MU-NLPC/Calc-aqua_rat huggingface dataset:
A basket of 1430 apples is divided equally among a group of apple lovers. If 45 people join the group, each apple lover would receive 9 apples less. How many W apples did each person get before 45 people joined the feast?	Choose the correct choice from the following:
A) 20.
B) 21.
C) 22.
D) 23.
E) 24.

Solution: Before solving it algebraically, let us prime factorize 1430 = 2*5*11*13.   Since number of apples per person * total persons W= 1430, the answer should be a factor of 1430. Only C is. And that's your answer.22.
Answer: C
Find the time between 7 and 8 o'clock when two hands are at right angles?  Pick one.
A) 2 2/11 minutes past 7 o'clock
B) 3 2/11 minutes past 7 o'clock
C) 21 9/11 minutes past 7 o'clock
D) 7 10/11 minutes past 7 o'clock
E) 8 10/11 minutes past 7 o'clock

Solution: angle=90 deg   so,   angle=30(h)-11/2(min)   => 90=30(7)-11/2(min)   =>210-90=11/2(min)   => (120*2)/11=min   => min=21 9/11 min   ANSWER:21 9/11 minutes past 7 o'clock
Answer: C
A boy bought a pen at 40% discount on its original price. He sold it at a 70% increase on the price he bought it. What percent of profit did he make on the original price?	Choose the correct choice from the following answers
A) 10%	B) 8%	C) 6%	D) 2%	E) 4%

Solution: Original price = 100   CP = 60   S = 60*(170/100)= 
60*(170/100) = 102
102   100 - 102= 2%   Answer: 2%
Answer: D
A can do a piece of work in 4 days. B can do it in 8 days. With the assistance of C they completed the work in 2 days. Find in how many days can C alone do it?  Select.
A) 8 days B) 2 days C) 6 days D) 7 days E) 4 days

Solution: C = 1/2 - 1/4 - 1/8 = 1/8   => 8 days   8 daysnswer: 8 days
Answer: A
A circular mat with diameter 40 inches is placed on a square tabletop, each of whose sides is 30 inches long. Which of the following is closest to the fraction of the tabletop covered by the mat?	Choices:
A) 5/12 B) 2/5 C) 1/2 D) 1.395 E) 5/6

Solution: C.   It is a circle inscribed in a square.   Square side=24---> square(table) area=24^2   Circle diameter=40---> Circle area=PiR^2=4*100Pi (where Pi=~3.14)   covered fraction=4*100*3.14/30*30=4*314/900=1.395   1.395
Answer: D
Three numbers are in the ratio 3:5:7. The largest number value is 42. Find difference between Smallest & largest number is?  Choose the correct choice from the following choices.
A) 24
B) 26
C) 27
D) 28
E) 32

Solution: == 3:5:7   Total parts = 15   = The largest number value is 42   = The largest number is = 7   = Then 7 parts -----> 42 ( 7 * 6 = 42 )   = smallest number = 3 & Largest number = 7   = Difference between smallest number & largest number is = 7 - 3= 
7 - 3 = 4
4= Then 4 parts -----> 24 (4 * 6 = 24)   24)
Answer: A
A four-digit code can consist of the digits 0 ~ 9 except that it does not contain the digits 1, 3, 4, and 5 at all. If repeated digits are allowed, what is the probability that it has at least one even digit?	Choose the correct choice from the following choices.
A) 35/36
B) 49/50
C) 80/81
D) 100/101
E) 120/121

Solution: P(no even digits) = 1/3*1/3*1/3*1/3 = 1/81   P(at least one even digit) = 1 - 1/81 = 80/81   The answer is 80/81.
Answer: C
Walking at 4/5 of her normal speed, a worker is 15 minutes later than usual in reaching her office. The usual time (in minutes) taken by her to cover the distance between her home and her office is	Choose one:	A) 45	B) 50	C) 55	D) 60	E) 65

