MU-NLPC/Calc-aqua_rat huggingface dataset:
A student missed 6% of the questions on a test. If the student missed 12 questions, how many questions were on the test?
Choices.
A) 100 B) 150 C) 200 D) 250 E) 300

Solution: 12 is 6% of the total answers on the test.   If the total number of answers on the test is X then   6/100 = 12/X   100/6 * 12 = X   1200/6= 
1200/6 = 200
X   200= X   200)
Answer: C
There are two clocks that are set at 8 0'clock in the morning. One clock is correct and the other clock gains 5 minutes per hour. When the faster clock shows the time 12:20 in the afternoon, what does the correct clock show?	Choose the correct choice from the following options:
A) 12:00:00	B) 11:45	C) 12:26	D) 11:50	E) 11:56

Solution: Faster clock gains 5 minutes per hour   At 8 0'clock both the clocks are set   At 9 0'clock -   The correct clock shows 9:00:00   The faster clock is at 9:05:00 (1 hour + gained 5 minutes)   At 10 0'clock   The correct clock is at 10:00:00   The faster clock is at 10:10:00 (2 hours + gains 10 minutes)   At 11 0'clock -   The correct clock is at 11:00:00   The faster clock is at 11:15:00 (3 hours + gains 15 minutes)   In 4 hours the faster clock would gain 20 minutes and shows 12:20:00 at that point which is 12 0'clock in the correct clock.   The answer is 12:00:00
Answer: A
80% of a number is added to 120, the result is the same number. Find the number?  Choose the correct choice from the following answers.
A) 600  B) 288  C) 1687  D) 997  E) 121

Solution: (80/100) * X + 120 = X   2X = 1200   X = 600   600nswer:600
Answer: A
Mr. Srinivas saves one coin of 5 on first day of the
week, three coins of 5 on the second day of the week.
Five coins of 5 on third day and so on. How much money will he has at the end of the week?
Options:
A) 238  B) 245  C) 2867  D) 987  E) 111

Solution: Number of   5 coins with him at the end of week = 5 × (1 + 3 + 5 + 7 + 9 + 11 + 13) = 5 × (sum of first 7 odd numbers) (By using the formula discussed earlier). ∴ Sum of all numbers = 5 × 72 = 245.   Answer:245
Answer: B
A popular website requires users to create a password consisting of the digits {1,2,3,4,5,6,7}. If no digit may be repeated and each password must be at least 6 digits long, how many passwords are possible?
Choose the most appropriate option.
A) 6! + 7!  B) 2 x 7!  C) 6! x 7!  D) 13!  E) 14!

Solution: If we choose the 7 different digits then they can be arranged in 7! ways.   The number of possible 6-digit passwords is 7*6*5*4*3*2 = 7!   The total number of passwords is 7! + 7! = 2*7!   The answer is 2 x 7!.
Answer: B
A train is 360 meter long is running at a speed of 45 km/hour. In what time will it pass a bridge of 140 meter length? Choose the most appropriate option
A) 30	B) 80	C) 40	D) 70	E) 60

Solution: Speed = 45 Km/hr = 45*(5/18) m/sec = 25/2 m/sec   Total distance = 360+140= 
360+140 = 500
500 meter   Time= Distance/speed   = 500 * (2/25)= 
500 * (2/25) = 40
40 seconds   Answer: Option 40
Answer: C
A began business with 12500 and is joined afterwards by B with 50000. When did B join, if the profits at the end of the year are divided equally?
Choose the most appropriate option:
A) 8 months B) 9 months C) 10 months D) 7 months E) None of these

Solution: Let B join after x months of the start of the business so that B’s money is invested for (12 – x) months.   ∴ Profit ratio is 12 × 12500 : (12 – x) × 50000   or 12 : 4(12 – x)   Since profit is equally divided so   12 = 4(12 – x) or x = 9. Thus B joined after 9 months.   Answer 9 months
Answer: B
How many words can be formed by using all letters of the word 'BIHAR' ?	Choose the correct option
A) 112
B) 120
C) 157
D) 136
E) 142

