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PERMUTATIONS AND COMBINATIONS Question

A student has to answer 10 questions, choosing at least 4 from each of Parts A and B. If there are 6 questions in Part A and 7 in Part B, in how many ways can the student choose 10 questions?

LCM & HCF Sample Questions

1.The product of two 2 digit numbers is 2028 and their HCF is 13. What are the numbers ?

A. 26, 78         B. 39, 52         C. 13, 156       D. 36, 68

2.Six bells commence tolling together and toll at intervals of 2, 4, 6, 8 10 and 12 seconds respectively. In 30 minutes, how many times do they toll together ?

A. 4                  B. 10               C. 15                D. 16

3.N is the greatest number which divides 1305, 4665 and 6905 and gives the same remainder in each case. What is the sum of the digits in N?

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

4.Which greatest possible length can be used to measure exactly 15 meter 75 cm, 11 meter 25 cm and 7 meter 65 cm

A. 45cm                      B. 255cm                    C. 244cm                    D. 55cm

5.Let N be the greatest number that will divide 1305, 4665 and 6905, leaving the same remainder in each case. Then sum of the digits in N is:

A. 4                  B. 5                  C. 6                  D. 8

6.A, B and C start at the same time in the same direction to run around a circular stadium. A completes a round in 252 seconds, B in 308 seconds and c in 198 seconds, all starting at the same point. After what time will they again at the starting point ?

A. 36 minutes 22 seconds                B. 46 minutes 22 seconds

C. 36 minutes 12 seconds                D. 46 minutes 12 seconds

7.An electronic device makes a beep after every 60 sec. Another device makes a beep after every 62 sec. They beeped together at 10 a.m. The time when they will next make a beep together at the earliest, is

A. 10:28 am                B. 10:30 am                C. 10:31 am                D. None of above

 8.What is the LCM of 2/3, 5/6 and 4/9 ?

A. 3/10                       B. 3/20                       C. 10/3                       D. 20/3

9.The smallest number which when diminished by 7, is divisible 12, 16, 18, 21 and 28 is:

A. 1008                       B. 1015                       C. 1022                       D. 1032

10.What is the HCF of 9/10,12/15, 18/35 and 21/40 is :

A. 3/5                                     B. 252/5                     C. 1/280                     D. 63/700

Syllogism 10 Questions Set

Directions (Q. 1 – 10): In each question below are given three statements followed by two conclusions numbered I and II. You have to take the given statements to be true even if they seem to be at variance with commonly known facts. Read all the conclusions and then decide which of the given conclusions logically follows from the given statements, disregarding commonly known facts. 

Give answer 

A) if only conclusion I follows. 

B) if only conclusion II follows. 

C) if either conclusion I or conclusion II follows. 

D) if neither conclusion I nor conclusion II follows. 

E) if both conclusion I and conclusion II follow. 

(1 – 2): 

Statements: 

All stars are moons.                           

All moons are planets.                          

All planets are round. 

1. Conclusions:

                      I. All moons being stars is a possibility.                            

                     II. All stars are round. 

2. Conclusions: 

                     I. At least some planets are stars.                              

                    II. All stars if they are moon will be planet. 

(3 – 4): 

Statements: 

All shirts are pants.                          

 No pant is trousers.                          

 Some jackets are pants. 

3. Conclusions: 

                  I.All shirts being jackets is a possibility.                             

                 II.No trousers are shirt. 

4. Conclusions: 

                  I.There is a possibility that all shirts are trousers.                              

                 II.All pants being jackets is a possibility. 

5. Statements: 

 Some cakes are pastries.                                

 Some breads are pastries. 

Conclusions:

 I.All pastries being cakes is a possibility.                      

 II.There is a possibility that some cakes are breads. 

(6 – 7): 

Statements: 

All princes are kings.                          

 All braves are princes.                          

 No queen is a king.

 6. Conclusions: 

             I.All princes being brave is a possibility.                             

            II.At least some kings are brave. 

7. Conclusions: 

             I.A prince can never be a queen.                            

           II.All those princes who are kings are queens. 

(8 – 9): 

Statements: 

All squares are circles.                          

 All circles are triangles.                          

Some rectangles are triangles. 

8. Conclusions: 

            I.All circles being rectangles is a possibility.                             

          II.Some triangles are squares. 

9. Conclusions: 

            I.All squares being rectangle is a possibility.                              

           II.At least some rectangles are circles. 

10. Statements: 

  Some flowers are white.                                 

  No flower is black. 

Conclusions:

           I.No black is white.                         

          II.All whites being flowers is a possibility.

 Answers:

1. E 

2. E 

3. E 

4. B 

5. E

6. E 

7. A 

8. E

9. A 

10. B

Question of the day leaps model

Three leaps of the hare are equal to 4 leaps of Jackal. For every six leaps of the hare, the Jackal takes five leaps. Find the ratio of the speeds?
A. 64:25
B. 8:5
C. 5:8
D. 25:64
E.None of these

Question Of the Day - Ratio Proportion Leaps Model

A dog takes 4 leaps for every 5 leaps of a cat but 3 leaps of the dog are equal to 4 leaps of the cat. Find the time taken by the dog to cover 150 meters if the cat can cover 225 meters in 18 minutes.