Solution: Let V be her normal speed and let T be her normal time.   60 = (4/5)V * (T+15)   Since the distance is the same we can equate this to a regular day which is 60 = V*T   V*T = (4/5)V * (T+15)   T/5 = 12   T=60   The answer is 60.
Answer: D
In the xy-plane, line e passes through point (3,-2) and intersect perpendicularly with line n that passes through points (0,3) and (3,5). What is the equation of line e? Answers:  A) 3x+2y-5=0  B) 3x+2y+5=0  C) 2x-3y-12=0  D) 2x+3y=0  E) 4x+3y-6=0

Solution: If two lines intersect perpendicularly, we get -1 when we multiply two slopes together. The slope of a line n is (5-3)/(3-0)=2/3. Hence, the slope of a line e should be -3/2. Since it crosses (3,-2), if we calculate we get 3x+2y=5. Hence, the correct answer is 3x+2y-53 +2= 
3 +2 = 5
5. Hence, the correct answer is 3x+2y-5=0.  3 +2 -5= 
  3 +2 -5 = 0
0.
Answer: A
Two varieties of wheat - A and B costing Rs. 9 per kg and Rs. 15 per kg were mixed in the ratio 3 : 7. If 5 kg of the mixture is sold at 25% profit, find the profit made?  Choose the correct choice
A) 13.5	B) 14.50	C) 15.50	D) 32:19	E) 16.50

Solution: Explanation:   Let the quantities of A and B mixed be 3x kg and 7x kg.   Cost of 3x kg of A = 9(3x) = Rs. 27x   Cost of 7x kg of B = 15(7x) = Rs. 105x   Cost of 10x kg of the mixture = 27x + 105x = Rs. 132x   Cost of 5 kg of the mixture = 132x/10x (5) = Rs. 66   Profit made in selling 5 kg of the mixture = 25/100 (cost of 5 kg of the mixture) = 25/100 * 66 = Rs. 16.50   Answer: Option 16.50
Answer: E
Average of 9 numbers is zero. At most how many numbers may be greater than zero  Choose the correct choice from the following choices:	A) 0	B) 1	C) 8	D) 9	E) 10

Solution: Answer: Option 8
Answer: C
The Price of 357 apples is Rs.2499. What will be the price of 49 dozens of such apples? Choose the most appropriate option:	A) Rs.3800	B) Rs.2816	C) Rs.4116	D) Rs.3116	E) Rs.5116

Solution: More apples, more cost(Direct)   357 *588 : : 2499 : x   x = (588*2499)/357= 
(588*2499)/357 = 4_116
4116   ANSWER:Rs.4116
Answer: C
When ticket sales began, Pat was the pth customer in line for a ticket, and customers purchased their tickets at the rate of x customers per minute. Of the following, which best approximates the time, in minutes, that Pat had to wait in line from the moment ticket sales began?	Options:
A) (p - 1) x  B) p + x –1  C) (p-1)/x  D) x/(p-1)  E) p/(x-1)

Solution: C. (p - 1) / x
Answer: C
If the average (arithmetic mean) of x, x + 2, and x + 4 is 33, what is the value of x? Choose one:
A) 30	B) 31	C) 32	D) 32	E) 37

Solution: AM of x, x + 2, and x + 4 = x + (x + 2) + (x + 4) / 3 = 3x + 6 /3 = x + 2   Given that x + 2 = 33   x = 31   Correct Option: 31
Answer: B
A fair coin is tossed 3 times. What is the probability of getting at least 2 tails? Pick.
A) 3/4 B) 3/2 C) 1/2 D) 3/4 E) 1/4

Solution: Let's find the probability of 2 tails , 3 tails   P(TTT)=((1/2)^3=1/8.   P(HTT)=(3!/2!)*(1/2)^3=3/8   Total Probablity = 1/8 + 3/8   =1/2   Answer(1/2)
Answer: C
If M:N is 3:9 and N:P is 9:12 then M:P is equal to	Choose the most appropriate option:
A) 1:5 B) 1:4 C) 1:6 D) 1:8 E) 1:7

