1) An amount of money was divided between some people in such a way that if there had been 4 more people, everyone would have got tk 16 less. However, if there had been 4 less people, everyone would have got tk 16 less. However, if there had been 4 less people, everyone would have got tk. 24 more. How many people were there in the group?
A) 32
B) 24
C) 20
D) 16
E) none
2) Anik, kun, and arefin, working independently, can build a wall in 10, 12, and 15 days respectively. The income from getting one wall up is tk 500. If the three work together for 16 days, how much is kun's income?
A) tk 333
B) tk 375
C) tk 667
D) tk 750
E) cannot be determined
3) Hisham noticed number at the back of his favorite mirinda bottle which consists two digits. The difference between the digits of the given number is not less than 3. If the digits of the number interchange position, the difference between the new number and the old number is 9 times the difference of the two digits. What is the number?
A) 48
B)33
C)14
D) 78
E) cannot be determined
4) Tirtho invented a board game where a square board with N number of rows with N number of squares in each row was used. Which of the following can be the possible number of squares which are not alongside the boundaries?
A) 26
B) 8
C)24
D)0
E) 82
5) Tanveer has three children. All of the children have integer ages and the product of their ages is 36. If only the sum of their ages is also known to us, figuring out their individual age is impossible unless it is also known that the oldest child has a pet dog. What are the ages of the three children?
A) 2,3,6
B) 1,2,18
C) 2,2,9
D) 3,3,4
E) Cannot be determinded
6) Nafiz had a cup filled with liquid, 3 parts of which are water and 5 parts syrup. How much of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup?
A) 1/3 B) 1/4 C) 1/5 D) 1/6 E) 1/7
7) Nawaz was looking for such a number that will always be a factor of a 5-digit number of the form xy0xy, where x can take values from 1 to 9 and y can take values from 0 to 9. Which of the following numbers qualifies Nawaz''s criteria?
I. 143 II. 77 III. 93
A) I only
B) II only
C) III only
D) I and II only
E) I and III only
8) Rituraj has an aquarium, and he will buy exactly 2 of 5 creatures. The available creatures are: two turtles, a goldfish, a catfish and a sucker fish. It is given that a turtle does not fight with the other, neither does it attack the sucker fish. However the turtle will eat any fish in the aquarium. None of the other creatures fights with one another. What is the probability that if Rituraj randomly chooses two creatures, both of them will live umharmed?
A) 6/25
B) 3/5
C) 5/7
D) 1/2
E) Cannot be determined
9) After receiving a call from Ehsan regarding a proxy class, Samia started towards Dhaka at a constant speed. At the same time, Ashfaq got a call from his teenage wife and started running towards chittagong from dhaka at a constant speed. After they crossed each other, it took Samia 40 minutes to reach Dhaka, and it took Ashfaq 90 minutes to reach chittagong. What is the ratio of samia's speed to ashfaq's speed?
A) 4:9
B) 9:4
C) 3:2
D) 13:8
E) cannot be determined
10) Walid and Andalib are playing a Board game. Both of their pieces start from opposite ends, and if Andalib's piece goes 3 steps, walids piece goes 2 steps. However, once the pieces cross each other , if Andalib's piece goes 3 steps, walid's piece goes 6 steps. If it takes 9 turns for Walid's piece to reach andalib's end, what is the number of places from one end to the other end of the board?
A) 24
B) 30
C) 45
D) 81
E) Cannot be determined
11) In a test consisting of 50 questions, a student scores 1 mark for a correct answer, -1/3 for a wrong answer, and -1/6 for not attempting a question. If Moutusi's final score is 32, the number of questions marked wrong by Moutusi cannot be less than:
A) 12 B) 9 C) 6 D) 3 E) Cannot be determined
12) Adib wanted to find a number 'n' which lies between 1 and 96, inclusive, for which it is true that n(n+1)(n+2) is divisible by 8. How many different numbers can Adib find?
A)12 B) 24 C) 32 D) 48 E) 60
13) In 2012, Abrar took four batches (A2, 2A, 4D, and 10A) in Mentors Containing a total of 100 students. If all the students were born in 1993, what is the probability that atleast two of Abrar's students will have the same birthday>
A) (100*99)/(365*364)
B) 1/365*364
C) 1-(100!/365!)
D) 1-(365!/265!*365^100)
E)1-(100!/365^100)
14) If Dave works alone, he will take 20 more hours to complete a task than if he worked with Diana to complete the task. If diana works alone, she will take 5 more hours to complete the task, what is the ratio of the time taken by Dave to that taken by Diana if each of them worked alone to complete the task?
A) 4:1
B) 2:1
C)10:1
D) 3:1
E) 1:2
15) The number of livestock in a farm at the beginning of year 2000 was 100,000. During the year, the number was increased by p%. During the next year 2001, there was a famine and the number decreased by q%. A census at the end of year 2001 revealed that the number of livestock in the farm was 100,000. Which of the following expressions is correct?
