Question of the day - 27th August, 2009

Question 1:

How many five-digit numbers are there, if the two leftmost digits are even, the other digits are odd and the digit 4 cannot appear more than once in the number?
a)1875
b)2000
c)2375
d)2500
e)3875

Question 2:

6 persons seat themselves at round table. What is the probability that 2 given persons are adjacent?
(A) 1/5
(B) 2/5
(C) 1/10
(D) 1/7
(E) 2/15

OA will be posted soon.

Thanks,

Quant-Master

Question of the day - 26th August, 2009

Question 1:

If x is an integer, is y an integer?
(1) The average (arithmetic mean) of x, y and y – 2 is x.
(2) The average (arithmetic mean) of x and y is not an integer.

Question 2:

Three types of pencils, J,K, and L, cost $0.05, $0.10, and $0.25 each, respectively. If a box of 32 of these pencils costs a total of $3.40 and if there are twice as many K pencils as L pencils in the box, how many J pencils are in the box?
(A) 6
(B) 12
(C) 14
(D) 18
(E) 20

Question 3:

Forty percent of the rats included in an experiment were male rats. If some of the rats died during the experiment and 30 percent of the rats that died were male rats, what was the ratio of the death rate among the male rats to the death rate among the female rats?
(A) 9/14
(B) 3/4
(C) 9/11
(D) 6/7
(E) 7/8

OA will be posted soon.

Thanks,

Quant-Master

Question of the day - 25th August, 2009

Question 1:

What is the probability for a family with three children to have a boy and two girls, assuming the probability of having a boy or a girl is equal?

a)1/8
b)¼
c)½
d)3/8
e)5/8

Question 2:

X,Y > 0 ,If X^3 = Y, is Y a fraction?

(1) X^2 is a fraction
(2) X >Y

OAs will be posted soon

Thanks,

Quant-Master

Finding last two digit of a number

sorry folks! it has been a long time since I posted fundas (busy in my new coaching job). anyways here is a funda to cover up my long pending quota

I am dividing this method into four parts and we will discuss each part one by one:

a. Last two digits of numbers which end in one
b. Last two digits of numbers which end in 3, 7 and 9
c. Last two digits of numbers which end in 2
d. Last two digits of numbers which end in 4, 6 and 8

Before we start, let me mention Binomial theorem in brief as we need it for calculation

(x+a)^n = Nc0*a^n+Nc1*a^n-1*x+Nc2*a^n-2*x^2+….. where NcR =n!/(r!(n-r)!)

a. Last two digits of numbers which end in one

This is best explained with an example.

What are the last two digits of 31^786?

Solution: 31^786 = (30+1)^786 = 786C0*1^786+786C1*1^785*30+786C2*1^784*30^2…..

Note that in the above expression, after the first two terms, all the terms will have two or more 0’s at the right hand side (since the expression is multiplied by 30^x). Hence to find the last two digits, only first two terms needs to be evaluated. First term equals to 1 and second term equals to 786*30 = 23580 hence last two digits will be 81 (which is last two digits of 23580 and +1 hence 80+1)

Wiyee!! That’s really long isn’t it? Well those who need a shortcut of this read on!!

Multiply the tenth digit ( 3 in the above example) with the unit digit of the exponent (6 in the above example) to get the tenth digit. Unit digit is always one when a number ends in 1.

Now it’s a two second job isn’t it??

Few exercises for you:

41^2789

71^56747

51^456*61^567

Post your answers using comment option

Now I have covered 25% of this exercise i.e. part A alone. Based on your response, if you find this useful, I will go ahead and post the approach for below kind of numbers

b. Last two digits of numbers which end in 3, 7 and 9
c. Last two digits of numbers which end in 2
d. Last two digits of numbers which end in 4, 6 and 8

Thanks,

Quant-Master

Question of the day - 22nd August, 2009

In a certain game played with red chips and blue chips, each red chip has a point value of X and each blue chip has a point value of Y, where X>Y and X and Y are positive integers. If a player has 5 red chips and 3 blue chips, what is the average (arithmetic mean ) point value of the 8 chips that the player has?


(1) The average point value of one red chip and one blue chip is 5.
(2) The average point value of the 8 chips that the player has is an integer.

OA will be posted soon.

Thanks,

Quant-Master