Solution: The two ratios given are having the same number 9 for N in both the ratios.   Hence- M:N = 3:9 N:P = 9:12   => M:P = 3:12 = > 1:4   Answer 1:4
Answer: B
A retailer buys a radio for Rs 225. His overhead expenses are Rs 15. He sellis the radio for Rs 300. The profit percent of the retailer is	Select the correct option
A) 10%	B) 50%	C) 25%	D) 52%	E) None of these

Solution: Explanation:   cost price = (225 + 15)= 
(225 + 15) = 240
240 sell price= 300   gain = (60/240)*100= 
(60/240)*100 = 25
25%. Answer: 25%
Answer: C
Mudit's age 18 years hence will be thrice his age four years ago. Find Mudit's present age? Pick one.
A) 12 years
B) 21 years
C) 18 years
D) 9 years
E) None of these

Solution: Let Mudit's present age be 'm' years.   m + 18 = 3(m - 4)   => 2m = 30 => m = 15 years.   ANSWNone of theseR:None of these
Answer: E
A group consists of 4 men, 6 women and 5 children. In how many ways can 3 men, 2 women and 3 children selected from the given group?  Choose the correct choice from the following.
A) 987 ways B) 346 ways C) 600 ways D) 157 ways E) 134 ways

Solution: The number of ways of selecting three men, two women and three children is:   = ⁴C₃ * ⁶C₂ * ⁵C₃   = (4 * 3 * 2)/(3 * 2 * 1) * (6 * 5)/(2 * 1) * (5 * 4 * 3)/(3 * 2 * 1)   = 4 * 15 * 10= 
4 * 15 * 10 = 600
600 ways.   Answer: 600 ways
Answer: C
A train passes a station platform in 36 sec and a man standing on the platform in 25 sec. If the speed of the train is 54 km/hr. What is the length of the platform?
Choices
A) 767 m  B) 240 m  C) 187 m  D) 176 m  E) 165 m

Solution: Speed = 54 * 5/18= 
54 * 5/18 = 15
15 m/sec.   Length of the train= 15 * 25= 
15 * 25 = 375
375 m.   Let the length of the platform be x m . Then,   (x + 375)/36= 15 => x = 165 m.   Answer:165 m
Answer: E
The variable x is inversely proportional to the square of the variable y. If y is divided by 4a, then x is multiplied by which of the following?
Select.
A) 1/16a
B) 1/16a^2
C) 1/4a
D) 16a
E) 16a^2

Solution: initially - did x= 1/y^2   But this yielded the wrong answer,   I then re examined the question and tried y^2/x =1   Which I then got y = SQR(X)   subbing into y/4a I got answer 16a^2)
Answer: E
Ram sold two bicycles, each for Rs.990. If he made 10% profit on the first and 10% loss on the second, what is the total cost of both bicycles?  Choose the correct choice from the following answers
A) 2000  B) 6657  C) 2776  D) 2679  E) 2551

Solution: (10*10)/100= 
(10*10)/100 = 1
1%loss   100 --- 99   ? --- 1980=> Rs.2000   2000nswer: 2000
Answer: A
What is the prime factors’ number of 28?	Choices:	A) 2	B) 3	C) 4	D) 5	E) 6

Solution: prime factors’ number, as I assume, for a number X=a^n*b^m*c^o*d^p... is = n+m+o+p...   So, 28 = 2^2*7^1   prime factors’ number will be 2+1= 
2+1 = 3
3.   Hence, answer is 3.
Answer: B
A began business with Rs.45000 and was joined afterwards by B with Rs.5400. When did B join if the profits at the end of the year were divided in the ratio of 2:1?  Choose the correct choice from the following.
A) 1 B) 6 C) 7 D) 8 E) 2

Solution: 45*12 : 54*x = 2: 1   x = 5   12 -5= 
12 -5 = 7
7   Answer: 7
Answer: C
When the number 209y913 is exactly divisible by 11, then the smallest whole number that can replace y?
Options.
A) 0 B) 1 C) 2 D) 5 E) 9

