Partnership Question

    Q)   P and Q invested Rs. 8,000/- and Rs. 15,000/- in a business. At the end of                 some months R joined them with Rs. 10,000/-. P withdraws Rs. 2,000/-                    after 4 months from the commencement of the business. At the end of 12                months, P got Rs. 8,000/- of the total  profit and R got Rs. 9,000/-. 

          What was Q's share?
          What was the total Profit?
          When did R join the business?

GRE Question of the day 1st December 2015

GRE Question of the day 30th November 2015

GRE Question of the Day 29th November 2015

PROFIT & LOSS

     A trader marks his product 40% above its cost.  He sells the product on credit and allows 10% trade discount.  In order to ensure prompt payment, he further gives 10%, discount on the reduced price.  If he makes a profit of Rs. 67 from the transaction, then the cost price of the product is

a. Rs. 300          

b. Rs. 400       

c. Rs. 325          

d. Rs. 500

GRE Question of the day 28th November 2015

Geometry Q

A person uses a sheet measuring 30cm by 40cm lengthwise. If a margin of 3cm is left on each side and a 3cm margin on top and bottom, then percent of the page used for typing is?

        (a) 50%                

        (b) 68%    

     

        (c) 80%             

     

        (d) None

GRE - Question of the day 27th Nov 2015

GRE Q of the day 26th Nov 2015

Simple Interest

1      A person borrowed Rs. 600 @ 3% per annum S.I and Rs. 800 @ 4.5 % per annum on the agreement that the whole sum will be returned only when the total interest becomes Rs. 246. The number of years, after which the borrowed sum is to be returned, is

a.     2 years

b.     3 years

c.      4 years

d.     5 years

Missing number

Find out the missing number in the following number series?

4, 18, 48, 100, 180, __

A) 322

B) 294

C) 448

D) 648

Number Puzzle

Find out the missing number in the given number series?

1469, 940, __ , 290, 121

a) 879

b) 779

c) 679

d) 579 

GRE - Q of the day 25th Nov 2015

Missing number

Find out the missing number in the following number series?
4, 14, 76, 364, __
a) 536
b) 756
c) 1030
d) 1364
e) 2010

GRE Q of the day 24th November 2015

GRE - Q of the day

GRE - Q of the day 22nd Nov

Q of the day 21st Nov 2015

Q of the day 20th Nov 2015

Question of the Day 19th November 2015

Question of the day 18th November 2015

Simple ratio Question

A teacher graded 180 bonus quizzes during the school year.
  The number of quizzes receiving A's, B's, and C's 
were in the ratio of 5 : 3 : 1, respectively.
  Find the number of bonus quizzes that received a grade of A
for the school year.

Standard Deviation - 2

Professor Halen has 184 students in his college mathematics lecture class.  The scores on the midterm exam are normally distributed with a mean of 72.3 and a standard deviation of 8.9.  How many students in the class can be expected to receive a score between 82 and 90?  Express answer to the nearest student.

Question of the Day 17th November 2015

Standard Deviation

 The amount of mustard dispensed from a machine at The Hotdog Emporium is normally distributed with a mean of 0.9 ounce and a standard deviation of 0.1 ounce.  If the machine is used 500 times, approximately how many times will it be expected to dispense 1 or more ounces of mustard.

A.    5          

         

B. 16          

C. 80

               

D. 100

Chess board Application

How many squares are there in a chess board?

1. 64
2. 65
3. 4096
4. 1296
5. 204

Maximum and Minimum Probability

Ms Li works at an office where the work timing is from 9:00 AM to 6:00 PM. 25% of a year she goes late to office and 35% of a year she leaves early from office. If P is the probability that she works at office the entire day then

A. 0.25 ≤ P ≤ 0.35

B. 0.25 ≤ P ≤ 0.65

C. 0.4 ≤ P ≤ 0.65

D. 0.35 ≤ P ≤ 0.4

E. 0.1 ≤ P ≤ 0.6

Question of the Day 16th November 2015

Percentage with Venn Diagram

   In an examination, 70% students passed in English, 65% passed in mathematics, 27% students failed in both the subjects. If only 248 students passed in both the subjects. Find the total number of students appearing at the examination?
        (1) 400     

             

             (2) 700

        (3) 600   

               

            (4) 500

            (5) 1000

Percentage as a Fraction

    Paul’s income is 40% less than Rex’s income; Quentin’s income is 20% less than Paul’s income and Sam’s income is 40% less than Paul’s income. If Rex gave 60% of his to Sam, and 40% income to Quentin, Quentin’s new income would be what fraction of Sam’s new income?

      a)      11/12    

          

      b)      13/17

      c)      13/19

      d)      12/11     

      e)      11/19

Percentage- Discount

Mark got a 30% discount on a movie ticket. When the price of the movie ticket increased by 50%, the amount of discount in dollars remained the same. what is the percentage discount that he received on the new ticket price?

