MU-NLPC/Calc-aqua_rat huggingface dataset:
When positive integer g is divided by 6, the remainder is 1. Which of the following must be true?
I. g is a prime number
II. g is odd
III. g is divisible by 7 Choose the correct answer:
A) I only  B) II only  C) III only  D) I and II only  E) II and III only

Solution: g=6q+1   Examine II) put q=0,1,2,3....... we have g=1,7,13,...25 so g must be odd   Examine III) 14/6 has reminder 249/7 has reminder 1 so not always true   Examine I) g= 7 true but while 2 is prime, it does not give reminder 1   Answer: II only
Answer: B
The length of the bridge, which a train 150 metres long and travelling at 45 km/hr can cross in 30 seconds, is? Choose the correct choice from the following options:	A) 245	B) 777	C) 282	D) 266	E) 225

Solution: Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (150 + x)/30 = 25/2 => 2(150 + x) = 750 => x = 225 m.   Answer: 225
Answer: E
How many pieces of 75 cm can be cut from a rope 57 meters long?	Options
A) 30
B) 40
C) 76
D) None
E) Cannot be determined

Solution: Explanation :   Total pieces of 75 cm that can be cut from a rope of 57 meters long is   = (57 meters)/(75 cm)   = (57 meters)/(0.75 meters)   = 76   Answer : 76
Answer: C
Each of the products produced yesterday was checked by worker x or worker y. 0.5% of the products checked by worker x are defective and 0.8% of the products checked by worker y are defective. If the total defective rate of all the products checked by worker x and worker y is 0.7%, what fraction of the products was checked by worker y?	Choose the correct choice from the following options.
A) 2/3	B) 5/6	C) 7/8	D) 4/5	E) 5/8

Solution: x: 0.5% is 0.2%-points from 0.7%.   y: 0.8% is 0.1%-points from 0.7%.   Therefore the ratio of products checked by y:x is 2:1.   Thus, worker y checked 2/3 of the products.   The answer is 2/3.
Answer: A
The salary of Charan was reduced by 10%. By what percent should his reduced salary be raised so as to bring it at par with his original salary? Choose one:  A) 12%  B) 11.11%  C) 11.5%  D) 13%  E) None of these

Solution: Explanation :   Solution: Let the original salary be Rs. 100. new salary = Rs. 90.   Increase on 90 = 10   Increase on 100 = ?   = 10*100/90 = 11 1/9%.   Answer : 11.11%
Answer: B
A certain college party is attended by both male and female students. The ratio of male to female students is 4 to 5. If 15 of the male students were to leave the party, the ratio would change to 1 to 2. How many total students are at the party?	Answers.
A) 60  B) 70  C) 80  D) 90  E) 100

Solution: The ratio is 4:5 = 8:10, so there are 8k males and 10k females.   If 15 males left, the ratio would be 1:2 = 5:10, so there would be 5k males and 10k females.   8k-5k = 15   k = 5   8k + 10k = 40 + 50= 
40 + 50 = 90
90   The answer is 90.
Answer: D
The length of a cold storage is double its breadth. Its height is 3 metres. The area of its four walls(including doors) is 108 m2. Find its volume.  Pick one:	A) 206	B) 216	C) 226	D) 246	E) 288

Solution: let xbe breadth ,then 2x is the length   then 2x*3*2+x*3*2=108   12x+6x=108   x=108/18= 
108/18 = 6
6   length 12,breadth 6 ,height 3   volume=12*6*3= 
12*6*3 = 216
216m^3   ANSWER:216
Answer: B
A can contain a mixture of two liquids A and B in the ratio 7:5 when 9 litres of mixture are drawn off and the can is filled with B, the ratio of A and B becomes 7:9. How many litres of liquid A was contained by the can initially?
Choose the correct choice from the following answers:
A) 28 litres
B) 21 litres
C) 45 litres
D) 36 litres
E) None of these