Solution: The word 120IHAR contains 5 different letters   Required number of words = 5P5 = 5! = 5*4*3*2*1= 
5*4*3*2*1 = 120
120   Answer is 120
Answer: B
In a three digit number, the hundred digit is 2 more than the tens digit and the units digit is 2 less than the tens digit. If the sum of the digits is 27, find the number?	Pick:
A) 867
B) 1179
C) 1196
D) 1098
E) 1197

Solution: 1197   1197   Let the three digit numbers be 100a + 10b + c   a = b + 2   c = b - 2   a + b + c = 3b = 27=> b = 9   So a = 11 and b = 7   Hence the three digit number is: 1197
Answer: E
Nina has exactly enough money to purchase 6 widgets. If the cost of each widget were reduced by $1.15, then Nina would have exactly enough money to purchase 8 widgets. How much money does Nina have?	Choose the correct option:
A) $22 B) $27.6 C) $30 D) $36 E) $40

Solution: B its is.   Let price = X   (x-1.15)8 = 6X   X= 4.6   hence total money = 6*4.6= 
6*4.6 = 27.6
27.6
Answer: B
A train crosses a platform of 120 m in 15 sec, same train crosses another platform of length 180 m in 18 sec. then find the length of the train? Choose one
A) 100
B) 180
C) 110
D) 120
E) 130

Solution: Length of the train be ‘X’   X + 120/15 = X + 180/18   6X + 720 = 5X + 900   X = 180m   Answer: Option 180
Answer: B
If a and b are multiples of 3 then which are all the multiples of 3
1) a/b
2) a^b
3) a+b
4) a-b
5) a*b Select the correct option
A) 1,3  B) 1,2,4,5  C) 1,2,5  D) all of these  E) 1,2,3,5

Solution: a*b a^b a+b a-b are multiples of 3 except a/b   ANSW1,2,3,5R:1,2,3,5
Answer: E
Three hundred students at College Q study a foreign language. Of these, 130 of those students study French, and 190 study Spanish. If at least 50 students who study a foreign language at College Q study neither French nor Spanish, then the number of students who study Spanish but not French could be any number from  Choose the correct choice from the following options.
A) 10 to 40	B) 40 to 100	C) 60 to 100	D) 60 to 120	E) 70 to 110

Solution: 130 students study French   170 students do not study French   190 students study Spanish   110 students do not study Spanish   50 students study neither French nor Spanish   170-110= 
170-110 = 60
60   170-50= 
170-50 = 120
120   D. 60 to 120
Answer: D
In how many different ways can the letters of the word MISSISSIPPI be arranged?  Choose the correct choice from the following answers:
A) 11!/(4!4!2!)
B) 11!/4!
C) 11!/2!
D) 11!
E) 2×11!

Solution: Number of ways 11 letter can be arranged = 11!   The 11! arrangement will also contain duplicates because of the characters   that are repeated   We have 4 S's =4! repeats   We have 4 I's =4! repeats   We have 2 P's =2! repeats   So the total possible arrangement will be 11!/4!4!2!   11!/(4!4!2!)ns 11!/(4!4!2!)
Answer: A
Find a a prime number from the options below.	Choose the correct choice from the following
A) 58  B) 59  C) 60  D) 62  E) 64

Solution: Clearly, 59 is a prime number.   59
Answer: B
One water pump can fill half of a certain empty tank in 7 hours. Another pump can fill half of the same tank in 7.5 hours. Working together, how long will it take these two pumps to fill the entire tank?	Options:	A) 7 7/13	B) 1 5/8	C) 3 1/4	D) 7 7/29	E) 3 1/2

