MU-NLPC/Calc-aqua_rat huggingface dataset:
A contractor hires 100 men to finish a job in 50 days. After 40 days, n men leave. After some more days, the contractor hires 2n more men to complete the job on time. For how many days did these 2n men work?
Options:
A) 20	B) 18	C) 16	D) 12	E) 5

Solution: Step1: Find Each day what % of work is finished ; it requires 50 days to complete which means each day 1/50= 2% work will be completed.   Step 2 : After 40 Days = 40* 2= 
40* 2 = 80
80% of work is finished. remaining is 20% ( which means if same 100 men were about to complete the job they would have required 10 more days)   Step3: Let us assume all people have left job. therefore contractor hires 2n people. initially it was taking 10 days to compete for n people. at present 2n people are present to finish job. hence 5 more days.   5
Answer: E
Each Machine of type A has 2 steel parts and 3 chrome parts. Each machine of type B has 3 steel parts and 5 chrome parts. If a certain group of type A and type B machines has a total of 40 steel parts and 32 chrome parts, how many machines are in the group  Pick one: A) 12 B) 13 C) 14 D) 15 E) 16

Solution: Look at the below representation of the problem:   Steel Chrome total   A 2 3 40 >>no. of type A machines=40/5= 
40/5 = 8
8   B 3 5 32 >>no. of type B machines=32/8= 
32/8 = 4
4   So the answer is 12 i.e A.   Hope its clear .
Answer: A
A and B started business in partnership investing Rs. 20,000 and Rs. 15,000 respectively. After six months, C joined them with Rs. 20,000. What will be B's share in the total profit of Rs. 25,000 earned at the end of 2 years from the starting of the business?  Choose the correct choice from the following answers:
A) 7500  B) 2878  C) 2662  D) 2992  E) 2772

Solution: A:B:C = (20000 * 24) : (15000 * 24) : (20000 * 18) = 4:3:3   B's share = 25000 * 3/10 = Rs. 7500.   7500nswer: 7500
Answer: A
A salesmanâ€™s terms were changed from a flat commission of 5% on all his sales to a fixed salary of Rs.1000 plus 2.5% commission on all sales exceeding Rs. 4,000. If his remuneration as per new scheme was Rs. 600 more than that by the previous schema, his sales were worth?  Choose the correct choice from the following options:  A) Rs. 14,000  B) Rs. 12,000  C) Rs. 30,000  D) Rs. 40,000  E) Rs. 45,000

Solution: Explanation:   [1000 + (X-4000) * (2.5/100)] - X * (5/100) = 600   X = 12000   ANSWER IS Rs. 12,000
Answer: B
A man buys s cycle for $100 and sells it at a loss of 40%. What is the selling price of the cycle? Choices:
A) $50	B) $60	C) $70	D) $80	E) $90

Solution: S.P. = 60% of the $100 = 60/100 * 100= 
60/100 * 100 = 60
$60   Answer is $60
Answer: B
The variables m and n are positive integers. When m is divided by 18, there is a remainder of 12, and when n is divided by 24, there is a remainder of 14. Which of the following are possible values of m + n?
I. 50
II. 68
III. 90	Pick one:
A) I only  B) III only  C) I and II  D) I only III  E) II and III

Solution: m = 18k + 12 --> Values are 12, 30, 48, 66, 84   n = 24k + 14 --> Values are 14, 38, 62, 86   I. 50 --> 12 + 38 --> Possible   II. 68 --> 30 + 38--> Possible   III. 92 --> Not possible   Answer: I and II
Answer: C
A shop sells two variants of chocolates - one that costs $3 and the other that costs $5. If the shop sold $151 chocolates on a given day, how many different combinations of (number of $3 sold, number of $5 sold) exist?	Choices
A) 8	B) 10	C) 12	D) 14	E) 16

