MU-NLPC/Calc-aqua_rat huggingface dataset:
The total number of plums that grow during each year on a certain plum tree is equal to the number of plums that grew during the previous year, less the age of the tree in years (rounded down to the nearest integer). During its 2nd year, the plum tree grew 50 plums. If this trend continues, how many plums will it grow during its 6th year?  Choose the correct answer.
A) 36  B) 38  C) 40  D) 42  E) 48

Solution: 1st year : 0-1 (age), we take age = 0 (as the question says that we have to(rounded down to the nearest integer))   2ndyear : 1-2 (age), we take age = 1   3rd year : 2-3 (age), we take age = 2   4th year : 3-4 (age), we take age = 3   5th year : 4-5 (age), we take age = 4   6th year : 5-6 (age), we take age = 5   Thus for the 2nd year = 50,   3rd year = 50- 2= 
50- 2 = 48
48   4th year= 48-3= 
48-3 = 45
45   5th year= 45-4= 
45-4 = 41
41.   6th year= 41-5= 
41-5 = 36
36   The correct answer is 36.
Answer: A
A thief is noticed by a policeman from a distance of 200 m. The thief starts running and the policeman chases him. The thief and the policeman run at the rate of 10 km and 11 km per hour respectively. What is the distance between them after 5 minutes?  Pick one: A) 120 m B) 200 m C) 170 m D) 100 m E) 250 m

Solution: Relative speed of the thief and policeman = 11 - 10= 
11 - 10 = 1
1 km/hr.   Distance covered in 5 minutes= 1/60 * 5 = 1/12 km = 80 m.   Distance between the thief and policeman = 200 - 80= 
200 - 80 = 120
120 m   120 m
Answer: A
What is the probability of rolling one six-sided dice, and getting a different number on each die? Choose the correct choice from the following options:
A) 1/12
B) 1/3
C) 1
D) 5/9
E) 7/18

Solution: MAGOOSHOFFICIAL SOLUTION   For the first die, we can roll any one of six numbers. For the second die, we can roll any number save for the number we rolled on the first die, giving us 5 possibilities. For the third die, we can roll four different numbers (we can’t roll the number we rolled on the first or second die.   6= 6 possibilities out of 216 total possibilities. (For total possibilities we get 6 = 6).   6/ 6= 
6/ 6 = 1
1   Answer: 1.
Answer: C
Ratio between two numbers is 3: 4 and their sum is 420. Find the smaller number?  Pick
A) 23	B) 180	C) 287	D) 137	E) 192

Solution: Explanation:   3x + 4x = 420   x = 60 => 3x = 180   Answer: 180
Answer: B
A and B together have Rs. 1210. If 4/15 of A's amount is equal to 2/5 of B's amount. How much amount B have.  Pick one: A) 83.5% B) 87.5% C) 88.5% D) 89.5% E) 484 rupees

Solution: Explanation:   In this type of question, we will first try to calculate the ratio of two persons. Once we get ratio then we can easily get our answer. So lets solve this.   4/15A= 2/5B   A=(2/5∗14/4)B   A=3/2B   A/B=3/2   A:B=3:2   B's Share = 2/5∗1210=484   Option 484 rupees
Answer: E
A man can swim in still water at 7.5 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is?
Choose the correct choice: A) 1.7 B) 1.4 C) 2.5 D) 1.5 E) 1.1

Solution: M = 7.5   S = x   DS = 7.5 + x   US = 7.5 + x   7.5 + x = (7.5 - x)2   7.5 + x = 15 -2x   3x = 7.5   x = 2.5   Answer: 2.5
Answer: C
A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. How far is the place?
Choose the correct choice from the following.
A) 2.89	B) 2.88	C) 2.82	D) 2.87	E) 2.84

