Solve these 😃
http://www.jotoshob.blogspot.in/2015/02/number-systemproblem-set-1number.html
Please tell me... how to prepare for Quant systematically.. and sources, books, et cetera to follow... will be very helpful..
Please solve this:
P & Q are two distinct two digit numbers. A & B denote the sum of the digits in P & Q. If P/A=Q/B, the find the minimum possible value of A+B.
A. 8 B.9 C.6 D.3
If x is the smallest positive integer that is not prime and not a factor of 50!, what is the sum of the factors of x?
A. 51
B. 54
C. 72
D. 162
E. 50!+2
If a and b are distinct integers and a^b=b^a , how many solutions does the ordered pair (a, b) have?
(A) None
(B) 1
(C) 2
(D) 4
(E) Infinite
Two different primes may be said to "rhyme" around an integer if they are at the same distance from the integer on the number line. For instance, 3 and 7 rhyme around 5. What integer between 1 and 20, inclusive, has the greatest number of distinct rhyming primes around it?
(A) 12
(B) 15
(C) 17
(D) 18
(E) 20
How many 4 digit integers are perfect squares and have only even digits? Any method to do this excluding hit and trial?
What sum will give 244 as diff between SI and CI at 10% for 1.5 years compounded half yearly
For a positive integer n, Let P(n) be product of digits of n. and S(n) denote the sum of digits of n . The number of integers between 10 and 1000 for which p(n) + S(n) = n is ?
For any integer k > 1, the term "length of an integer" refers to the number of positive prime factors, not necessarily distinct, whose product is equal to k. For example, if k = 24, the length of k is equal to 4, since 24 = 2 x 2 x 2 x 3. If x and y are positive integers such that x > 1, y > 1, and x + 3y (Less than) 1000
what is the maximum possible sum of the length of x and the length of y?
A. 5
B. 6
C. 15
D. 16
E. 18
Two vessels of equal volumes are completely filled with milk and water solutions. The ratio of milk and water in first vessel is 2 : 3 and that in second vessel is 4 : 1. Next a certain fraction of solution is taken out from first vessel and a certain fraction (not necessarily same as that for first vessel) is taken out from second vessel and are then poured into the other vessels. The fractions removed are such that solution in neither of the vessel spills out and also the ratio of milk and water in first vessel becomes 1 : 1. Find the ratio of milk and water in second vessel.
a. 1:1
b. 2:3
c. 2:5
d. 3:8
e. 7:3
If x and y are distinct prime numbers, each greater than 2, which of the following must be true?
(I) x+y is divisible by 4
(II)x * y has even number of factors
(III)x+y has an even number of factors
A. I only
B. II only
C. I and III only
D. II and III only
E. I and II only
If a and b are positive integers divisible by 6, is 6 the greatest common divisor of a and b?
(1) a = 2b + 6
(2) a = 3b
Use Data sufficiency options to answer
The positive integer k has exactly two positive prime factors, 3 and 7. If k has a total of 6 positive factors, including 1 and k, what is the value of K?
(1) 3^2 is a factor of k
(2) 7^2 is NOT a factor of k
Use DS options
If the product of all the unique positive divisors of n, a positive integer which is not a perfect cube, is n^2 , then the product of all the unique positive divisors of n^2 is
(A) n^4
(B) n^8
(C) n^9
(D) n^3
(E)n^12
A high school has a strange principal. On the first day, he has his students perform an odd opening day ceremony:
There are one thousand lockers and one thousand students in the school. The principal asks the first student to go to every locker and open it. Then he has the second student go to every second locker and close it. The third goes to every third locker and, if it is closed, he opens it, and if it is open, he closes it. The fourth student does this to every fourth locker, and so on. After the process is completed with the thousandth student, how many lockers are open?
A 45
B 31
C 77
D 131
E 93
Lukas have a banana plantation and a camel. He wants to transport his 3000 bananas to the market, which is located after the desert. The distance between his banana plantation and the market is about 1000 kilometer. So he decided to take his camel to carry the bananas. The camel can carry at the maximum of 1000 bananas at a time, and it eats one banana for every kilometer it travels. What is the largest number of bananas that Lucas can deliver at the market?
In a room of 23 people what is the probability of 2 people having the birthday on same date?
The director of a prison offers 100 prisoners on death row, which are numbered from 1 to 100, a last chance. In a room there is a cupboard with 100 drawers. The director puts in each drawer the number of exactly one prisoner in random order and closes the drawers afterwards. The prisoners enter the room one after another. Each prisoner may open and look into 50 drawers in any order and the drawers are closed again afterwards. If during this search every prisoner finds his number in one of the drawers, all prisoners are pardoned. If just one prisoner does not find his number, all prisoners have to die. Before the first prisoner enters the room, the prisoners may discuss their strategy, afterwards no communication of any means is possible. what is the maximum probability of their survival.
n! has x number of zeroes at the end and (n+1)! has x+3 zeroes at the end. Find the number of possible values of n if n is a three digit number.