Solution: $151 = 29*$5 + 2*$3   We can find other combinations by reducing the $5 chocolates by 3 (which is -$15)and increasing the $3 chocolates by 5 (which is +$15).   The number of $5 chocolates can be 29, 26, 23, 20,...,2 for a total of 10 combinations.   The answer is 10.
Answer: B
In a graduating class of 234 students, 144 took geometry and 119 took biology. What is the difference between the greatest possible number and the smallest possible number of students that could have taken both geometry and biology?
Options
A) 144 B) 115 C) 113 D) 88 E) 31

Solution: Greatest Possible Number taken both should be 144 (As it is maximum for One)   Smallest Possible Number taken both should be given by   Total - Neither = A + B - Both   Both = A+B+Neither - Total (Neither must be 0 to minimize the both)   So 144 + 119 + 0 - 234= 
144 + 119 + 0 - 234 = 29
29   Greatest - Smallest is  144-29= 
 144-29 = 115
115   So answer must be B. 115
Answer: B
John drove for 3 hours at a rate of 50 miles per hour and for 2 hours at 60 miles per hour. What was his average speed for the whole journey?  Choose the most appropriate option: A) The average speed is 54 miles per hour. B) The average speed is 32 miles per hour. C) The average speed is 44 miles per hour. D) The average speed is 60 miles per hour. E) The average speed is 72 miles per hour.

Solution: Step 1: The formula for distance is   Distance = Rate × Time   Total distance = 50 × 3 + 60 × 2 = 270   Step 2: Total time = 3 + 2= 
3 + 2 = 5
5   Step 3: Using the formula   average speed formula    270/5= 
 270/5 = 54
54   The average speed is 54 miles per hour.nswer(The average speed is 54 miles per hour.)
Answer: A
If 18 bindres bind 900 books in 10 days , How many binders will be required to bind 660 books in 12 days?
Answers
A) 71
B) 12
C) 18
D) 11
E) 29

Solution: Explanation:   Let the required no of binders be X.   Less books , Less binders (11irect Proportion)   More days, Less binders (Indirect proportion)   \inline \fn_jvn \left.\begin{matrix} Books\: 900:600\\ 11ays\: \: 12:10 \end{matrix}\right\}::18:x   \inline \fn_jvn \therefore \inline \fn_jvn (900\times 12\times x)=(600\times 10\times 18) \inline \fn_jvn \Leftrightarrow x= \inline \fn_jvn \frac{600\times 10\times 18}{900\times 12} = 11   Answer: 11
Answer: D
In a class, there are 20 boys whose average age is decreased by 2 months, when one boy aged 21 years replaced by a new boy. The age of the new boy is?
Pick.
A) 14 years 8 months  B) 15 years  C) 16 years 4 months  D) 17 years 8 months  E) 17 years

Solution: Total decrease = (20 x 2) months   = 3 years 4 months   Age of the new boy   = 21 years - 3 years 4 months.   = 17 years 8 months.   ANSWER:17 years 8 months
Answer: D
If 100 cats kill 100 mice in 100 days, then 4 cats would kill 4 mice in how many days ?	Choose the correct choice from the following options:
A) 1 day
B) 4 days
C) 40 days
D) 100 days
E) 50 days

Solution: as   100 cats kill 100 mice in 100 days   1 cats kill 1 mouse in 100 days   then   4 cats kill 4 mice in 100 days   ANSWER:100 days
Answer: D
A cistern has a leak which would empty the cistern in 20 minutes. A tap is turned on which admits 4 liters a minute into the cistern, and it is emptied in 24 minutes. How many liters does the cistern hold?
Choose the correct option:
A) 480
B) 456
C) 345
D) 356
E) 368

Solution: 1/x - 1/20 = -1/24   x = 120   120 * 4= 
120 * 4 = 480
480   480nswer: 480
Answer: A
Reduce
803876
to the lowest terms Options:
A) 1112 B) 2324 C) 2627 D) 47 E) None of these