Solution: One pump can fill a tank in 7 hours and another in 7.5 hours   so the rate at which both can half fill the tank is (1/7+1/7.5) => 29/105   Thus half of the tank can be filled in 105/29   so for filling the complete tank => 105/29*2 = 210/29 =7 7/29   ANSWER:7 7/29
Answer: D
If the annual interest on a principal is 4%, how many years before the amount is double?	Choose the correct choice:
A) 22
B) 25
C) 12
D) 13
E) 17

Solution: P = (P*4*R)/100   R = 20%   Answer: 25
Answer: B
A and B started a business with an investment of Rs.26000 and Rs.28000. After two months C joined in the business with an investment of Rs.32000, what is share of C in the half year profit of Rs.9040 ?  Choose one:	A) 3360	B) 3120	C) 2940	D) 2560	E) 3550

Solution: Investment x Time.   A = 26000 x 6 = 156000.   B = 28000 x 6 = 168000.   C = 32000 x 4 = 128000.   Ratio of shares A : B : C = 39 : 42 : 32 = [ Total 113 units ]   Share of C in the profit = 9040 × 32 / 113 = 2560   Option 2560
Answer: D
A brick measures 20 cm * 10 cm * 7.5 cm how many bricks will be required for a wall 25 m * 2 m * 0.75 m? Choose the correct choice from the following options.
A) 22377 B) 27782 C) 27891 D) 25000 E) 18771

Solution: 25 * 2 * 0.75 = 20/100 * 10/100 * 7.5/100 * x   25 = 1/100 * x => x = 25000   Answer: 25000
Answer: D
A,B,C together can do a work in 10 days. A alone can do the work in 50days and B alone can do the same work in 60 days. Find in what time C alone can do that work?
Choose one.
A) 15.8days  B) 17days  C) 19.5days  D) 20.6days  E) 25.4days

Solution: The required answer is = 10*50*60 / 50*60-10(50+60)   = 30000/1900 = 15.8days   15.8daysnswer is 15.8days
Answer: A
The cash difference between the selling prices of an book at a profit of 4% and 6% is $ 3. The ratio of the two selling prices is:
Choose the correct choice from the following answers:
A) 50:53
B) 58:53
C) 52:53
D) 42:36
E) 38:53

Solution: C   52:53   Let C.P. of the book be $ x.   Then, required ratio = 104% of x / 106% of x   = 104/106 = 52/53 = 52:53
Answer: C
The speed at which a man can row a boat in still water is 26 kmph. If he rows downstream, where the speed of current is 4 kmph, what time will he take to cover 150 metres?  Select
A) 18  B) 27  C) 28  D) 12  E) 25

Solution: Speed of the boat downstream = 26 + 4= 
26 + 4 = 30
30 kmph= 30 * 5/18 = 8.33 m/sHence time taken to cover 150 m = 150/8.33= 18 seconds.18nswer:18
Answer: A
A T.V was sold at a loss of 10%. If it was sold for Rs.3500 more, there would have been a gain of 10%. What is the cost price?
Answers.
A) Rs. 17000
B) Rs. 18500
C) Rs.17500
D) Rs. 15500
E) Rs.15000

Solution: 90%   110%   --------   20% ---- 3500   100% ---- ? => Rs.17500   Answer:Rs.17500
Answer: C
At the end of three years what will be the compound interest at the rate of 10% p.a. on an amount of Rs.20000?  Choose the correct option.
A) 6620	B) 6628	C) 6629	D) 6624	E) 6622

Solution: 6620 = 20000(11/10)3   = 26620   = 20000   ----------   6620   6620nswer: 6620
Answer: A
A train passes a station platform in 36 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 answers.
A) 230 B) 240 C) 250 D) 260 E) 270

Solution: Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train = (15 x 20)m = 300 m. Let the length of the platform be x meters. Then, (x + 300)/36 = 15 ==> x + 300 = 540 ==> x = 240 m.   Answer: Option 240
Answer: B
Machine A can do a certain job in 8 hours. Machine B can do the same job in 10 hours. Machine C can do the same job in 12 hours. All three machines start the job at 9:00 a.m. Machine A breaks down at 11:00 a.m., and the other two machines finish the job. Approximately what time R will the job be finished?  Choose the correct choice from the following choices
A) Noon
B) 12:30 p.m.
C) 1:00 p.m.
D) 1:30 p.m.
E) 2:00 p.m.