Solution: Explanation :   Let, the can initially contains 7x and 5x litres of mixtures A and B respectively.   When 9 litres of mixture are drawn off, quantity of A in mixture left :-   =>7x−(7/12)×9=7x−(21/4) litres.   Similarly, quantity of B in mixture left:   =>5x−(5/12)×9=5x−(15/4) litres.   The ratio becomes :   =>(7x−21)/(5x−(15/4)+9)=7/9.   =>(28x−21)/(20x+21)=7/9.   =>252x−189=140x+147.   =>112x=336.   =>x=3.   Hence, the required initial amount of A is :   =>7×x=7×3=21 litres.   Answer : 21 litres
Answer: B
A number when divided by a divisor leaves a remainder of 24. When twice the original number is divided by the same divisor, the remainder is 11. What is the value of the divisor?  Pick one:	A) 37	B) 30	C) 25	D) 28	E) 40

Solution: Original no be a   let divisor be d & let the quotient of the division of a by d be x   => a/d = x and the remainder is 24   a = dx+24   when twice the original no is divided by d, 2a is divided by d   =>the problem state that (2dx + 48) / d leaves a remainder of 11   2dx is perfectly divisible by d and will not leave remainder   the remainder of 11 was obtained by dividing 48 by d   when 48 is divided by 37 the remainder that one will obtain is 11   the divisor is 37   37NSWER 37
Answer: A
Two persons , Ram & Lakshman , who are at a distance of 100 km from each other, move towards each other from two places P and Q at speeds of 20 kmph and 25 kmph respectively. Lakshman reaches P, returns immediately and meets Ram at R, who started on the return journey to P immediately after reaching Q. What is the distance between Q and R?	Choose the correct choice from the following options.
A) 33 1/3 km
B) 25 km
C) 30km
D) 27 1/3 km
E) 28 1/3 km

Solution: Ram takes 100/20= 
100/20 = 5
5 hours to cover the distance from P to Q. By that time Lakshman covers   covers 5 *25= 
5 *25 = 125
125 km   Lakshman covers 25 km more than the distance PQ . Now the distance between them= 75 km   Time taken by them to meet = Distance/ Relative speed = 75/(20+25) = 75/45 = 5/3 hrs.   Distance between Q and R is nothing but the distance covered by Ram in 5/3 hours = 20 *5/3 = 100/3 km or 33 1/3 km   33 1/3 kmNSWER:33 1/3 km
Answer: A
If f(x) = (x^2 - 1)/(x), what is f(1/x) in terms of f(x)? Choose the correct choice from the following choices
A) -1*f(x) B) f(x) C) 1/f(x) D) -1/f(x) E) 2*f(x)

Solution: f(1/x) = ((1/x)2 - 1) / ((1/x))   = ((1/x^2) - 1) / (1/x)   = ((1-x^2)/(x^2)) / (1/x   = (1-x^2)/(x^2)   = - ( (x^4) -1) / (x)   = -1* f(x)   -1*f(x)nswer is -1*f(x).
Answer: A
Two watches are set for an alarm at 10 0'clock in the night. One watch gains 2 minutes per hour. When the faster watch shows 4:12 in the morning when the alarm rings what does the correct watch show?	Choices:
A) 5:00 B) 4:00 C) 4:10 D) 5:20 E) 6:00

Solution: The faster watch gains 2 minutes per hour   The two watches show 10:00 at 10 0'clock   At 11 0'clock -   The correct watch is at 11:00   The faster watch is at 11:02 (1 hour + gains 2 minutes per hour)   At 12 midnight -   The correct watch is at 12:00   The faster watch is at 12:04 ( 2 hours + gains 4 minutes per 2 hours)   In 6 hours the faster watch gains 6*2= 
6*2 = 12
12 minutes and is at 4:12 and the correct watch is at 4:00   Answer is 4:00
Answer: B
The average weight of a class of 24 students is 35 kg. If the weight of the teacher be included, the average rises by 400 g. The weight of the teacher is :	Options:
A) 45 kg B) 46 kg C) 47 kg D) 48 kg E) 49 kg

Solution: Explanation:   Weight of the teacher = (35.4 x 25 - 35 x 24) kg = 45 kg. 45 kgnswer: 45 kg
Answer: A
which of the following inequalities indicates the set of all values of d for which the lengths A of the three sides of a triangle can be 3,4, and d? Choose the correct choice from the following answers
A) 0<d<1  B) 0<d<5  C) 0<d<7  D) 1<d<5  E) 1<d<7