A. 12.5 minutes

B. 18 Minutes

C. 10.25 Minutes

D. 11.25 Minutes

Time and Distance Advanced problem..

Two ants start simultaneously from two ant holes towards each other. The first ant covered 8% of the distance between the two ant holes in 3 hours, the second ant covered 7/120 of the distance in 2 hours 30 minutes. Find the speed (feet/h) of the second ant if the first ant traveled 800 feet to the meeting point.

(A) 15 feet/h

(B) 25 feet/h

(C) 45 feet/h

(D) 35 feet/h

(E) 40 feet/h

Question of the day - partnership - Advanced problem 2

Two partners invested Rs. 1,250 and Rs. 850 respectively in a business. Both the partners distributed 60% of the profit equally and distributes the rest 40% as the interest on their capitals. If one partner received Rs. 30 more than the other, find the total profit [approximately].

A. 250

B. 350

C. 394

D. 450

Question of the day - partnership - Advanced problem - 1

A, B, and C invest 4,000, 5,000 and 6,000 respectively in a business and A gets 25% of profit for managing the business, the rest of the profit divided by A, B and C in the proportion of their investments. If in a year, A gets Rs. 2000 less than B and C together, what was the total profit for the year.

A. Rs. 20,000

B. Rs. 30,000

C. Rs. 40,000

D. Rs. 50,000

Question of the Day - Time and Distance - Advanced Problem

Two Rabbits start running towards each other, one from A to B and another from B to A. They cross each other after one hour and the first rabbit reached B, 5/6 hours before the second rabbit reaches point A. If the distance between A and B is 50 Km, What is the speed of the slower Rabbit?

A. 20 Kmph

B. 10 Kmph

C. 15 Kmph

D. 25 Kmph

Time and Distance - Averages Model - Advanced problem

Ramesh Walked 6 Km to reach the station from his house, then he boarded a train whose average speed was 60 Kmph and thus he reached his destination. In this way he took a total time of 3 hours. If the average speed of the entire journey was 32 Kmph then the average speed of walking is?

A. 5 Kmph

B. 8 Kmph

C. 2 Kmph

D. 4 Kmph

Time and Distance - Advanced Problem

Ramesh and Suresh leaves points A and B towards B and A respectively & simultaneously and travel in the same route. After meeting each other on the way, Ramesh takes 4 hours to reach his destination ans Suresh takes 9 hours to reach his destination. If the Speed of Ramesh is 48 Kmph, Find the speed of Suresh?

A. 32 Kmh

B. 45 Kmph

C. 72 Kmph

D. None of these

Time and Work - Efficiency Model

1) A is thrice as good a workman as B and takes 10 days less to do a piece of work than B takes. the number of days taken by B to finish the work is:

a) 12                      b) 15                 c) 20                   d) 30

2) A does half as much work as B in 3/4 of the time. If together they take 18 days to complete the work, how many days will B take to do it?

a) 30                    b) 35                 c) 40                    d) 45

3) A works twice as fast as B. If B can complete a piece of work independently in 12 days, then the number of days taken by A and B together to finish the work is:

a) 4                        b) 6                 c) 8                          d) 18

4) A and B working separately can do a piece of work in 9 and 12 days respectively.If they work for a day alternately, A beginning, in how many days, the work will be completed?

a) 10 1/2            b) 10 1/4           c) 10 2/3             d) 10 1/3

5) A cistern has a leak which would empty it in 8 hours. A tap is turned on which admits 6 liters a minute into the cistern and it is now empited in 12 hours. how many litres does the cistern hold.

a) 7580              b) 7960             c) 8290              d) 8640

6) two pipes M and N can fill a cistern in 24 min and 32 min , repectively. If both the pipes are opened together, then after hoe many minutes N should be closed so that the tank is full in 18 minutes ?

a) 6                     b) 8                    c) 10                   d) 21x

SAT - Problem Solving - Question of the Day

Three lighthouses are visible from the promenade at Rivermouth. One flashes every 1½ minutes, another flashes every 2 minutes, and the third flashes every 50 seconds.

All three have just flashed at the same time.

How long will it be before they all flash at the same time again?

A. 6.0 minutes

B. 7.5 minutes

C. 10.0 minutes

D. 30.0 minutes

E. 150.0 minutes

Thinking Skills Assessment Problem Solving...

It is 4.30 pm and Jane, Jean and June

have just arrived together at the Ritzy

 cinema. Jane wants to see 'The Rock',

but Jean is determined to see 'Mission

Impossible' and June would rather see

'Empire Records', so they decide to

 split up.

What is the earliest possible time

 that Jane, Jean and June can

arrange to meet together after their

 films?