Solution: Explanation:   HCF of 803 and 876 is 73, Divide both by 73, We get the answer 11/12   1112nswer: Option 1112
Answer: A
A 25 cm wide path is to be made around a circular garden having a diameter of 4 meters. Approximate area of the path is square meters is?	Choose the correct choice from the following answers: A) 3.34 B) 3.32 C) 3.2 D) 3.08 E) 3.17

Solution: 3.34rea of the path = 3.34rea of the outer circle - 3.34rea of the inner circle   = ∏{4/2 + 25/100}2 - ∏[4/2]2   = ∏[2.252 - 22] = ∏(0.25)(4.25) { (a2 - b2 = (a - b)(a + b) }   = (3.14)(1/4)(17/4) = 53.38/16   = 3.34 sq m   3.34nswer: 3.34
Answer: A
Two tailors X and Y are paid a total of Rs. 550 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week?	Choose the correct choice from the following:
A) Rs. 200  B) Rs. 250  C) Rs. 300  D) Rs. 350  E) None

Solution: Solution   Let the sum paid to Y per week be Rs. z.   Then, z + 120% of z = 550.   ‹=›z + 120 / 100 z = 550   ‹=› 11 / 5 z = 550   ‹=›z = [550 x 5 / 11] = 250.   Answer Rs. 250
Answer: B
here are 6 periods in each working day of a school. In how many ways can one organize 5 subjects such that each subject is allowed at least one period?
Choose the correct choice from the following:
A) 2120
B) 4123
C) 3621
D) 1800
E) 1450

Solution: 5 subjects can be arranged in 6 periods in 6P5 ways.   Any of the 5 subjects can be organized in the remaining period (5C1 ways).   Two subjects are alike in each of the arrangement. So we need to divide by 2! to avoid overcounting.   Total number of arrangements   = 6P5× 5C1 /2!=1800   Ans: 1800
Answer: D
If (18^a) * 9^(3a – 1)= (2^5)(3^b) and a and b are positive integers, what is the value of a?  Choices
A) 22  B) 11  C) 9  D) 6  E) 5

Solution: (18^a) * 9^(3a – 1)= (2^5)(3^b)   = 2^a . 9^a . 9^(3a – 1) = (2^5)(3^b)   Just compare powers of 2 from both sides   Answer = 5 = 5
Answer: E
A dishonest dealer professes to sell his goods at Cost Price but still gets 35% profit by using a false weight. What weight does he substitute for a kilogram?	Answers
A) 740 1/7 grams B) 740 20/27 grams C) 740 8/3 grams D) 740 1/3 grams E) 740 1/27 grams

Solution: If the cost price is Rs.100, then to get a profit of 35%, the selling price should be Rs.135.   If 135kg are to be sold, and the dealer gives only 100kg, to get a profit of 35%.   How many grams he has to give instead of one kilogram(1000 gm).   135 gm ------ 100 gm   1000 gm ------ ?   (1000 * 100)/135 = 740 20/27 grams.   Answer:740 20/27 grams
Answer: B
If the probability of rain on any given day in Chicago during the summer is 20%, independent of what happens on any other day, what is the probability of having exactly 3 rainy days from July 4 through July 7 inclusive? Choose the correct choice from the following options:
A) 2/25
B) 3/125
C) 7/125
D) 12/625
E) 16/625

Solution: One possible case is: rainy-rainy-rainy-not rainy.   The probability of this case is 1/5*1/5*1/5*4/5 = 4/625   The number of possible cases is 4C3 = 4.   P(exactly 3 rainy days) = 4*4/625 = 16/625   The answer is 16/625.
Answer: E
Vishal invested 10% more than Trishul. Trishul invested 10% less than Raghu. If the total sum of their investments is Rs. 5780, how much amount did Raghu invest ?	Choose the correct choice:
A) 1287  B) 2887  C) 2000  D) 1129  E) 1192