Solution: The given number =209y913   Sum of the odd places =3+9+9+2= 
3+9+9+2 = 23
23   Sum of the even places= 1+y+0   (Sum of the odd places)- (Sum of even places) = Number (exactly divisible by 11)   23-(1+y) = divisible by 11   22 � y = divisible by 11.   Y must be 0, to make given number divisible by 11.   0
Answer: A
If the number 98348*0 is exactly divisible by 72, then the minimum value of * is?
Choose one.
A) 1	B) 2	C) 3	D) 4	E) 5

Solution: 72=8*9   divisibility 0f 8 last 3place should be divisible by 8   lly divisibility of 9 sum of digit should be divisible by 9   840 divisible by 8 nd 36 divisible by 9   ANSWER:4
Answer: D
In a certain series, each term is m greater than the previous term. If the 14th term is 600 and the 11th term is 540, what is the first term?  Select the correct option:  A) 40  B) 80  C) 140  D) 200  E) 240

Solution: a + 13m = 660 (14th term)   a + 10m = 540 (11th term)   You get a = 140 and m = 40   Answer: 140
Answer: C
A man can row a boat at 30 kmph in still water. If the speed of the stream is 8 kmph, what is the time taken to row a distance of 70 km upstream?  Choose the correct choice.
A) 35/9 B) 35/10 C) 35/11 D) 35/12 E) 35/13

Solution: Speed upstream = 30-8= 
30-8 = 22
22 kmph.   Time required to cover 60 km downstream= d/s = 70/22 = 35/11 hours. Answer:35/11
Answer: C
The decimal 0.1 is how many times greater than the decimal (0.001)^4? Choose the correct choice from the following choices:
A) 10^8  B) 10^9  C) 10^10  D) 10^11  E) 10^12

Solution: 0.1 = 10^-1   (0.001)^4 = (10^-3)^4 = 10^-12   10^11 * 10^-12 = 10^-1   The answer is 10^11.
Answer: D
The average salary of all the workers in a workshop is Rs. 8000. The average salary of 7 technicians is Rs. 18000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is: Select
A) 23 B) 19 C) 42 D) 20 E) 21

Solution: Let the total number of workers be x. Then,   8000x = (18000 * 7) + 6000(x - 7)   = 2000x = 84000   = x = 42.   ANSWER:42
Answer: C
A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:? Choose the correct option:
A) 56 km/hr
B) 50 km/hr
C) 59 km/hr
D) 34 km/hr
E) 67 km/hr

Solution: Speed of the train relative to man   = (125/10) m/sec = (25/2) m/sec. [(25/2) * (18/5)] km/hr   = 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed   = (x - 5) km/hr. x - 5 = 45 ==> x = 50 km/hr.   Answer: 50 km/hr
Answer: B
What number has a 5:1 ratio to the number 12?  Choose the correct option
A) 22  B) 50  C) 88  D) 52  E) 60

Solution: 5:1 = x: 12   x = 60   Answer: 60
Answer: E
A father was as old as his son's present at the time of your birth. If the father's age is 40 years now, the son's age 5years back was?  Choose the correct choice from the following options.
A) 10 years
B) 12 years
C) 14 years
D) 16 years
E) 15 years

Solution: Let the son's present age be x years. Then, (40 - x) = x   2x = 40.   x = 20.   Son's age 5 years back (20 - 5)= 
(20 - 5) = 15
15 years.   15 years
Answer: E
A man can swim in still water at 4.5 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is?  Choose the correct choice from the following answers.
A) 3.9	B) 4.2	C) 5.3	D) 1.5	E) 5.2

Solution: M = 4.5   S = x   1.5S = 4.5 + x   US = 4.5 + x   4.5 + x = (4.5 - x)2   4.5 + x = 9 -2x   3x = 4.5   x = 1.5   Answer:1.5
Answer: D
Find a positive number which when increased by 17 is equal to 60 times the reciprocal of the number? Select the correct option.
A) 3
B) 5
C) 6
D) 7
E) 9

