square of any 20 consecutive odd numbers is divided by 40 ?

RE: Quant Boosters  Hemant Malhotra  Set 14
Q22) What is the probability of forming word from the letters of word “IMPEACH” such that all vowels come together?

RE: Quant Boosters  Hemant Malhotra  Set 14
Q21) If a, b, c are whole numbers, and a^b + b^c + c^a = 17 and a^c + c^a = 17, what could be the possible sum of a and c?
a) 17
b) 18
c) 0
d) 11
e) None of these 
RE: Quant Boosters  Hemant Malhotra  Set 14
Q20) 5 boys and 5 girls sit in a row. Which of the following is true?
A) The probability that all the boys do not sit together is 41/42
B) The probability that boys and girls sit alternate to each other is (5! × 4!)/9!
C) The probability that one of the boys Aman sits with one of the girls Tanushree is 1/5
D) The probability that all the boys sit together and all the girls sit together is 2/10!a) A and B
b) A, B and C
c) B, C and D
d) C and D
e) D 
RE: Quant Boosters  Hemant Malhotra  Set 14
Q19) Four friends P, Q, R and S have Rs. 200 among them. They made the following statements about the money with them.
P: Q has Rs. 60 and if I give Rs. 10 to R, then Q and R will have equal amounts of money.
Q: I have more money than R and two people have the same amount of money
R: The person(s) with the lowest amount has (ve) Rs. 30 and S does not have the highest amount.
S: Q and I have the same amount of money and if R gives Rs. 10 to Q, he would have Rs. 5 less than Q.Only one of the statements is completely incorrect.
How much money does S have?a) Rs. 50
b) Rs. 60
c) Rs. 20
d) Rs. 30
e) Cannot be determined 
RE: Quant Boosters  Hemant Malhotra  Set 14
Q18) 10 students are going to perform 10 different items in school’s annual program. What is the number of ways in which these 10 items can be arranged, if Amar will perform before Bindu, Bindu will perform before Chetan, and Chetan will perform before David?

RE: Quant Boosters  Hemant Malhotra  Set 14
Q17) What is the units digit of 1^1 + 2^2 + 3^3 + … + 2008^2008?

RE: Quant Boosters  Hemant Malhotra  Set 14
Q16) A loan of Rs. 48,000 is borrowed at an interest rate of 10% per annum compounded annually and repaid in 3 equal yearly installments of Rs. X starting after one year. What is the approximate value of X?
a) Rs. 19300.50
b) Rs. 19300.75
c) Rs. 19301
d) Rs. 19301.25
e) Rs. 19301.50 
RE: Quant Boosters  Hemant Malhotra  Set 14
Q15) For what values of k does the equation log(kx) = 2 log(x + 1) have only one real root?

RE: Quant Boosters  Hemant Malhotra  Set 14
Q14) Given that log 3 = 0.477, log 7 = 0.845, log 2 = 0.301. Find the number of digits in y if y = 252^10

RE: Quant Boosters  Hemant Malhotra  Set 14
Q13) If [ x ] + [ 2x ] + [ 3x ] = n, where [ x ] is the greatest integer less than or equal to x, then how many different values n can take if 1 ≤ n ≤ 2007 ?