(A) 10%

(B) 15%

(C) 20%

(D) 25%

(E) 30%

Percentage Application

Q:
         During the years 1990 to 1995, 10% of the population of a city migrated to another city in      
            search of a green pastures. The percentage of migrated people from 1990 to 2000 was                         recorded as 20%. What is the percentage of migrated people during the years 1995 to 2000?

           (A) 100/11 %

           (B) 10%

           (C) 100/9 %

           (D) 18%

           (E) 100/3 %

Question of the Day 14th Nov 2015

PROBABILITY QUESTIONS WITH SOLUTIONS

1.The probability that a student will get an A in statistics is .20, the probability that she will get an A in French is .25, and the probability that she will get an A in both is .05. What is the probability that she will get an A in neither subject?

 solution: 

To begin, we need to recognize that P(A in neither subject) = 1 - P(A in Statistics or A in French)
So, we need to find P(A in Statistics or A in French)

We'll use the formula P(X or Y) = P(X) + P(Y) - P(X and Y)
So, P(A in Statistics or A in French) = P(A in Statistics) + P(A in French) - P(A in Statistics and A in French)
= 0.2 + 0.25 - 0.05
So, P(A in neither subject) = 1 - 0.4
= 0.6

Or

Probability of getting A in Statistics --> 0.20
Probability of getting A in French --> 0.25
Probability of getting A in both --> 0.05

Total Probability = Probability of getting A only in Statistics + Probability of getting A only in French + Probability of getting A in both + Probability of getting A in neither = 1

i.e. 1 = (0.20 - 0.05) + (0.25 - 0.05) + 0.05 + x
--> x = 1 - 0.15 - 0.20 - 0.05 = 0.6

2.Eight world leaders are lined up randomly to be photographed at an international summit. If the leaders of Brazil and Hungary are among the eight leaders, what is the probability that they will be standing next to each other in the photograph?

A 1/64    B 3/32     C 1/8     D 1/4     E 1/2

If one of the delegates ends up in one of the six middle spots (which has probability 3/4), the probability the other will be next to them is 2/7, but if one is placed on the end (which has probability 1/4), the probability of them being next to each other is only 1/7.

So the total probability is (1/4)(1/7)+(3/4)(2/7) = 7/28 = 1/4

==> Answer is D.

Or

suppose leaders are L₁, L₂, L₃, L₄, L₅, L₆, L₇ and L₈

all possible formation = ⁸P₈ = 8!

from 8 positions, we can choose 2 side-by-side positions in 7 ways -
i.e. L₁-L₂, L₂-L₃, L₃-L₄ ...

these 2 positions will be used by 2 ways - brazil-hungary and hungary-brazil

we have 6 positions remained, now 6 people can be placed in to 6 places = ⁶P₆ = 6!

probability = (2 X 7 X 6!)/8! = (2 X 7!)/(8 X 7!) = ¼

or

Take those two individual as ONE. SO there are 7 people who can be arranged in 7! ways. And 8 people can be arranged in 8! ways. Again those two can arranged themselves in 2 ways. So the Probability is 2 X (7!/8!) = 2 / 8 = ¼

1.There are 9 beads in a bag. 3 beads are red, 3 beads are blue, and 3 beads are black. If two beads are chosen at random, what is the probability that they are both blue?

A. 1/81   B. 1/12   C. 2/9    D. 1/3    E. ¼

Sol B
Probability of getting one blue bead = 3/9 = 1/3
Porbability of getting second blue bead = 2/8 = 1/4
Probability of getting blue bead in both picks = 1/3*1/4 = 1/12

2 A letter is randomly selected from the word Mississippi. What is the probability that the letter will be an s?

A. 1/11   B. 3/10    C. 4/11    D. 1/4    E. 1/3

Sol: 
Probability of choosing s = 4/11

3. A certain deck of cards contains 2 blue cards, 2 red cards, 2 yellow cards, and 2 green cards. If two cards are randomly drawn from the deck, what is the probability that they will both are not blue?