Solution: Let the number be x.   Then, x + 17 = 60   x   x2 + 17x - 60 = 0   (x + 20)(x - 3) = 0   x = 3   Option 3
Answer: A
At a supermarket, a variety of cookies was priced at 75 cents per 100 grams. Subsequently, the price was revised to 40 cents for 30 grams of the same cookies. By approximately what percent did the ratio of price to weight increase from the initial price of 75 cents per pound?
Choose the correct choice from the following answers
A) 65  B) 78  C) 44  D) 18  E) 36

Solution: Initial price/weight ratio = 75 / 100 = 225/300   Revised price/weight ratio = 40 / 30 = 400/300   Answer: 78
Answer: B
In a recent election, Ms. Robinson received 8000 voters cast by independent voters, that is, voters not registered with a specific political party. She also received 20 percent of the votes cast by those voters registered with a political party. IF N is the total number of votes cast in the election and 40 percent of the votes cast were cast by independent voters, which of the following represents the number of votes that Mrs. Robbins received?
Select.
A) 0.06N+3200 B) 0.1N+7200 C) 0.4N+7200 D) 0.12N+8000 E) 0.06N+8000

Solution: 40% of N are independent voters, hence 60% of N are not independent voters. From this group she received 20% votes so, 0.2*0.6*N plus 8,000 votes from independents: total=0.2*0.6*N+8,000=0.12*N+8,000.   Answer: 0.12N+8000.
Answer: D
A number consists of 3 digits whose sum is 10. The middle digit is equal to the sum of the other two and the number will be increased by 99 if its digits are reversed. The number is:  Choose the correct choice from the following.
A) 145 B) 253 C) 253 D) 352 E) None

Solution: EXPLANATION   Let the middle digit be x.   Then, 2x = 10 or x = 5. So, the number is either 253 or 352.   Since the number increases on reversing the digits, so the hundred’s digits is smaller than the unit’s digit.   Hence, required number = 253.   Answer 253
Answer: B
If each of 3 digit code is formed of integers from 1 to 40, inclusively, and each of the digits are different, how many possible codes are there?
Choose the correct choice from the following options
A) 54230
B) 59365
C) 59280
D) 25789
E) 57690

Solution: Code consists of 3 digits and no digit is repeated.   First digit of the code can have 40 possibilities   Second digit can have 39 possibilities   Third digit can have 38 possibilities   Total number of possible codes = 40*39*38= 
40*39*38 = 59_280
59280   Answer: 59280
Answer: C
Find the odd man out. 121, 144, 169, 196, 225, 256, 288, 324, 361	Choose the correct answer
A) 121  B) 169  C) 225  D) 288  E) 361

Solution: Explanation :   Each of the given numbers except 288 is a perfect square   Answer : Option 288
Answer: D
If an integer n is to be chosen at random from the integers 1 to 96, inclusive, what is the probability that n(n + 1)(n + 2) will be divisible by 12?
Pick one
A) 1/48 B) 234/8 C) 1/24 D) 5/8 E) 3/4

Solution: I get 5/8 as well   1 to 96 inclusive means we have 48 odd and 48 even integers   E O E / 12 = Integer, therefore we have 48 / 96 numbers divisible by 8   O E O / 12= Not Integer   We cannot forget multiples of 12 from 1 to 96   We have 8 numbers that are multiple of 12   Therefore, 48/96 + 8/96 = 23/48   answer : 234/8
Answer: B
The Diagonals of two squares are in the ratio of 2:5. find the ratio of their areas.
Choose the correct choice from the following answers.
A) 4:25	B) 4:15	C) 3:25	D) 3:15	E) None of these

Solution: Explanation:   Let the diagonals of the squares be 2x and 5x.   Then ratio of their areas will be   4:25rea of square=1/2∗Diagonal2   1/2∗2x2:1/2∗5x2   4x2:25x2=4:25   Option 4:25
Answer: A
A retail appliance store priced a video recorder at 20 percent above the wholesale cost of $200. If a store employee applied the 20 percent employee discount to the retail price to buy the recorder, how much did the employee pay for the recorder?	Choose the correct option:
A) $198	B) $216	C) $192	D) $230	E) $240