Solution: M = 6   S = 1.2   DS = 6 + 1.2= 
6 + 1.2 = 7.2
7.2   US= 6 - 1.2= 
6 - 1.2 = 4.8
4.8   x/7.2 + x/4.8= 1   x = 2.88   Answer:2.88
Answer: B
A boat can move upstream at 30 kmph and downstream at 35 kmph, then the speed of the current is?	Pick: A) 5 B) 6 C) 7 D) 8 E) 2.5

Solution: US = 30   DS = 35   M = (35 - 30)/2= 
(35 - 30)/2 = 5/2 = around 2.5
2.5   Answer: 2.5
Answer: E
The ratio of two numbers is 3:4 and their sum is 14. The greater of the two numbers is?
Choose the most appropriate option.
A) 12 B) 14 C) 16 D) 8 E) 19

Solution: 3:4   Total parts = 7   = 7 parts --> 14 (7 Ã— 2 = 14)   = 1 part ---->2 (1 Ã— 2 = 2)   = The greater of the two number is = 4   = 4 parts ----> 2 (2 Ã— 4 = 8)   8)
Answer: D
The average marks of a class of 30 students is 40 and that of another class of 50 students is 60. Find the average marks of all the students?	Pick:
A) 52.7	B) 52.9	C) 52.4	D) 52.5	E) 52.1

Solution: Sum of the marks for the class of 30 students = 30 * 40= 
30 * 40 = 1_200
1200   Sum of the marks for the class of 50 students= 50 * 60= 
50 * 60 = 3_000
3000   Sum of the marks for the class of 80 students=   1200 + 3000= 
1200 + 3000 = 4_200
4200   Average marks of all the students= 4200/80= 
4200/80 = 105/2 = around 52.5
52.5   Answer: 52.5
Answer: D
A dishonest dealer professes to sell goods at the cost price but uses a false weight and gains 25%. Find his false weight age?  Pick one:
A) 878 B) 768 C) 800 D) 778 E) 876

Solution: 25 = E/(1000 - E) * 100   1000 - E = 4E   1000 = 5E => E = 200   1000 - 200= 
1000 - 200 = 800
800   Answer:800
Answer: C
A man saves Rs 150 at the end of each year and lends the money at 5% compound interest. How much will it become at the end of 3 years.	Choose the correct answer:
A) Rs 452
B) Rs 492.01
C) Rs 496.52
D) Rs 496.03
E) None of these

Solution: Explanation:   =[150(21/20Ã—21/20Ã—21/20)+150(21/20Ã—21/20)+150(21/20)]=496.52   Option Rs 496.52
Answer: C
A number when divided by 214 gives a remainder 35, what remainder will be obtained by dividing the same number 14?
Select
A) 7 B) 10 C) 11 D) 2 E) 3

Solution: Explanation:   214 + 35= 
214 + 35 = 249
249/14= 11 (Remainder)   Answer: 11
Answer: C
If x is chosen at random from the set {1, 2, 3, 4} and y is to be chosen at random from the set {5, 6, 7}, then what is the probability that xy will be even? Choose the correct answer
A) 5/6	B) 2/6	C) 2by3	D) 1/2	E) 1/4

Solution: S = {(1,5), (1,6), (1,7), (2,5), (2,6), (2,7), (3,5), (3,6), (3,7), (4,5), (4,6), (4,7)}   Total element n(S) = 12   xy will be even when even x or y or both will be even.   Events of xy being even is E.   E = {(1,6), (2,5), (2,6), (2,7), (3,6), (4,5), (4,6), (4,7)}   n(E) = 8   P(E) = n(E)/n(S)   = 8/12   = 2/3   ANSWER:2by3
Answer: C
A circular jogging track forms the edge of a circular lake that has a diameter of 2 miles. Johanna walked once around the track at the average speed of 5 miles per hour. If t represents the number of hours it took Johanna to walk completely around the lake, which of the following is a correct statement?  Choose the correct choice from the following choices.
A) 0.5< t < 0.75  B) 1.75< t < 2.0  C) 1.0 < t < 1.5  D) 2.5 < t < 3.0  E) 3 < t < 3.5