Solution: This question is a good way to apply one of the most basic relation between the 3 sides of a triangle. In a triangle (ANY TRIANGLE), any side MUST be greater than the positive difference of the other two sides and less than than the sum of the other 2 sides. Let the sides of a triangle be a,b,c .   Thus,   |a-b| < c < a+b   |b-c| < a < b+c   |c-a| < b < a+c   Thus, if the sides of the triangle are 3,4 and d,   4-3<d<4+3 ---=""> 1<d<7. Thus 1<d<7 is the correct answer.</d<4+3>
Answer: E
A train 125 m long passes a man, running at 9 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) 35 km/hr  B) 50 km/hr  C) 54 km/hr  D) 65 km/hr  E) 87 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 - 9) km/hr. x - 9 = 45 ==> x = 54 km/hr.   Answer: 54 km/hr
Answer: C
Simple interest on a certain sum is 16/25 of the sum. Find the rate percent and time, If both are numerically equal.  Options:
A) 1
B) 8
C) 5
D) 4
E) 2

Solution: Explanation:   Let sum = X. Then S.I = 16x/25   Let rate = R% and Time = R years.   Therefore, (x * R * R)/100 = 16x/25 or R^2 = 1600/25, R = 40/5= 
40/5 = 8
8   Therefore, Rate= 8% and Time = 8 years.Answer:   8) Rate = 8% and Time = 8 years.
Answer: B
if a die has 1 6 and 3 4 and 2 5 opposite each other how many such dies can be made  Choose the correct choice from the following answers
A) 10
B) 11
C) 12
D) 13
E) 14

Solution: if one face have 1,3,2, then the corossponding face will be occupied by respective pair i.e (6,4,5).   so there r 3 place and we have 3 place soit can be arranged in 3! way i.e 6 way and every pair will be suffled in 2 way so ans will be 6*2= 
 6*2 = 12
12.   ANSWER:12
Answer: C
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 5 seconds. What is the length of the fast train ? Choose the correct option:
A) 27 7/9
B) 28 7/9
C) 29 7/9
D) 30 7/9
E) None of these

Solution: Explanation:   27 7/9s 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=50/9∗5   =250/9   =27 7/9   Option 27 7/9
Answer: A
If log1087.5 = 6.9421, then the number of digits in (875)10 is?	Select the correct option: A) 30 B) 28 C) 80 D) 26 E) 25

Solution: X = (875)10 = (87.5 x 10)10   Therefore, log10X = 10(log1087.5 + 1)   = 10(6.9421 + 1)   = 10(7.9421) = 79.421   X = antilog(79.421)   Therefore, number of digits in X = 80.   ANSWER:80
Answer: C
Ashok and Pyarelal invested money together in a business and share a capital of Ashok is 1/9 of that of Pyarelal.if the incur a loss of Rs 670 then loss of Pyarelal?  Options.
A) 603	B) 703	C) 800	D) 903	E) 1000

Solution: Let the capital of Pyarelal be x, then capital of 603shok=x/9   So ratio of investment of Pyarelal and 603shok = x : x/9 =9x : x   Hence out of the total loss of 670, loss of Pyarelal= 670*9x/10x=603   603NSWER:603670*9 /10= 
670*9 /10 = 603
603   603NSWER:603
Answer: A
What is the sum of all remainders obtained when the first 120 natural numbers are divided by 9?  Choose the correct choice from the following choices
A) 397
B) 401
C) 403
D) 405
E) 399

Solution: A positive integer can give only the following 9 remainders when divided by 9: 1, 2, 3, 4, 5, 6, 7, 8, and 0.   1 divided by 9 gives the remainder of 1;   2 divided by 9 gives the remainder of 2;   ...   8 divided by 9 gives the remainder of 8;   9 divided by 9 gives the remainder of 0.   We'll have 11 such blocks, since  99/9= 
 99/9 = 11
11. The last will be:   91 divided by 9 gives the remainder of 1;   92 divided by 9 gives the remainder of 2;   ...   98 divided by 9 gives the remainder of 8;   99 divided by 9 gives the remainder of 0.   The last number, 100, gives the remainder of 1 when divided by 9, thus the sum of all remainders will be:   11(1+2+3+4+5+6+7+8+0)+1=405.   Answer: 405.
Answer: D
A can do a piece of work in 12 days. He worked for 15 days and then B completed the remaining work in 10 days. Both of them together will finish it in. Answers
A) 11 1/2 days	B) 15 1/2 days	C) 15 1/2 days	D) 16 1/2 days	E) 12 1/2 days