Solution: Let money invested by Raghu = Rs. x   Money invested by Trishul = 9/10= 
9/10 = 9/10 = around 0.9
0.9x   Money invested by Vishal= 9/10x * 110/100 = 0.99x   Also, x+0.9x+0.99x 9/10  * 110/100= 
9/10  * 110/100 = 99/100 = around 0.99
0.99x   Also, x+0.9x+0.99x= 5780   = x= 5780/2.89= 
5780/2.89 = 2_000
2000   Therefore, amount invested by Raghu is Rs. 2000.   Answer: 2000
Answer: C
P beats Q by 125 meter in a kilometer race. Find Q's speed if P's speed is 32 meter/sec.
Choose the most appropriate option:	A) 21 meter/sec	B) 7 meter/sec	C) 14 meter/sec	D) 18 meter/sec	E) 28 meter/sec

Solution: P's speed = 32 m/s   P's distance = 1000m (as it is a km race)   t = 1000/32= 
1000/32 = 125/4 = around 31.25
31.25 sec   Q's distance= 1000-125= 
1000-125 = 875
875m   Q's time to complete this distance is also 62.5 sec.   Q's speed= dist/time = 875/31.25= 
875/31.25 = 28
28 m/s   Hence 28 meter/sec is the answer.
Answer: E
Pipes A and B can fill a cistern in 8 and 24 minutes respectively. They are opened an alternate minutes. Find how many minutes, the cistern shall be full?	Select:
A) 11	B) 12	C) 99	D) 75	E) 72

Solution: 1/8 + 1/24 = 1/6   6 * 2= 
6 * 2 = 12
12   Answer: 12
Answer: B
x =1 2 3
y= 4 5 18 then what is the relation between x and y	Choose the most appropriate option
A) 1*X)^1 B) 1*X)^6 C) 1*X)^7 D) 1*X)^4 E) 1*X)^2

Solution: Y=(1*X)^2   4=(1*2)^2   4=4   ANSW1*X)^2R:1*X)^2
Answer: E
The area of a parallelogram is 128sq m and its altitude is twice the corresponding base. Then the length of the base is?  Choose the correct choice from the following answers: A) 8 B) 9 C) 6 D) 5 E) 1

Solution: 2x * x = 128 => x   = 8   8nswer:8
Answer: A
The average weight of a group of boys is 30 kg. After a boy of weight 35 kg joins the group, the average weight of the group goes up by 1 kg. Find the number of boys in the group originally ?  Select:	A) 4	B) 7	C) 6	D) 8	E) 6

Solution: Let the number off boys in the group originally be x.   Total weight of the boys = 30x   After the boy weighing 35 kg joins the group, total weight of boys = 30x + 35   So 30x + 35 + 31(x + 1) = > x = 4.   4nswer:4
Answer: A
a, b, c, d, and e are five consecutive numbers in increasing order of size. Deleting one of the five
numbers from the set decreased the sum of the remaining numbers in the set by 20%. Which one of
the following numbers E was deleted?	Choose one.
A) a
B) b
C) c
D) d
E) e

Solution: a+b+c+d+e => 1+2+3+4+5= 
1+2+3+4+5 = 15
15   20%*15= 3 =>c
Answer: C
A can do a piece of work in 30 days. He works at it for 5 days and then B finishes it in 20 days. In what time can A and B together it ?
Choose the correct option:
A) 15 1/3 days  B) 13 1/3 days  C) 19 1/3 days  D) 11 1/3 days  E) 12 1/3 days

Solution: 13 1/3 days   13 1/3 days   5/30 + 20/x = 1   x = 24   1/30 + 1/24 = 3/40   40/3 = 13 1/3 days
Answer: B
A boat running downstream covers a distance of 16 km in 2 hours while for covering the same distance upstream,it takes 4 hours.What is the speed of the boat in still water ?	Select the correct option: A) 4 km/hr B) 6 km/hr C) 8 km/hr D) Data inadequate E) None of these