A. 15/28    B. 1/4   C. 9/16   D. 1/32   E. 1/16

Sol:
 A
Probability for first card to be not blue - 6/8 = 3/4
Probability for second card to be not blue - 5/7
Probablility for both cards to be not blue - 3/4*5/7 = 15/28

4. A fair coin is tossed, and a fair six-sided die is rolled. What is the probability that the coin come up heads and the die will come up 1 or 2?

A. 1/2    B. 1/4   C. 1/6     D. 1/12     E. 1/3

Sol:  C
Probability for heads - 1/2
Probability for 1 or 2 - 1/3
Probability for heads and 1 or 2 - 1/2*1/3 = 1/6

5. A bag of 10 marbles contains 3 red marbles and 7 blue marbles. If two marbles are selected at random, what is theprobability that at least one marble is blue?

A. 21/50     B. 3/13   C. 47/50   D. 14/15   E. 1/5

Sol: . D
Atleast on blue marble can be selected in three ways, The GRE Big Book, RB and BR
Probability of getting The GRE Big Book - 7/10*6/9 = 7/15
Probability of getting RB - 3/10*7/9 = 7/30
Probability of getting BR - 7/10*3/9 = 7/30
Probability of getting atlease on blue - 7/15 + 7/30 + 7/30 = 14/15

6. A fair, six-sided die is rolled. What is the probability that the number will be odd?

A. 1/4     B. 1/2   C. 1/3   D. 1/6    E. 1/5

Sol:
B
There are three odd numbers 1,3 and 5
Probability of getting odd number - 3/6 = 1/2

7. A letter is randomly select from the word studious. What is the probability that the letter be a U?

A. 1/8    B. 1/4    C. 1/3    D. 1/2    E. 3/8

Sol:
 B
Probability of choosing u - 2/8 = 1/4

8. A bag contains 2 red beads, 2 blue beads, and 2 green beads. Sara randomly draws a bead from the bag, and then Victor randomly draws a bead from the bag. What is the probability that Sara will draw a red marble and Victor will draw a blue marble?

A. 2/13    B. 1/5      C. 1/3     D. 1/10      E. 2/15

Sol:
E
Probability that Sara draws a red marble - 2/6 = 1/3
Probability that victor draws a blue marble - 2/5
Probability that Sara draws a blue marble and Victor draws a red marble - 1/3 x 2/5 = 2/15

9. If two fair, six-sided dice are rolled, what is the probability that the sum of the numbers will be 5?

A. 1/6     B. 1/4     C. 1/36    D. 1/18    E. 1/99.
sol:There are 36 pairs of numbers when two dice are rolled. There four combinations that gives the sum of 5 - (1,4), (2,3), (3,2) and
(4,1)
Probability of the sum to be 5 - 4/36 = 1/9

10. If four fair coins are tossed, what is the probability of all four coming up heads?

A. 1/4       B. 1/6       C. 1/8     D. 1/16     E. 1/32

Sol: D
Probability of getting all four heads - 1/2 x 1/2 x 1/2 x 1/2 = 1/16

11. The probability that a certain event will occur is 5/9. What is the probability that the event will NOT occur?

A. 5/9   B. 4/9     C. 2/9    D. 1/4     E. 1/2
sol: B
Probability of the event not to occur = 1 - 5/9 = 4/9

12. A certain bag contains red, blue, yellow, and green marbles. If a marble is randomly drawn from the bag, the probabilityof drawing a blue marble is .2, the probability of drawing a red marble is .3, and the probability of drawing a yellow marble is .1. What is the probability of drawing a green marble?

A. .5      B. .6      C. .2     D. .4       E. .3

Sol: D
Probability of drawing green marble = 1 - (0.2 + 0.3 + 0.1) = 0.4

13. A bag contains 3 red marbles, 3 blue marbles, and 3 green marbles. If a marble is randomly drawn from the bag and a fair, six-sided die is tossed, what is the probability of obtaining a red marble and a 6?