Solution: Ans: C (1:00pm)   From 9:00-11:00c(2 hrs)   A can do 1/8 Job/hr. so in 2 hours he can do 1/4 job.   B can do 1/10 job/hr so in 2 hrs. he can do 1/5 Job.   C can do 1/12 job/hr so in 2 hours he can do 1/6 job.   Total = 1/4+1/5+1/6 = 37/60 Job   Now balance work needs to be done by B and C.   Balance Work= 23/60 Job   Combined rate of B and C = 1/10+1/12 = 11/60 job/hr.   So they will do 22/60 work in 2 hrs (approx. to the balance work of 23/60)   Hence the Job will be completed 2hrs. after 11:00 i.e. @ 1:00pm=R   Ans: 1:00 p.m. (1:00pm)
Answer: C
The perimeter of a triangle is 32 cm and the inradius of the triangle is 2.5 cm. What is the area of the triangle?
Choose the correct choice from the following answers:  A) 76 cm2  B) 56 cm2  C) 18 cm2  D) 98 cm2  E) 40 cm2

Solution: Area of a triangle = r * s   Where r is the inradius and s is the semi perimeter of the triangle.   Area of triangle   = 2.5 * 32/2= 
2.5 * 32/2 = 40
40 cm2   Answer:40 cm2
Answer: E
6 friends went to a hotel and decided to pay the bill amount equally. But 5 of them could pay Rs. 100 each as a result 6th has to pay Rs. 100 extra than his share. Find the amount paid by him.
Choose the correct choice from the following answers:
A) 156	B) 220	C) 130	D) 240	E) None

Solution: Explanation:   Average amount paid by 5 persons = Rs. 100   Increase in average due to Rs. 120 paid extra by the 6th men = Rs. 100/5= Rs. 20   Therefore, Average expenditure of 6 friends = Rs. 100 + Rs. 20 = Rs. 120   Therefore, Amount paid by the 6th men = Rs. 120+ Rs. 100 = Rs. 220   Correct Option: 220
Answer: B
The average of 11 numbers is 10.9. If the average of the first six numbers is 10.5 and that of the last six numbers is 11.4,then the middle number is?
Choose the correct choice from the following options:
A) 11.5 B) 12.6 C) 15.3 D) 9.3 E) 10.6

Solution: Middle number = 10.5*6 + 11.4*6 - 10.9*11 = 131.4-119.9= 
131.4-119.9 = 11.5
11.5   11.5nswer is 11.5
Answer: A
If the mode of Set Q is equal to the median of Set Q, Set Q could be  Choose the correct choice from the following answers.
A) [0, 1, 2, 2, 3, 4, 5, 6]	B) [2, 2, 5, 7, 9]	C) [x, x+1, x+2, x+2, x+3, x+3]	D) [10, 102, 105, 105]	E) [4, 7, 10, 11, 25/2, 13, 13, 17, 29, 51, 51, 51]

Solution: Correct Answer: (C)   Set Q could be The mode is the most common number; the median is the middle number when the numbers are arranged from least to greatest. Any number plus an integer value is greater than the original number, so x + 1 is greater than x, x + 2 is greater than x + 1, etc., so set (C) is arranged from least to greatest. Its median is the average of (x+2) and (x+2), which must be (x+2). (x+2) is also the most common number, so the mode of set [x, x+1, x+2, x+2, x+3, x+3] is equal to the median of set [x, x+1, x+2, x+2, x+3, x+3].
Answer: C
If 5<x<8<y<13, then what is the greatest possible positive integer difference of x and y?  Choose the correct option.
A) 3	B) 4	C) 5	D) 6	E) 7