Solution: Solution   Rate downstream =(16/2)= 
(16/2) = 8
8 kmph, Rate upstream=(16/4)= 
(16/4) = 4
4 kmph.   ∴ Speed in still water=1/2(8+4) kmph = 6 kmph. Answer 6 km/hr
Answer: B
During the second quarter of 1984, a total of 2,976,000 domestic cars were sold. If this was 24% greater than the number sold during the first quarter of 1984, how many were sold during the first quarter ?  Choose the correct option.
A) 714,240	B) 2,261,760	C) 2,400,000	D) 3,690,240	E) 3,915,790

Solution: Let number of cars sold in 1st quarter = x   Number of cars sold in 2nd quarter = 24% greater than the number sold during the first quarter = (1 + 24/100)= 
(1 + 24/100) = 31/25 = around 1.24
1.24 x   1.24 x= 2,976,000   => x = 2,400,000   So, answer will be 2,400,000
Answer: C
The two trains of lengths 400 m, 600 m respectively, running at same directions. The faster train can cross the slower train in 180 sec, the speed of the slower train is 48 km. then find the speed of the faster train? Choose the correct choice from the following options.
A) 66 Kmph
B) 68 Kmph
C) 86 Kmph
D) 99 Kmph
E) 55 Kmph

Solution: Length of the two trains = 600m + 400m   Speed of the first train = X   Speed of the second train= 48 Kmph   1000/X - 48 = 180   1000/x - 48 * 5/18 = 180   50 = 9X - 120   X = 68 Kmph .Answer: 68 Kmph
Answer: B
Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 4 seconds. What is the length of the fast train ?	Choose the correct choice from the following answers:	A) 22 2/9	B) 28 7/9	C) 29 7/9	D) 30 7/9	E) None of these

Solution: Explanation:   22 2/9s Trains are moving in same direction,   So, Relative Speed = 40-20= 
40-20 = 20
20 kmph= 20*(5/18) = 50/9 m/sec   Length of Train= Speed * Time   Length=50/9âˆ—4   =200/9   =22 2/9   Option 22 2/9
Answer: A
A pool can be filled in 4 hours and drained in 5 hours. The valve that fills the pool was opened at 1:00 pm and some time later the drain that empties the pool was also opened. If the pool was filled by 9:00 pm and not earlier, when was the drain opened?
Choose one
A) at 2:00 pm	B) at 2:30 pm	C) at 3:00 pm	D) at 3:30 pm	E) at 4:00 pm

Solution: The filling rate is 1/4 and the draining rate is 1/5.   The combined rate of filling and draining is 1/4 - 1/5 = 1/20.   Let x be the number of hours before the drain was opened.   x/4 + (8-x)/20 = 1   5x + 8 - x = 20   4x = 12   x = 3   The answer is 4:00 pm.   The answer is at 4:00 pm.
Answer: E
A man engaged a servant on the condition that he would pay him Rs.900 and a uniform after 1year service. He served onlyfor 9 months and received uniform & Rs.650, find the price of the uniform? Choose the correct choice from the following answers:
A) Rs.90  B) Rs.100  C) Rs.150  D) Rs.190  E) Rs.200

Solution: 9/12 = 3/4 * 900= 
3/4 * 900 = 675
675   650   -------------   25   1/4 -------- 25   1 --------- ?=> Rs.100   Rs.100
Answer: B
9 friends bought a franchise for 500,000 dollars. If they all have to pay the same amount and none of them have bills smaller than $1, how much money would they have to pay?	Choose the correct option
A) 500,003
B) 500,001
C) 500,004
D) 500,000
E) 500,005

Solution: In order to divide the sum in 9 parts, the amount must be divisible by 9   Divisibility rule of 9: The sum of the digits must be divisible by 9   Sum of digits of 500,000 = 5 and 9 is divisible by 9.   Hence, we need to add 4 to this number for it to be divisible by 9   500,004orrect Option: 500,004
Answer: C
The ratio of the number of ladies to gents at a party was 1:2 but when 2 ladies and 2 gents left, the ratio became 1:3. How many people were at the party originally?	Options:
A) 18 B) 17 C) 12 D) 19 E) 11