A. 6.45         B. 7.05

C. 7.10         D. 7.20

E. 8.20

Thinking Skills Assessment (TSA) ... Problem Solving Question

Gumbey and Sons have decided it is time to modernise their image. To go with their new steel and glass office building they have decided to change the company name. A number of acronyms have been shortlisted and, to help choose between them, the company chairman suggests they should choose a name which, when painted vertically from top to bottom on the new glass front door will read the same from inside and out.

Which of the following names should they choose?

A. TIME  

B. NONA

C. DOOD  

D. MITA

E. WEEM

SAT - Heart of Algebra problem

   Devin is a landscaper who needs to prepare different types of grass seed for his customers' yards. Bluegrass seed costs $2.00 per pound while drought-resistant seed costs $3.00 per pound. If for a particular day the two types of grass seed totaled $68.00 and together weighed 25 pounds, how many pounds of bluegrass seed did Devin prepare?

  a. 4

  b. 7

  c. 18

  d. 21

  e. 25

Thinking Skills Assessment Test (TSA).......

Lenton Cars hire out cars at a cost of £50.00 per day if the number of miles travelled is less than 80. There is an extra charge of £1.00 for every mile travelled over 80 miles. Dunford Hire charge £60.00 per day for taking the car out and then 50 p for every mile travelled.

For how many miles travelled would the cost of hiring a car be the same for both hire companies?

A. 100

B. 130

C. 140

D. 170

E. 180

Question of the day - Number Theory

Three Vice Presidents (VP) regularly visit the plant on different days. Due to labour unrest, VP (HR) regularly visits the plant after a gap of 2 days. VP (Operations) regularly visits the plant after a gap of 3 days. VP (sales) regularly visits the plant after a gap of 5 days. The VPs do not deviate from their individual schedules. CEO of the company meets the VPs when all the three VPs come to the plant together. CEO is on leave from January 5^th to January 28^th, 2012. Last time the CEO met the VPs on January 3, 2012. When is the next time the CEO will meet all the VPs?

1. February 6, 2012
2. February 7, 2012
3. February 8, 2012
4. February 9, 2012
5. None of the above

Quiz - Time and Work

Ques 1.

Two pipes P and Q can fell a cistern in 24 min. and 36 min. respectively . Third pipe R can empty it in 36 min. If all the three pipes are opened , find the taken to fill the cistern.
(a) 1 hour
(b) 24 mins
(c) 36 mins
(d) 30 mins

Ques 2.

A tank has a leak which would empty it in 8 hours. A tap is turned on which admit 6 liters a minute into the tank and it now emptied in 12 hours . How many literes does the tank holds?

(a) 8260 ltr
(b) 8640 ltr
(c) 8560 ltr
(d) 8800 ltr

Ques 3.

When the waste pipe is closed , two taps can separately fill a cistern in 10 and 12 minutes respectively .when the waste pipe is opened they together fill it in 15 minutes . How long does it take waste pipe to empty the cistern , when the taps are closed?
(a) 8 min. 34 sec.
(b) 7 min.10 sec.
(c) 12 min.
(d) 10 min

Ques 4.

Two pipes can fill a tank in 10 minutes and 30 minutes respectively and a third pipe can empty the full tank in 20 minutes . If all the three pipes are opened simultaneously, the tank will be filled in:
(a) 12 minutes
(b) 10 minutes
(c) 8 minutes
(d) 6 minutes

Ques 5.

Two pipes can fill a cistern in 14 hours and 16 hours respectively . The pipes are opened simultaneously and it is found that due to leakage in the bottom , 32 minutes extra are taken for the cistern to be filled up. When the cistern is full , in what time will the leak empty it ?
(a) 108 hours
(b) 112 hours
(c) 116 hours
(d) 120 hours

Ques 6.

A cistern can be filled by pipes A and B in 12 minutes and 10 minutes respectively . The full tank can be emptied by a third pipe C in 8 minutes only .If all the pipes be turned on at the same time,the cistern will be full in :
(a) 17 min
(b) 171/7 min.
(c) 17 2/7 min.
(d) 18 min.

Ques 7.

If two pipes function simultaneously , the reservoir will be filled in 12 hours. One pipe fills the reservoir 10 hours faster than the other. How many hours does it take the second pipe to fill the reservoir?
(a) 20 hours
(b) 25 hours
(c) 30 hours
(d) 40 hours

Ques 8.

A tank is filled in hours by three pipes A, B and C . The pipe C is twice as fast as B and B is twice as fast as A. How much time will pipe A alone take to fill the tank?
(a) 40 hours.
(b) 35 hours
(c) 30 hours
(d) 25 hours

Ques 9.

Three pipes P , Q and R can fill a tank in 6 hours , After working it at together for 2 hours , R is closed and P and Q can fill the remaining part in 7 hours . How much time will R take alone to fill the tank?
(a) 16 hours
(b) 14 hours
(c) 12 hours
(d) 10 hours

Ques 10.

Three taps P, Q and R can fill a tank in 12, 15 and 20 hours respectively . If P is opened all the time and Q and R are opened for one hour each alternately , the tank will be full in
(a) 5 hours
(b) 6 hours
(c) 6 2/3 hours
(d) 7 hours