Solution: 12 1/2 days   12 1/2 days   15/25 + 10/x = 1 => x = 25   1/25 + 1/25 = 2/25   25/2 = 12 1/2 days
Answer: E
What should be added to 4440 so that it may become a perfect square?
Choose the correct choice from the following choices:
A) 44
B) 45
C) 46
D) 47
E) 49

Solution: 67x67=4489   4489-4440= 
4489-4440 = 49
49   If added to 49 get perfect square   answer=49
Answer: E
The average weight of a group of boys is 20 kg. After a boy of weight 33 kg joins the group, the average weight of the group goes up by 1 kg. Find the number of boys in the group originally ? Choose the most appropriate option:
A) 12  B) 14  C) 18  D) 24  E) 10

Solution: Let the number off boys in the group originally be x.   Total weight of the boys = 20x   After the boy weighing 33 kg joins the group, total weight of boys = 20x + 33   So 20x + 33 = 21(x + 1) = > x = 12.   12NSWER:12
Answer: A
The sides of a rectangular field are in the ratio 3 : 4. If the area of the field is 9408 sq. m, the cost of fencing the field @ 25 paise per metre is  Options: A) Rs. 55.50 B) Rs. 67.50 C) Rs. 86.50 D) Rs. 98.00 E) None of these

Solution: Solution   Let length = (3x) metres and breadth = (4x) metres.   Then, 3x × 4x = 9408 ⇔ 12x2 = 9408 ⇔ x2 = 784 ⇔ x = 28.   So, length = 84 m and breadth = 112 m.   Perimeter = [2(84 + 112)] m = 392 m.   ∴ Cost of fencing = Rs. (0.25 × 392) = Rs. 98.00. Answer Rs. 98.00
Answer: D
A 600 meter long train crosses a signal post in 20 seconds. How long will it take to cross a 3 kilometer long bridge, at the same speed?
Choose the correct choice from the following answers
A) 4 min B) 2 min C) 8 min D) 9 min E) 5 min

Solution: S = 600/20 = 1530 mps   S = 3600/30= 
3600/30 = 120
120 sec= 2 min   Answer: 2 min
Answer: B
If the speed of a man is 66 km per hour, then what is the distance traveled by him in 30 seconds ?  Choose the correct answer
A) 550m B) 500m C) 375 m D) 420 m E) 440 m

Solution: The distance traveled in 30 sec = 66*(5/18) *30= 
66*(5/18) *30 = 550
550m   550mNSWER:550m
Answer: A
In a family gathering, there is a basket in which there are oranges, bananas and apples. Half of the people in the family eat oranges, half of the other half eat bananas and the rest eat apples. If the number of people who eat oranges are 10 less than the total number of people, find the number of people in the gathering.
Pick one:  A) 5  B) 10  C) 15  D) 20  E) 25

Solution: Let the number of people who eat oranges be X. Then,   total number of people= X + (X/2) + (X/2)= 2X   => 2X-10=X   =>X=10   => Total number of people were 2X=20   Option 20
Answer: D
A cistern is filled by a tap in 6 1/2 hours. Due to leak in the bottom of the cistern, it takes half an hour longer to fill the cistern. If the cistern is full how many hours will it take the leak to empty it?  Choices
A) 81	B) 85	C) 88	D) 91	E) 95

Solution: filling rate - leak rate = net rate   1/6.5 - leak rate = 1/7   leak rate = 2/13 - 1/7 = 1/91   The answer is 91.
Answer: D
A telephone number contains 10 digit, including a 3-digit area code. Bob remembers the area code and the next 5 digits of the number. He also remembers that the remaining digits are not 0, 1, 2, 4, or 7. If Bob tries to find the number by guessing the remaining digits at random, the probability that he will be able to find the correct number in at most 2 attempts is closest to which of the following ?  Pick.
A) 1/625  B) 2/625  C) 4/625  D) 50/625  E) 25/625