Solution: x, 2x   (x-2):(2x-2) = 1:3   3x-6 = 2x-2   x = 4   x+2x = 3x   => 3*4= 
3*4 = 12
12   Answer: 12
Answer: C
What number should replace the question mark?
100, 93, 79, 53, ?.	Choose the correct choice from the following choices.
A) 30
B) 36
C) 32
D) 41
E) 44

Solution: 30   30   The sequence progresses –7, –14, –21, –28.
Answer: A
There are 14 balls in a jar: 8 red, 3 blue and 3 green. If a single ball is drawn from the jar, what is the probability of that it is either blue or red? Choose the correct choice from the following answers.
A) 1/12  B) 11/14  C) 1/2  D) 2/3  E) 3/4

Solution: 11/14lue + Red =11   Total number of balls is  8+3+3= 
 8+3+3 = 14
14   So the answer is 11/14=11/14   Answer 11/14
Answer: B
Jill, who lives in City C, plans to visit 7 different cities, M, L, P, I, Y, B and S. She plans to visit each city exactly once and return to City C after the 7 visits. She can visit the cities in any order. In how many different orders can she visit the 7 cities? Choose the correct choice from the following answers.
A) 3000 B) 5040 C) 8000 D) 9000 E) 12000

Solution: 7! = 5040 =5040
Answer: B
There are three boats B1, B2 and B3 working together they carry 60 people in each trip. One day an early morning B1 carried 50 people in few trips alone. When it stopped carrying the passengers B2 and B3 started carrying the people together. It took a total of 10 trips to carry 300 people by B1, B2 and B3. It is known that each day on an average 300 people cross the river using only one of the 3 boats B1, B2 and B3. How many trips it would take to B1, to carry 150 passengers alone?	Pick:  A) 15  B) 30  C) 25  D) 10  E) 15

Solution: Explanation:   Combined efficiency of all the three boats = 60 passenger/trip   Now, consider option(a)   15 trips and 150 passengers means efficiency of B1 = 10p/t   which means in carrying 50 passengers B1 must has taken 5 trips. So the rest trips equal to 5 (10-5 = 5) in which B2 and B3 together carried remaining 250 (300 - 50 = 250) Passengers.   Therefore the efficiency of B2 and B3 = 250/5= 
250/5 = 50
50 p/t   Since, the combined efficiency of B1, B2 and B3 is 60. Which is same as given in the first statement hence option(a) is correct   15nswer: 15
Answer: A
If x and y are integers and xy = 660, x or y must be divisible by which of the following numbers?  Choose the correct choice from the following answers:
A) 4
B) 5
C) 6
D) 20
E) 30

Solution: xy = 660 = 2 * 2 * 3 * 5 * 11   One of x or y must be divisible by 5.   The answer is 5.
Answer: B
Lovely shop runs a sale on goldfish and platys. If one customer buys 13 goldfish and 12 platys for $5.60, and another buys 14 goldfish and 21 platys for $8.05, what is the ratio of the price of goldfish to platys?	Choose the correct choice from the following answers.
A) 0.8	B) 0.75	C) c) 8/9	D) 5/7	E) 6/8

Solution: The approach of plugging in the numbers is a fine approach. But, in this case, the answer was the first option and thus, by plugging in a number in the ration given, we arrived at the answer quickly!   However, what if the correct ratio was option D or C?   In any case, the algebraic solution isn't that complex if you realize a key concept:   The number 7 can be factored out of the second equation!   Here's the working:Lovely shop runs a sale on goldfish and platys.   13x + 12y = 5.60 <<<<< Equation 1   14x + 21y = 8.05 <<<<< Equation 2   2x + 3y = 1.15 [Factor Out 7 from equation 2] <<<<< Equation 3   8x + 12y = 4.6 [Multiply Equation 3 with 4]   5x = 1.0 [Equation 1 - Equation 2]   x = 0.2   3y = 1.15 - 0.4= 
1.15 - 0.4 = 0.75
0.75 [Substitute for x in Equation 1]   y= 0.25   x/y = 0.2/0.25 = 20/25 = 4/5= 
4/5 = 4/5 = around 0.8
0.8 [Answer A]   The whole thing must have taken me about 45 s :5/7
Answer: D
How many solutions does the equation
sin(x) sin(2x) sin(3x) · · · sin(11x) sin(12x) = 0
have in the interval (0,π] ? Choices:
A) 11
B) 12
C) 24
D) 46
E) 68