Solution: Wholesale cost of video recorder = 200 $   Video recorder was priced at 20 percent above 200 = 240 $   % discount given by store employee = 20   Emlpoyee paid = .8 * 240= 
.8 * 240 = 192
192 $   Answer $192
Answer: C
What positive number, when squared, is equal to the cube of the positive square root of 18?	Choose the correct choice from the following choices.
A) 64  B) 32  C) 8  D) 4  E) 9

Solution: Let the positive number be x   x^2 = ((18)^(1/2))^3   =>x^2 = 4^3 = 81   => x = 9   Answer 9
Answer: E
A book club rented the party room of a local restaurant to meet and discuss its current novel over dinner. The total charge, including food and service, was $ 790. If each member of the club paid at least $ 32, then what is the greatest possible number of members in the club? Choose the correct choice from the following answers.
A) 19	B) 20	C) 21	D) 23	E) 25

Solution: Given: Each person spends $32.   By looking at the options, we see that if there were 20 members, each person will spend atleast $32   Hence the greatest number of members = 25Option 25
Answer: E
A train running at a speed of 60 kmph crosses a pole in 3 seconds.What is the length of the train?  Choose the correct choice:  A) 120 m  B) 180 m  C) 190 m  D) 150 m  E) 50 m

Solution: 60 kmph=50/3 m/sec   50/3*3= 
50/3*3 = 50
50 m   ANSW50 mR:50 m
Answer: E
Robert ate 9 chocolates, Nickel ate 2 chocolates. How many more chocolates did Robert ate than nickel? Answers
A) A)4
B) B)7
C) C)9
D) D)5
E) E)2

Solution: 9-2= 
9-2 = 7
7. Answer is 7
Answer: B
244,180,131,95, ? Options:
A) 42
B) 43
C) 44
D) 70
E) 39

Solution: 244 - 180= 
244 - 180 = 64
64= 8^2   180 - 131= 
180 - 131 = 49
49= 7^2   131 - 95= 
131 - 95 = 36
36= 6^2   so we can write   95 - x = 25 = 5^2 , where x is the next number   x = 95 - 25= 
95 - 25 = 70
70   so the next number will be 70   ANSWER:70
Answer: D
Virat buys an old car for Rs. 50000 and spends Rs. 1000 on its repairs. If he sells the scooter for Rs. 60000, his gain percent is: Pick:
A) 3 (4/7) %
B) 11 (1/9) %
C) 12 (2/3) %
D) 12%
E) 17.64%

Solution: Explanation:   C.P. = Rs. (50000 + 1000) = Rs. 51000   S.P. = Rs. 60000.   Gain% = ( (9000 / 51000) * 100 ) % = 17.64%   ANSW17.64%R 17.64%
Answer: E
Find the angle between the hour hand and the minute hand of a clock when the time is 3.25
Choose the correct answer
A) 47.5 B) 47.9 C) 47.6 D) 47.2 E) 47.1

Solution: Explanation:   At 3 O'clock, Minute hand is at 12 while the Hour hand is at 3. Again the minute hand has to sweep through ( 30 x 5 ) ie 150° for reaching the figure 5 to show 25 mins.   Simultaneously the Hour hand will also rotate for 25 mins. Thus starting from the mark, 3 the hour hand will cover an angle = (25 x 30) / 60 = 12.5°   Hence, 47.5ngle between Hour and the Minute hand = ( 60 - 12.5 )= 
( 60 - 12.5 ) = 47.5
47.5°   47.5nswer: 47.5) 47.5 degrees
Answer: A
A, B and C are partners in a business. Their capitals are respectively, Rs.5000, Rs.6000 and Rs.4000. A gets 30% of the total profit for managing the business. The remaining profit is divided among three in the ratio of their capitals. In the end of the year, the profit of A is Rs.200 more than the sum of the profits of B and C. Find the total profit.  Choose one
A) 2882  B) 778  C) 268  D) 3000  E) 2882