Solution: D=2, and R=1   circumference thus is 2pi miles   we know that she walked 5mph   knowing the formula rt=D, we can deduce that t= D/r   D is 2pi miles and r is 5mph   t = 2pi/5   pi can be rewritten as 22/7   2*22/7 = 44/7 and multiply this by 1/5 = 44/35. This is greater than 1, but less than 1.5, therefore, 1<t<1.5. Answer choice 1.0 < t < 1.5.
Answer: C
A horse and cow were sold for Rs.12000 each. The horse was sold at a loss of 20% and the cow at a gain of 20%. The entire transaction resulted in : Options:
A) No loss or gain  B) Loss of Rs.1000  C) Gain of Rs.1000  D) Gain of Rs.2000  E) None of these

Solution: Explanation:   In the special case of profit and loss percentages are equal and Selling price is same, then the transaction always results in Loss. This loss percentage is given by a simple formula −(x/10)2   So in this case, Profit% = Loss% = 20. So x = 20   Loss percentage = −(20/10)2=−4   Total S.P = Rs.24000   Cost price = 24000×100/96 = 25000   Loss = Rs.1000   Correct Option : Loss of Rs.1000
Answer: B
A train passes a station platform in 42 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?  Choose the correct choice from the following options.
A) 177 m B) 176 m C) 240 m D) 187 m E) 330 m

Solution: Speed = [54 * 5/18] m/sec = 15 m/sec.   Length of the train = (15 * 20)= 
(15 * 20) = 300
300 m.   Let the length of the platform be x meters.   Then, x + 300 / 42= 15   x + 300 = 630   x = 330m.   Answer: 330 m
Answer: E
The sum of the present ages of a father and his son is 60 years. Six years ago, father's age was five times the age of the son. After 6 years, son's age will be?
Select the correct option
A) 77 years
B) 67 years
C) 20 years
D) 55 years
E) 61 years

Solution: Explanation:   20 yearslue : (60 - x) - 6 = 5(x - 6)   Answer: 20 years
Answer: C
In how many ways can you seat 7 people on a bench if one of them, Rohit, does not want to sit on the middle seat or at either end?  Pick
A) 720  B) 1720  C) 2880  D) 5040  E) 10080

Solution: Since Rohit does not want to sit on the middle seat or at either end (3 chairs), then he can choose 4 chairs to sit. The remaining 6 people can sit in 6! ways. Thus the # of arrangements is 4*6! = 2,880.   Answer: 2880.
Answer: C
Which of the following fractions is the largest?  Choices
A) 5/6
B) 11/14
C) 12/15
D) 17/21
E) 29/35

Solution: another way is by taking LCM of denominators(2*3*5*7)   (a) 175 (as lcm is 2*3*5*7 where 2*3 part is already in denominator just multiply 5*7 to numerator) ,similarly   (b) 165   (c)168   (d)170   (e)174   clearly (a) is largest..   5/6ns 5/6
Answer: A
Ramesh purchased a refrigerator for Rs. 12500 after getting a discount of 20% on the labelled price. He spent Rs. 125 on transport and Rs. 250 on installation. At what price should it be sold so that the profit earned would be 10% if no discount was offered?
Select the correct option:
A) 17608 B) 17606 C) 17604 D) 17600 E) 117601

Solution: Price at which the TV set is bought = Rs. 12,500   Discount offered = 20%   Marked Price = 12500 * 100/80 = Rs. 15625   The total amount spent on transport and installation = 125 + 250 = Rs. 375\Total price of TV set = 15625 + 375 = Rs. 16000   The price at which the TV should be sold to get a profit of 10% if no discount was offered = 16000 * 110/100 = Rs. 17600.Answer: 17600
Answer: D
An automobile company has a production target to get profits annually. The target production this year is 1/10 of last year's production. If the target production is reduced by 20% of last year's target what percentage of target production of last year's target does he need to complete in order to get profit?	Choose the correct choice from the following choices:
A) 15/20 B) 17/10 C) 6/20 D) 4/5 E) 14/20