Solution: If x is a solution of the equation, then lx = k for some integers k and l with 1 _<l_<12. Thus   x = k   lπ. Since we want x to be in (0;π], the number of solutions equals the number of fractions in   (0,1] with numerator an integer, and denominator a positive integer _<12. Since we want to avoid   counting the same solution twice (for example 2π/=3 = 4π/6), we need to count only fractions in   lowest terms. Let φ(n) be the number of fractions in lowest terms in (0,1] with denominator n.   Then φ(1) = 1, φ(2) = 1,φ(3) = 2, φ(4) = 2,φ(5) = 4, φ(6) = 2,φ(7) = 6, φ(8) = 4,   φ(9) = 6, φ(10) = 4,φ(11) = 10, and φ'(12) = 4. Adding the above values of φ we get that the   number of solutions is 46.   correct answer 46
Answer: D
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 ?	Pick one:
A) 4  B) 10  C) 15  D) 16  E) None

Solution: L.C.M. of 2, 4, 6, 8, 10, 12 is 120.   So, the bells will toll together after every 120 seconds(2 minutes).   In 30 minutes, they will toll together  30/2 + 1= 
 30/2 + 1 = 16
16 times   Answer 16
Answer: D
A bag of n peanuts can be divided into 9 smaller bags with 6 peanuts left over. Another bag of m peanuts can be divided into 12 smaller bags with 4 peanuts left over. Which of the following is the remainder when nm is divided by 12?  Choose the correct choice from the following.
A) 4  B) 3  C) 2  D) 1  E) 0

Solution: n = 9x + 6   m = 12y + 4   nm = (9x + 6)*(12y + 4) = 108xy + 36x + 72y + 24   Remainder of nm/12 = (108xy + 36x + 72y + 24)/12   Observe that the all four terms are a multiple of 12   Hence mn/12 will have no remainder   Correct Option: 0
Answer: E
The probability of Sam passing the exam is 1/4. The probability of Sam passing the exam and Michael passing the driving test is 1/2. What is the probability of Michael passing his driving test?  Choose the correct choice from the following answers:
A) 1/24.  B) 2.  C) 1/3.  D) 2/3.  E) 2/5

Solution: 1/4 *1/m= 1/2 , 1/m = 2   Answer 2.
Answer: B
If $0.90 is the commission for sales of $3,000, what percent of the sales amount is the commission?  Choose the correct choice from the following
A) 3%  B) 0.3%  C) 0.03%  D) 0.003%  E) 0.0003%

Solution: % of sales amount of commission   = (0.03%ommission/Total Value) *100   = (0.9/3000) * 100= 
(0.9/3000) * 100 = 0.03
0.03%   The answer is 0.03%.
Answer: C
What annual instalment will discharge a debt of Rs 1092 due in 3 years at 12% simple interest? Choose the correct choice from the following choices:
A) 325 B) 234 C) 998 D) 277 E) 991

Solution: Let each instalment be Rs.x .   1st year = [x + (x * 12 * 2)/100]   2nd year = [ x + (x *12 * 1)/100]   3rd year = x   Then, [x + (x * 12 * 2)/100] + [ x + (x *12 * 1)/100] + x =1092   3x + ( 24x/100 ) + ( 12x/100 ) = 1092   336x =109200   x = 325   Each instalment = Rs. 325   325nswer: 325) Rs.325
Answer: A