Solution: A:B:C = 5:6:4   Let the total profit = 100 - 30= 
100 - 30 = 70
70   5/15 * 70= 70/3   A share = 70/3 + 30 = 160/3   B + C share = 100 - 160/3 = 140/3   A-(B+C) = 160/3 - 140/3 = 20/3   20/3 ---- 200   100 ---- ? => 3000.Answer: 3000
Answer: D
The greatest number of four digits which is divisible by 15, 25, 40 and 75 is:	Choose the correct choice from the following answers
A) 9400	B) 9600	C) 9800	D) 9000	E) 9200

Solution: Greatest number of 4-digits is 9999.   L.C.M. of 15, 25, 40 and 75 is 600.   On dividing 9999 by 600, the remainder is 399.   Required number  (9999 - 399)= 
 (9999 - 399) = 9_600
9600.   answer :9600
Answer: B
A, B and C play a cricket match. The ratio of the runs scored by them in the match is A:B = 2:3 and B:C = 2:5. If the total runs scored by all of them are 75, the runs scored by B are?
A. 15 B. 18	Choose the correct choice from the following:	A) 22	B) 18	C) 99	D) 77	E) 24

Solution: A:18 = 2:3   18:C = 2:5   A:18:C = 4:6:15   6/25 * 75= 
6/25 * 75 = 18
18   Answer: 18
Answer: B
Two trains 140 m and 200 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?  Pick
A) 17.9 sec
B) 11.8 sec
C) 27.7 sec
D) 10.8 sec
E) 12.24 sec

Solution: Relative speed = 60 + 40= 
60 + 40 = 100
100 km/hr.= 100 * 5/18 = 250/9 m/sec.   Distance covered in crossing each other = 140 + 200= 
140 + 200 = 340
340 m.   Required time= 340 * 9/250= 
340 * 9/250 = 306/25 = around 12.24
12.24 sec.   Answer: 12.24 sec
Answer: E
If the sides of a rectangle are increased by 15%, what is the percentage increase in the area?	Choose the correct choice from the following answers
A) 32.25%  B) 40%  C) 37.50%  D) 36.75%  E) 32%

Solution: Say both sides of the rectangle are equal to 100 (so consider that we have a square). In this case the area is 100*100=10,000.   The area of new rectangle would be 115*115=13,225, which is 32.25% greater than the old area.   32.25%nswer: 32.25%.
Answer: A
All numbers from 1 to 200 (in decimal system) are written in base 6 and base 7 systems. How many of the numbers will have a non-zero units digit in both base 6 and base 7 notations? Choose one:	A) 143	B) 200	C) 157	D) 122	E) 132

Solution: DETAILED SOLUTION   If a number written in base 6 ends with a zero, it should be a multiple of 6. In other words, the question wants us to find all numbers from 1 to 200 that are not multiples of 6 or 7. There are 33 multiples of 6 less than 201. There are 28 multiples of 7 less than 201. There are 4 multiples of 6 & 7 (or multiple of 42) from 1 to 200.   So, total multiples of 6 or 7 less than 201 = 33 + 28 - 4= 
33 + 28 - 4 = 57
57. Number of numbers with non-zero units digit= 200 - 57= 
200 - 57 = 143
143.   Correct 143nswer : 143
Answer: A
If |10−2y|=|3y+5|, which of the following could be a value of y?	Choose the correct option.
A) -15
B) 9/5
C) -1
D) 5
E) 2/3

Solution: 10 - 2y = 3y + 5 or 10 - 2y = -3y - 5   5y = 5 or -y = 15   y = 1 or x = -15   -15nswer: -15
Answer: A
Find three rational numbers between 3 and 5. Choose the correct choice from the following options
A) 6/2 B) 7/2, 8/2 C) 8/2 D) 7/2, 9/2 E) 10/2

Solution: Sol. 1st rational number = (3 + 5)/2 = 8/2= 
8/2 = 4
4   2nd rational number (i.e., between 3 and 4)= (3 + 4)/2 = 7/2   3rd rational number (i.e., between 4 and 5)   = (4 + 5)/2 = 9/2   Answer 7/2, 9/2
Answer: D