Solution: I think most of the answers are missing a point. Let me try to put it across:   Total number of possible numbers are : 5x5 = 25   Correct number =1   Case 1: When he gets it right in first attempt: P(E1) = 1/25   Case 2: He gets 1st attempt wrong and second right:   When he gets it wrong then the probability of getting wrong is 24/25.   Now there are 24 cases with him and he chooses the right one this time.   Probability of right case is 1/24   Thus, P(E2) = 24/25 x 1/24   =1/25   Probability of getting it right in at most two cases = P(E1) + P(E2)   = 1/25 + 1/25   = 2/25   = 50/625   Option (50/625) is therefore right as most of you mentioned but the method employed was wrong.
Answer: D
A, B and C rent a pasture. A puts 10 oxen for 7 months, B puts 12 oxen for 5 months and C puts 15 oxen for 3 months for grazing. If the rent of the pasture is Rs. 210, how much must C pay as his share of rent?
Answers
A) 45
B) 50
C) 54
D) 65
E) none

Solution: Sol.   A : B : C = 10 * 7 : 12 * 5 : 15 * 3 = 70 : 60 : 45 = 14 : 12 : 9.   âˆ´ Câ€™s rent = Rs. [210* 9/35] = Rs. 54.   Answer 54
Answer: C
If 4 (P's Capital ) = 6 ( Q's Capital ) = 10 ( R's Capital ) , then out of the total profit of Rs 3410 , R will receive Choose the most appropriate option: A) 660 B) 700 C) 800 D) 900 E) None of these

Solution: Explanation :   Let P's capital = p, Q's capital = q and R's capital = r   Then   4p = 6q = 10r   => 2p = 3q = 5r   =>q = 2p/3   r = 2p/5   P : Q : R = p : 2p/3 : 2p/5   = 15 : 10 : 6   R's share = 3410 * (6/31) = 110*6= 
110*6 = 660
660. 660nswer : Option 660
Answer: A
Three pieces of timber 42 m, 49 m and 63 m long have to be divided into planks of the same length, What is the greatest possible length of each plank ? Choose the correct choice from the following answers:
A) 7 m
B) 14 m
C) 42 m
D) 63 m
E) None of these

Solution: 7 mnswer   Greatest possible length of each plank = H.C.F of 42, 49, 63 = 7 m   Correct Option: 7 m
Answer: A
Two horses start trotting towards each other, one from A to B and another from B to A. They cross each other after one hour and the first horse reaches B, 5/6 hour before the second horse reaches A. If the distance between A and B is 50 km. what is the speed of the slower horse?  Choices
A) 70 km/h  B) 60 km/h  C) 40 km/h  D) 20 km/h  E) 10 km/h

Solution: Explanation:   If the speed of the faster horse be \inline f_{s} and that of slower horse be \inline s_{s} then   \inline f_{s}+s_{s}=\frac{50}{1}=50   and \inline \frac{50}{s_{s}}-\frac{50}{f_{s}}=\frac{5}{6}   Now, you can go through options.   The speed of slower horse is 20km/h   Since, 20+30=50   and \inline \frac{50}{20}-\frac{50}{30}=\frac{5}{6}   Answer: 20 km/h
Answer: D
A gets 3 times as much money as B gets, B gets only Rs.25 more then what C gets. The three gets Rs.625 in all. Find the share of B? Select.
A) 130  B) 120  C) 218  D) 140  E) 145

Solution: 130+B+C = 625   130 = 3B   3B+B+B-25 = 625   5B = 650   B = 130   130nswer: 130
Answer: A
In a certain pet shop, the ratio of dogs to cats to bunnies in stock is 3 : 7 : 12. If the shop carries 375 dogs and bunnies total in stock, how many dogs are there?  Choose the correct choice.
A) 42
B) 66
C) 75
D) 112
E) 154

Solution: Let us assume the number of dogs, cats and bunnies to be 3x, 7x and 12x   Total dogs and bunnies = 15x.   And we are given that 15x = 375.   Hence x = 25.   Dogs = 3x = 3*25= 
3*25 = 75
75 (Option 75)
Answer: C
If f(a)=5b, what is the value of (f(a)-f(6b)) ? Options:
A) 32b  B) 25b  C) 6a-6b  D) 3a+2b  E) 52a