Solution: Let x=5.1 and y=12.1   Greatest possible difference=12.1-5.1= 
12.1-5.1 = 7
7   Answer 7
Answer: E
How many different 3 letter combinations can be created from the letters A,B and C?  Options:	A) 81	B) 3	C) 9	D) 27	E) 243

Solution: This is a case of number of arrangements possible with repetition.   Thus you have 3 options each for the 1st,2nd and 3rd letter giving you a total of   3*3*3= 
  3*3*3 = 27
27 number of possible combinations.   Answer : 27
Answer: D
Today is Monday. A person wants to meet a lawyer and as that lawyer is busy he asks him to come three days after the before day of the day after tomorrow? On which day the lawyer asks the person to come?  Choose the correct choice from the following answers
A) SUNDAY	B) MONDAY	C) TUESDAY	D) WEDNESDAY	E) FRIDAY

Solution: Today is Monday   after three days--->Thursday   now, (thursday)after before day--->Wednesday   then, (Wednesday)day after tomorrow--->Friday   ANSWFRIDAYR:FRIDAY
Answer: E
A farmer had d animals, all of which the farmer bought for the same price. The farmer decided to sell the animals. 16 of the animals were sold at a profit of 10% each while the rest were sold at a loss of 20% each. Overall, the farmer made neither a profit nor a loss. Which of the following is equal to d? Choose the correct choice from the following.
A) 20
B) 24
C) 28
D) 32
E) 36

Solution: Let P be the price the farmer paid for each animal.   The total profit on the 16 animals is 16*0.1*P.   The total loss on the other (d-16) animals is (d-16)*0.2*P.   (d-16)*0.2*P = 16*0.1*P   0.2*d = 1.6 + 3.2   d = 24   The answer is 24.
Answer: B
How many ways can six girls be selected from a group of ten girls? Choose the correct choice from the following options
A) ⁶C₄ B) ¹⁰C₄ C) 4C₄ D) ¹⁰P₄ E) ¹⁰P₅

Solution: Six members can be selected from ten members in   ¹⁰C₆ = ¹⁰C₄ ways   ¹⁰C₄
Answer: B
What is the sum of the multiples of 4 between 34 and 135 inclusive? Pick one:  A) 2000  B) 2100  C) 2150  D) 2200  E) 2500

Solution: the fastest way in an AP is to find the average and multiply with total integers..   between 34 and 135, the smallest multiple of 4 is 36 and largest =132..   average=(36+132)/2=84..   total numbers = (132-36)/4 + 1= 24+1=25..   sum=25*84= 
25*84 = 2_100
2100   ans 2100
Answer: B
A total of $20,000 was invested in two certificates of deposit at simple annual interest rates of 6 percent and 12 percent, respectively. If the total interest on the two certificates was $1,440 at the end of one year, what fractional part of the $20.000 was invested at the higher rate?  Choose the correct choice:
A) 3/8
B) 2/5
C) 1/5
D) 3/5
E) 3/4

Solution: x * 6/100 * 1 + (20000 - x) * 12/100 * 1 = 1440   6x - 12x = 144000 - 240000   => -6x = -96000   => x = 16000   So 4000/20000 = 1/5   Answer - 1/5
Answer: C
How many seconds will a train 70 meters long take to cross a bridge 80 meters long if the speed of the train is 36 kmph?  Pick
A) 22 sec  B) 27 sec  C) 25 sec  D) 15 sec  E) 11 sec

Solution: Explanation:   15 sec = 70 + 80= 
70 + 80 = 150
150   S= 36 * 5/18= 
36 * 5/18 = 10
10 mps   T= 150/10= 
150/10 = 15
15 sec   Answer: Option 15 sec
Answer: D
What are the last two digits of (301*402*503*604*645*547*448*349)^2	Answers
A) 96 B) 76 C) 56 D) 36 E) 00