Solution: We have 1/10 and 20% that is 1/5   Let us assume the last year's target to be 20   This year's target is 20% less than last year's target=16   The target reached this year is   1/10*20= 
  1/10*20 = 2
2   Remaining is  16-2= 
 16-2 = 14
14   Required 14/20   Answer (14/20)
Answer: E
A merchant has announced 25% rebate on prices of ready-made garments at the time of sale. If a purchaser needs to have a rebate of Rs. 400, then how many shirts, each costing Rs. 320, should he purchase?
Answers:
A) 10  B) 7  C) 6  D) 5  E) 4

Solution: Solution: Discount on one shirt,   = 25% of 320 = 320*25/100 = Rs. 80.   Hence, number of shirt he must buy to get a rebate of Rs. 400 = 400/80= 
400/80 = 5
5.   Answer: Option 5
Answer: D
A, B, C enter into a partnership investing Rs. 35,000, Rs. 45,000 and Rs. 55,000 respectively. The respective shares of A, B, C in annual profit of Rs. 40,500 are? Pick:  A) Rs. 10,500, Rs. 13,500, Rs. 16,500  B) Rs. 10,500, Rs. 13,500, Rs. 16,509  C) Rs. 10,500, Rs. 13,500, Rs. 16,555  D) Rs. 10,500, Rs. 13,500, Rs. 16,506  E) Rs. 10,500, Rs. 13,500, Rs. 16,504

Solution: A:B:C = 35000 : 45000 : 55000 = 7:9:11   A's share = 40500 * 7/27 = Rs. 10500   B's share = 40500 * 9/27 = Rs. 13500   C's share = 40500 * 11/27 = Rs. 16500   Rs. 10,500, Rs. 13,500, Rs. 16,500nswer: Rs. 10,500, Rs. 13,500, Rs. 16,500
Answer: A
If k is a positive even integer, what is the smallest possible value of k such that 3675*k is the square of an integer?
Choose the correct choice from the following:	A) 3	B) 9	C) 12	D) 15	E) 20

Solution: 3675=31∗52∗72   Now , is the most important part of this question   K must be even ( negate options A, B and D ) W e are left with C and E   Try one to confirm the answer...   Let's try (E)   20=22∗51   3675∗20=22∗31∗53∗72 ( 12an not square of an Integer )   So, Answer must be (12)....
Answer: C
Two trains are traveling on parallel tracks in the same direction. The faster train travels at 130 miles per hour, while the slower train travels at 80 miles per hour. At 2 o’clock the faster train is 20 miles behind the slower one. How far apart are the two trains at 5 o'clock? Options
A) 60 miles B) 80 miles C) 90 miles D) 130 miles E) 400 miles

Solution: Answer = D. 130 miles   Relational speed = 130 - 80= 
130 - 80 = 50
50 miles per hour   In 3 hours, difference= 50 * 3= 
50 * 3 = 150
150 miles   Fast train trailing 20 miles, so effective difference= 150 - 20= 
150 - 20 = 130
130 miles
Answer: D
An oil cylinder was 3/4th full. When SIX bottles of oil is poured into it, it is 4/5th full. How many bottles of oil
can the full cylinder hold? Pick:  A) 120  B) 115  C) 140  D) 130  E) 135

Solution: (4/5 -3/4) cylinder is filled by 6 bottles     0.8 -0.75= 
  0.8 -0.75 = 0.05
0.05 cylinder is filled by 6 bottles   1 cylinder is filled by   6/0.05= 
  6/0.05 = 120
120 bottles   120NSWER:120
Answer: A
How many cuboids of length 5 m, width 6 m and height 3 m can be farmed from a cuboid of 18 m length, 15 m width and 2 m height. Select the correct option:  A) 4  B) 6  C) 10  D) 8  E) 11