A. 1/15    B. 1/6     C. 1/3     D. 1/4      E. 1/18

Sol:  E
Probability getting red marble = 3/9 = 1/3
Probability of getting 6 = 1/6
Probability of getting red marble and 6 = 1/3 x 1/6 = 1/18

14. A fair, six-sided die is rolled. What is the probability of obtaining a 3 or an odd number?

A. 1/6

B. 1/5

C. 1/4

D. 2/3

E. ½

Sol:  E
As 3 itself is an odd number, probability of getting odd number = 3/6 = 1/2

15. At a certain business school, 400 students are members of the sailing club, the wine club, or both. If 200 students are members of the wine club and 50 students are members of both clubs, what is the probability that a student chosen at random is a member of the sailing club?

A. 1/2      B. 5/8       C. 1/4      D. 3/8       E. 3/5

Sol: B
Members in sailing club = 250
Probability of choosing member from sailing club = 250/400 = 5/8

16. A bag contains six marbles: two red, two blue, and two green. If two marbles are drawn at random, what is theprobability that they are the same color?

A. 1/3       B. 1/2      C. 1/8     D. 1/4       E. 1/5

Sol:  E
First marble can be any color.
Probability of choosing second marble of the same color as the first one = 1/5

17. There are five students in a study group: two finance majors and three accounting majors. If two students are chosen at random, what is the probability that they are both accounting students?

A. 3/10     B. 2/5        C. 1/5       D. 3/5        E. 4/5

sol:Probability of first student to be accounting student - 3/5
Probability of second student to be accounting student - 2/4 = 1/2
Probability that both students to be accounting students - 3/5 x 1/2 = 3/10

18. Seven beads are in a bag: three blue, two red, and two green. If three beads are randomly drawn from the bag, what is the probability that they are not all blue?

A. 5/7          B. 23/24      C. 6/7      D. 34/35      E. 8/13

sol; D
Probability of selecting all blue marbles in 3 picks - 3/7 x 2/6 x 1/5 = 1/35
Probability that all three of them are not blue = 1 - 1/35 = 34/35

19. A bag has six red marbles and six blue marbles. If two marbles are drawn randomly from the bag, what is the probabilitythat they will both be red?

A. 1/2        B. 11/12     C. 5/12       D. 5/22      E. 1/3

sol:

 D
Probability that both are red marbles = 6/12 x 5/11 = 5/22

Sqaure, Square Roots, Cubes and Cube Roots

1. The least positive integer k for which 15k is the cube of an integer is 
          answer: 225

     2. If k is a positive integer, the smallest value of  k  such that  60k is a perfect square is
    answer: 15
     
      3.A perfect cube is an integer whose cube root is an integer. For example, 27, 64 and 125 are perfect cubes. If p and q are perfect cubes, which of the following will not necessarily be a perfect cube?

A. 8p
B. pq
C. pq + 27
D. -p
E. (p - q)6
answer: c

4.  n is the least possible no. such that 18n is a perfect square. m is the least no. such that 9m is a perfect square.

                         Col A : n                                  Col B : m
answer: B

5. If y is the smallest positive integer such that 3,150 multiplied by y is the square of an integer, then y must be
A. 2
B. 5
C. 6
D. 7
E. 14

answer: E

6. If x and y are perfect squares, then which one of the following is not necessarily a perfect square? 
A. x^2
B. xy
C. 4x
D. x+y
E. x^5

answer: D

7.Which of the following numbers is a perfect square?
A. 1266
B. 1444
C. 2022
D. 4034
E. 8122
answer: B

8. If x^(1/6) = 6, then √x^6 is ?
A. 6
B. 6√6
C. 6^6
D. 6^18
E. 6^36
answer: D

9. If (x - 3)^2 = 225, which of the following could be the value of x + 3 ?
(A) -15
(B) -12
(C) -9
(D) 15
(E) 18
answer: C

10. The mean of (54,820)^2 and (54,822)^2 =
(A) (54,821)^2
(B) (54,821.5)^2
(C) (54,820.5)^2 
(D) (54,821)^2 + 1
(E) (54,821)^2 – 1
answer: D

11. If m^(-1) = -1/3 then m^(-2) is equal to
(A) -9
(B) -3
(C) -1/9
(D) 1/9
(E) 9
answer: D

12. If (x - 1)^2 = 400, which of the following could be the value of x - 5?
(A) 15
(B) 14
(C) -24
(D) -25
(E) -26
answer: C