Solution: ((301*402*503*604*645)*(547*448*349))^2   If you observe above digits, last digit are: 1,2,3,4,5,7,8,9; 6 is missing; so I have rearranged them so that multiplication will be easy for me as initial 4 digits have last two digits as 01,02,03,04,45 and final three as 47*48*49.   Solving for only last two digits and multiplying them we get:( (06*04*45)(56*49))^2 = (00*44)^2=00^2=00   Hence answer is 00
Answer: E
What is the difference between the place values of two sevens in the numeral 54207479 ?	Choose one.
A) 699990
B) 99990
C) 99980
D) 699930
E) None of these

Solution: None of thesexplanation:   Required Difference   = 7000 - 70= 
7000 - 70 = 6_930
6930   Answer is None of these
Answer: E
Find a two digit number which is doubled and after that add +2 in it. and then reverse the number we would get the actual number.  Choices
A) 23	B) 24	C) 25	D) 26	E) 27

Solution: Let the two digit number be 10x+y   Adding 2 after doubling the number is reverse of the number.   So 2(10x+y)+2 = 10y+x   19x -8y +2=0   Above equation satisfies for the value, x=2, y=5   So the number is   10*2+5= 
  10*2+5 = 25
25   ANSWER:25
Answer: C
Ten cards numbered 1 to 10 are placed in a box and then one card is drawn randomly. If it is known that the number on the drawn card is more than 4, what is the probability that it is an even number?	Pick
A) 1/2	B) 1/5	C) 1/7	D) 1/9	E) 1/10

Solution: There are 6 numbers higher than 4 and 3 of them are even.   The probability is 3/6=1/2.   The answer is 1/2.
Answer: A
Running at the same constant rate, 6 identical machines can produce a total of 300 bottles per minute. At this rate, how many bottles could 10 such machines produce in 4 minutes?	Choose one
A) 648	B) 1800	C) 2000	D) 10800	E) 10900

Solution: Let the required number of bottles be x.   More machines, More bottles (Direct Proportion)   More minutes, More bottles (Direct Proportion)   Machines	6	:	10	:: 300 : x   Time (in minutes)	1	:	4   6 x 1 x x = 10 x 4 x 300   x =	(10 x 4 x 300)/(6)   x = 2000.   ANSWER:2000
Answer: C
If P represents the product of the first 16 positive integers, then P is NOT a multiple of	Options:
A) 99	B) 84	C) 72	D) 65	E) 51

Solution: Answer is E.   Since prime factor of 51 is 3x17. 17 is a prime number and not part of the first 15 positive integers.   A) 9 x 11   B) 12 x 7   C) 12 x 6   D) 13 x 5   51) 3 x 17
Answer: E
A mixture of 50 litres of milk and water contains 10% water. How many litres of water should be added to the mixture so that the mixture contains 15% water?
Select the correct option.
A) 15 B) 20 C) 25 D) 30 E) 10

Solution: Quantity of milk in the mixture = 90/100 (50) = 45 litres.   After adding water, milk would form 60% of the mixture.   Hence, if quantity of mixture after adding x liters of water, (60) / 100 x = 45 => x = 75   Hence 75 - 50= 
75 - 50 = 25
25 litres of water must be added.   Answer: 25
Answer: C
How many positive three-digit integers are divisible by both 4 and 5?
Pick
A) 40  B) 42  C) 45  D) 50  E) 60

Solution: A number to be divisible by both 4 and 5 should be divisible by the least common multiple of 4 and 5 so by 20.   Multiples of 20 between 100 and 999, inclusive is   (last-first)/multiple+1=(980-100)/20+1=44+1= 
44+1 = 45
45   Answer: 45.
Answer: C
A can finish a piece of work in 5 days. B can do it in 10 days. They work together for two days and then A goes away. In how many days will B finish the work? Choose the correct choice from the following answers:
A) 4
B) 5
C) 6
D) 8
E) 2