Solution: (18 Ã— 15 Ã— 12)/(5 Ã— 3 Ã— 2) = 6   Answer is 6.
Answer: B
What is the units digit of (22^4)(16^3)(41^8)? Answers
A) 2	B) 3	C) 4	D) 5	E) 6

Solution: The units digit of 22^4 is the units digit of 2^4 which is 6.   The units digit of 16^3 is the units digit of 6^3 which is 6.   The units digit of 41^8 is the units digit of 1^8 which is 1.   The units digit of 6*6*1 is 6.   The answer is 6.
Answer: E
A bus starts from city X. The number of women in the bus is half of the number of men. In city Y, 14 men leave the bus and seven women enter. Now, number of men and women is equal. In the beginning, how many passengers entered the bus ?  Choose the correct option:  A) 63  B) 30  C) 36  D) 45  E) 46

Solution: Explanation:   Originally, let number of women = x. Then, number of men = 2x.   So, in city Y, we have : (2x - 14) = (x + 7) or x = 21.   Therefore Total number of passengers in the beginning = (x + 2x) = 3x = 63.   63nswer: 63
Answer: A
A box contains 10 black,5 red and 4 green marbles. 3 marbles are drawn from the box at random. What is the probability that all the three marbles are of the same color?  Choose the correct choice from the following options:
A) 143/969
B) 134/969
C) 120/969
D) 19/969
E) 120/134

Solution: Explanation:   Total marbles in a box = 10 black + 5 red + 4 green marbles = 19 marbles   3 marbles are drawn from 19 marbles at random. Therefore,   n(S) = 19C3= 969 ways   Let A be the event that 2 marbles drawn at random are of the same color. Number of cases favorable to the event A is   n(A) = 10C3+ 5C3 + 4C3 = 120 +10 + 4= 
120 +10 + 4 = 134
134   Therefore, by definition of probability of event A,   P(A)= n(A)/n(S) = 134/969   ANSWER:134/969
Answer: B
The cost price of 12 articles is equal to the selling price of 10 articles. What is the profit percent?	Choose the correct option:
A) 10%
B) 20%
C) 30%
D) 40%
E) 50%

Solution: 10*SP = 12*CP   SP = 1.2*CP   The profit percent is 20%.   The answer is 20%.
Answer: B
Anmol can eat 27 pastries in a hour.
Aakriti can eat 2 pastries in 10 minutes.
Divya can eat 7 pastries in 20 minutes.
How long will it take them to eat a 180 pastries ?  Choose the correct choice from the following
A) 2 hours.	B) 1 hours.	C) 5 hours.	D) 4 hours.	E) 3 hours.

Solution: In one hour, Anmol eats 27 pastries, Aakriti eats 12, and Divya eats 21. A total of 60 pastries. Therefore 180 pastries would take 180 ÷ 60 = 3 hours.   ANSW3 hours.R 3 hours.
Answer: E
For any non-zero a and b that satisfy |ab| = ab and |C| = -c
|b - 4| + |ab - b| = ?	Choose the correct choice from the following options:	A) a) ab - 4	B) b) b - 2b + 4	C) c) ab + 4	D) d) 2b - ab - 4a	E) e) 4 - ab

Solution: |a| = -a Suggests that 'a' is Negative   |ab| = ab Suggests that 'ab' is Positive   'ab' is Positive Suggests that 'a' and 'b' have same Sign i.e. either both positive or both negative   But since 'a' is Negative therefore 'b' is Negative too.   Since b is negative so |b - 4| = -b+4   Since ab is Positive and b is Negative so |ab - b| = ab - b   i.e. |b - 4| + |ab - b| = -b+4 + ab - b =ab - 2b + 4   Answer: Option b) b - 2b + 4
Answer: B
An automobile parts supplier charges $25 per package of gaskets. When a customer orders more than 10 packages of gaskets, the supplier charges 4/5 the price for each package in excess of 10. During a certain week, the supplier sold 50 packages of gaskets. If 20 percent of the gaskets went to Company X, 15 percent to Company Y, and the rest to Company Z, what was the total amount, in dollars, that the parts supplier received in payment for the gaskets?	Options
A) 1105 B) 1245 C) 1275 D) 1215 E) 1150