A) P>Q
B) Q>P
C) P=Q
D) with the exception of 1 instance, p will be equal to q
E) there is no relation between p and q
A) 32
B) 24
C) 20
D) 16
E) none
2) Anik, kun, and arefin, working independently, can build a wall in 10, 12, and 15 days respectively. The income from getting one wall up is tk 500. If the three work together for 16 days, how much is kun's income?
A) tk 333
B) tk 375
C) tk 667
D) tk 750
E) cannot be determined
3) Hisham noticed number at the back of his favorite mirinda bottle which consists two digits. The difference between the digits of the given number is not less than 3. If the digits of the number interchange position, the difference between the new number and the old number is 9 times the difference of the two digits. What is the number?
A) 48
B)33
C)14
D) 78
E) cannot be determined
4) Tirtho invented a board game where a square board with N number of rows with N number of squares in each row was used. Which of the following can be the possible number of squares which are not alongside the boundaries?
A) 26
B) 8
C)24
D)0
E) 82
5) Tanveer has three children. All of the children have integer ages and the product of their ages is 36. If only the sum of their ages is also known to us, figuring out their individual age is impossible unless it is also known that the oldest child has a pet dog. What are the ages of the three children?
A) 2,3,6
B) 1,2,18
C) 2,2,9
D) 3,3,4
E) Cannot be determinded
6) Nafiz had a cup filled with liquid, 3 parts of which are water and 5 parts syrup. How much of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup?
A) 1/3 B) 1/4 C) 1/5 D) 1/6 E) 1/7
7) Nawaz was looking for such a number that will always be a factor of a 5-digit number of the form xy0xy, where x can take values from 1 to 9 and y can take values from 0 to 9. Which of the following numbers qualifies Nawaz''s criteria?
I. 143 II. 77 III. 93
A) I only
B) II only
C) III only
D) I and II only
E) I and III only
8) Rituraj has an aquarium, and he will buy exactly 2 of 5 creatures. The available creatures are: two turtles, a goldfish, a catfish and a sucker fish. It is given that a turtle does not fight with the other, neither does it attack the sucker fish. However the turtle will eat any fish in the aquarium. None of the other creatures fights with one another. What is the probability that if Rituraj randomly chooses two creatures, both of them will live umharmed?
A) 6/25
B) 3/5
C) 5/7
D) 1/2
E) Cannot be determined
9) After receiving a call from Ehsan regarding a proxy class, Samia started towards Dhaka at a constant speed. At the same time, Ashfaq got a call from his teenage wife and started running towards chittagong from dhaka at a constant speed. After they crossed each other, it took Samia 40 minutes to reach Dhaka, and it took Ashfaq 90 minutes to reach chittagong. What is the ratio of samia's speed to ashfaq's speed?
A) 4:9
B) 9:4
C) 3:2
D) 13:8
E) cannot be determined
10) Walid and Andalib are playing a Board game. Both of their pieces start from opposite ends, and if Andalib's piece goes 3 steps, walids piece goes 2 steps. However, once the pieces cross each other , if Andalib's piece goes 3 steps, walid's piece goes 6 steps. If it takes 9 turns for Walid's piece to reach andalib's end, what is the number of places from one end to the other end of the board?
A) 24
B) 30
C) 45
D) 81
E) Cannot be determined
11) In a test consisting of 50 questions, a student scores 1 mark for a correct answer, -1/3 for a wrong answer, and -1/6 for not attempting a question. If Moutusi's final score is 32, the number of questions marked wrong by Moutusi cannot be less than:
A) 12 B) 9 C) 6 D) 3 E) Cannot be determined
12) Adib wanted to find a number 'n' which lies between 1 and 96, inclusive, for which it is true that n(n+1)(n+2) is divisible by 8. How many different numbers can Adib find?
A)12 B) 24 C) 32 D) 48 E) 60
13) In 2012, Abrar took four batches (A2, 2A, 4D, and 10A) in Mentors Containing a total of 100 students. If all the students were born in 1993, what is the probability that atleast two of Abrar's students will have the same birthday>
A) (100*99)/(365*364)
B) 1/365*364
C) 1-(100!/365!)
D) 1-(365!/265!*365^100)
E)1-(100!/365^100)
14) If Dave works alone, he will take 20 more hours to complete a task than if he worked with Diana to complete the task. If diana works alone, she will take 5 more hours to complete the task, what is the ratio of the time taken by Dave to that taken by Diana if each of them worked alone to complete the task?
A) 4:1
B) 2:1
C)10:1
D) 3:1
E) 1:2
15) The number of livestock in a farm at the beginning of year 2000 was 100,000. During the year, the number was increased by p%. During the next year 2001, there was a famine and the number decreased by q%. A census at the end of year 2001 revealed that the number of livestock in the farm was 100,000. Which of the following expressions is correct?
A) P>Q
B) Q>P
C) P=Q
D) with the exception of 1 instance, p will be equal to q
E) there is no relation between p and q