Solution: 2/5 + (2 + x)/10 = 1 => x = 4 days   4nswer: 4
Answer: A
If four machines working at the same rate can do 3/4 of a job in 30 minutes, how many minutes would it take two machines working at the same rate to do 3/5 of the job?
Select:
A) 48
B) 60
C) 75
D) 80
E) 100

Solution: using the std formula   m1d1h1/w1=m2d2h2/w2   substituting the values we have   4*1/2*4/3=2*5/3*x (converted 30 min into hours =1/2)   8/3=10/3*x   x=4/5 hour   so 48 minutes   48NSWER:48
Answer: A
Pipe A can fill a tank in 32 minutes. Pipe B can fill the same tank 4 times faster than pipe A. If both the pipes are connected to the tank so that they fill the tank simultaneously, how long will it take for the empty tank to overflow? Choose the correct option: A) 16/3 minutes B) 32/7 minutes C) 192/7 minutes D) 224/7 minutes E) 28 minutes

Solution: Pipe A can fill a tank in 32 minutes --> the rate of A = 1/32 tank/minute;   Pipe B can fill the same tank 4 times fasterthan pipe A --> the rate of B = 1/32 + 4/32 = 5/32 tank/minute.   Their combined rate = 1/32 + 5/32 = 3/16 tank/minute;   Therefore, A and B can fill the tank in 16/3 minutes.   16/3 minutesnswer: 16/3 minutes.
Answer: A
An emploer pays Rs. 20 for each day a worker works, and forfeits Rs. 3 for each day he is idle. At the end of 60 days, a worker gets Rs. 280 . For how many days did the worker remain idle?
Choose the correct choice from the following answers
A) 30 days  B) 20 days  C) 10 days  D) 50 days  E) 40 days

Solution: Suppose the worker remained idle for x days .Then, he worked for (60-x)days   20(60-x)-3x=280   1200-23x=280   23x=920   x=40   so, the worker remained idle for 40 days   ANSW40 daysR: 40 days
Answer: E
Each person who attended a company meeting was either a stockholder in the company, an employee of the company, or both. If 57 percent of those 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 choices.
A) 47  B) 49  C) 51  D) 53  E) 55

Solution: 57+51= 
57+51 = 108
108 so 8% were both stockholders and employees.   The percent who were stockholders but not employees is  57-8= 
 57-8 = 49
49%   The answer is 49.
Answer: B
A Bus is running at 9/10 of its own speed reached a place in 22 hours. How much time could be saved if the bus would run at its own speed ?
Select the correct option:
A) 8.2 hrs	B) 6.2 hrs	C) 2.2 hrs	D) 1.2 hrs	E) 3.2 hrs

Solution: Explanation:   Let the original Speed be "s" kmph   And the usual time be "t" hrs   Given that if the bus is running at 9s/10 kmph the time is 22 hrs   => [9s/10] x 22 = t x s   => 99/5 = t   => t = 19.8 hrs   Answer: 2.2 hrs
Answer: C
If -1 ≤ a ≤ 2 and 1 ≤ b ≤ 3, then least possible value of (2a – 3b) is:  Pick:	A) -11	B) -3	C) -4	D) -5	E) -6

Solution: -1 ≤ a; so a = -1   b ≤ 3; so b = 3   Now, 2a – 3b = -2 - 9 = -11   Therefore, the least value is -11   -11NSWER:-11
Answer: A
The average age of a group of 5 members is 20 years. Two years later, a new member joins the group. The average age of the group becomes 23 years. What is the age of the new member ?  Select the correct option.
A) 20 years
B) 21 years
C) 28 years
D) 23 years
E) 24 years

Solution: The average age of a group of 5 members is 20 years --> the sum of the ages is  5*20= 
 5*20 = 100
100;   Two years laterthe sum of the ages of these 5 members would be 100+5*2= 
100+5*2 = 110
110;   Now, say the age of the new member is x years, so the sum of the ages of a new 6 member group is 110+x. Since given that the average age of this group of 6 members is 23 years then: 23*6=110+x --> x=28.   Answer: 28 years.
Answer: C