Solution: $25 per packet of gasket in case a customer orders less than 10   in case a customer orders > 10 price per gasket = 25*4/5= 
25*4/5 = 20
20   a certain week the supplier sold 60 gasket   1.he sold 20 % of the gaskets to X= 10 gaskets = 25*10= 
25*10 = 250
250   2.he sold 30 % of the gaskets to Y= 15 gaskets = 25*10+20*5= 
25*10+20*5 = 350
350   3.he sold remaining 50% to z=25 gaskets = 25*10= 
25*10 = 250
250 + 20*15= 
250 + 20*15 = 550
550   thus ,total money earned   250+350+550= 
250+350+550 = 1_150
1150   Answer is 1150
Answer: E
Average of all prime numbers between 40 to 50  Choose the correct option:
A) 37
B) 37.8
C) 43.6
D) 39.8
E) 40

Solution: Explanation:   Prime numbers between 40 and 50 are:   41, 43, 47   Average of prime numbers between 40 to 50 will be   (41+43+47 / 3)=131 / 3 =43.6   Option 43.6
Answer: C
Each person who attended a company meeting was either a stockholder in the company, an employee of the company or both. If 62 percent of these who attended the meeting were stockholders and 51 percent were employees. What percent were stockholders, who were not employees?	Choose the correct choice from the following:
A) 52	B) 49	C) 54	D) 55	E) 56

Solution: I came up with the same answer choice B, but my approach was slightly different!   51% were employees which shall cover those who were only employees and those who were both shareholders and employees.   Thus, the number of attendants who were only shareholders is 100% - 51% = 49%.  100  - 51= 
  100  - 51 = 49
49%.
Answer: B
What is the greatest 6-digit number when divided by 6, 7 ,8 , 9, and 10 leaves a remainder of 4, 5, 6, 7, and 8 respectively?	Choose the correct option
A) 456780 B) 678910 C) 997479 D) 997918 E) 997920

Solution: When you divide a positive integer by 10, the remainder will just be the units digit. We know the remainder is 8 when we divide by 10, so 997918 is the only possible answer.
Answer: D
What is the square root of 3,249?  Choose the correct answer
A) A)18  B) B)9  C) C)45  D) D)62  E) E)57

Solution: A square root of a number is a number times itself equals the original number.   Ex) The square root of 81 is 9 because 9 times itself(9) equals the original number(81).   57*57=3,249   3249 divided by x = 57   x=57   (57)57
Answer: E
There are 6 boxes numbered 1, 2,3,4,5 and 6. Each box is to be filled up either with a red or a green ball in such a way that at least 1 box contains a green ball & the boxes containing green balls are consecutively numbered. The total no. of ways in which this can be done is?  Select the correct option.
A) 18 B) 19 C) 21 D) 25 E) 27

Solution: If only one of the boxes has a green ball, it can be any of the 6 boxes. So, this can be achieved in 6 ways.   If two of the boxes have green balls and then there are 5 consecutive sets of 2 boxes. 12, 23, 34, 45, 56.   Similarly, if 3 of the boxes have green balls, there will be 4 options.   If 4 boxes have green balls, there will be 3 options.   If 5 boxes have green balls, then there will be 2 options.   If all 6 boxes have green balls, then there will be just 1 options.   Total number of options = 6 + 5 + 4 + 3 + 2 + 1= 
6 + 5 + 4 + 3 + 2 + 1 = 21
21   21
Answer: C
For integers M and N, when M is divided by N, the remainder is odd. Which of the following must be true?
Choose the correct choice from the following choices
A) The sum M + N is odd	B) M and N share no common factors other than 1	C) MN is odd	D) M is odd	E) either integer M or integer N is odd

Solution: either integer M or integer N is odd   either integer M or integer N is odd
Answer: E
There are 6561 balls out of them 1 is heavy.Find the min. no. of times the balls have to be weighed for finding out the haevy ball.	Choose the correct choice from the following options:
A) 7	B) 8	C) 9	D) 10	E) 11

Solution: The simple logic is to divide total balls into three sets. Weigh any two sets against each other(these two must contain equal number of balls). From this we can identify which set contains the heavy ball. Divide this set into three and repeat until you find the heavier ball. Under this logic, the minimum number of weighings required turns out to be the smallest integer greater than or equal to log(n), where n is the total number of balls and the base of logarithm is 3. Or simply [log(n)/log(3)] with any base. Here, n = 6561. log 6561 / log 3 = 8   ANSWER:8
Answer: B
A can finish a work in 24 days, B in 9 days and C in 12 days. B and C start the work but are forced to leave after 3 days. When A done the work?
Choose the correct choice from the following answers.
A) 10 days	B) 12 days	C) 13 days	D) 9 days	E) 14 days

Solution: B+C ==>1/9+1/12 = 7/36   B ,C =in 3 days = 7/36*3 = 7/12   remaining work = 1-7/12 = 5/12   1/24 work is done by 10 days in 1 day   5/12 work is done 10 days 24*5/12= 
24*5/12 = 10
10 days   10 daysNSWER 10 days
Answer: A
What is the area of a square with perimeter 12P ? Choices
A) 16p^2  B) 4P  C) 9P^2  D) P/16  E) P^2/16

Solution: Each side is 3p   A = (3p)^2 = 9p^2   Answer 9P^2
Answer: C
Average of first five multiples of 3 is	Pick:
A) 9
B) 11
C) 13
D) 15
E) 17

Solution: Explanation:   9verage=3(1+2+3+4+5) / 5=45 / 5= 
45 / 5 = 9
9   Option 9
Answer: A
A bag contains 7 red balls, 5 green balls and 6 white balls. A ball is drawn at
random from the box. What is the probability that the ball drawn is either red or green?	Choose the correct choice from the following choices:
A) 2/3 B) 3/5 C) 1/5 D) 7/15 E) 8/15

Solution: Total number of balls = (7 + 5 + 6)= 
(7 + 5 + 6) = 18
18.   Therefore, n(S)= 18.   Let E1 = event of drawing a red ball.   and E2 = event of drawing a green ball.   Then, E1 n E2 = f.   P (E1 n E2) = P(E1) + P(E2) = (7/18 + 5/18) = 2/3.   2/3NSWER:2/3
Answer: A
The average of five numbers is 9. The average of first two numbers is 7 and the average of last two numbers is 12. What is the middle number?	Choose the correct choice from the following:  A) 7  B) 8  C) 5  D) 10  E) 6

Solution: The total of five numbers = 5x9 = 45   The total of first 2 and last 2 numbers is = 2 X 7+2 X 12 = 38   So, the middle number is  (45 - 38 )= 
 (45 - 38 ) = 7
7   7
Answer: A
A man is 24 years older than his son. In two years, his age will be twice the age of his son. The present age of this son is Choose the correct choice from the following answers:
A) 78 years B) 22 years C) 88 years D) 66 years E) 65 years

Solution: Let's Son age is x, then Father age is x+24.   => 2(x+2) = (x+24+2)   => 2x+4 = x+26   => x = 22 years   Answer: 22 years
Answer: B
What is the smallest 6 digit number exactly divisible by 111?
Select the correct option
A) 100010  B) 100012  C) 100011  D) 100013  E) 120012

Solution: Smallest 6 digit number = 100000   100000/111 = 900, remainder = 100. Hence 11 more should be added to 100000   to get the smallest 6 digit number exactly divisible by 111   => smallest 6 digit number exactly divisible by 111 = 100000 + 11= 
100000 + 11 = 100_011
100011   Answer is 100011
Answer: C