Solution: f(a)=5b   f(6b) = 30b   (f(6b)-f(a)) = 30b-5b = 25b   Answer is 25b30 -5= 
30 -5 = 25
25b   Answer is 25b
Answer: B
The sum of two numbers is 16. The difference is 2. What are the two numbers? Pick: A) 10-6 B) 8-8 C) 9-7 D) 11-5 E) 13-3

Solution: 9+7= 
9+7 = 16
16   9 - 7= 
9 - 7 = 2
2   The Answer is 9-7
Answer: C
A certain amount earns simple interest of 1750 after 7 years. Had the interest been 2% more, how much more interest would it have earned? Choose the correct choice from the following choices.
A) 35  B) 245  C) 350  D) Cannot be determined  E) None

Solution: Explanation: We need to know the S.I., principal and time to find the rate.   Since the principal is not given, so data is inadequate.   Answer: Option Cannot be determined
Answer: D
A is twice as good a workman as B and they took 7 days together to do the work B alone can do it in?
Choices:
A) 25 days
B) 88 days
C) 21 days
D) 11 days
E) 13 days

Solution: W21 days = 2:1   2x + x = 1/7   x = 1/21 => 21 days   Answer: 21 days
Answer: C
If below equations are true,
24 $ 6 = 64
35 $ 5 = 87
63 $ 7 = 99
Then based on similar logic what's the value of below equation
88 $ 8 = ?  Choose the correct choice from the following answers:
A) 1729	B) 1129	C) 3186	D) 2311	E) 1611

Solution: 1611   1611   1611xplanation:   The number on the right side is formed as (sum of digits of the 1st number)(number1/number2)   example,   24 $ 6 = 64 (2+4 = 6) (24/6 = 4)   35 $ 5 = 87 (3+5=8) (35/5 = 7)   63 $ 7 = 99 (6+3 =9) (63/7 =9)   Simillarly,   88 $ 8 = (8+8 = 16) (88/8 = 11)
Answer: E
A 50 kg metal bar made of alloy of tin and silver lost 5 kg of its weight in the water. 10 kg of tin loses 1.375 kg in the water; 5 kg of silver loses 0.375 kg. What is the ratio of tin to silver in the bar?	Choose the correct choice from the following answers:  A) 1/4  B) 2/5  C) 1/2  D) 3/5  E) 2/3

Solution: you can simply use this formula to avoid confusion:   w1/w2 = (A2 - Aavg)/(Avg - A1)   Here is how you will find the values of A1 an A2.   We have an overall loss (average loss). The average loss is 5 kg when 50 kg alloy is immersed.   This is a loss of (5/50)*100= 
(5/50)*100 = 10
10%.   This is Aavg   The loss of tin is 1.375 kg for every 10 kg.   This means it loses   (1.375/10)*100= 
  (1.375/10)*100 = 13.75
13.75% of its weight in water.   This is A1.   The loss of silver is .375 kg for every 5 kg.   This means it loses   (.375/5)* 100= 
  (.375/5)* 100 = 7.5
7.5% of its weight in water.   This is A2.   Weight of Tin/Weight of Silver= (Silver's loss - Avg loss)/(Avg loss - Tin's loss)   X/Y = (7.5 - 10)/(10 - 13.75) = 2/3   2/3
Answer: E
The distance between Delhi and Mathura is 110 kms. A starts from Delhi with a speed of 20 kmph at 7 a.m. for Mathura and B starts from Mathura with a speed of 25 kmph at 8 p.m. from Delhi. When will they meet?
Choose the most appropriate option:
A) 11 a.m  B) 10 a.m  C) 77 a.m  D) 55 a.m  E) 65 a.m

Solution: D = 110 – 20 = 90   RS = 20 + 25= 
20 + 25 = 45
45   T= 90/45= 
90/45 = 2
2 hours   8 a.m. + 2= 10 a.m.   Answer: 10 a.m
Answer: B
In an examination 65% failed in Math and 35% failed in French. If 22% failed in both. What % of students passed in both. Choose the correct choice from the following choices:
A) 22% B) 15% C) 20% D) 30% E) 10%

Solution: Passed in Math = 100 - 65= 
100 - 65 = 35
35%   Passed in French= 100 - 35= 
100 - 35 = 65
65%   Students who passed Math or French= 100 -22= 
100 -22 = 78
78%   Students passed in Math and French= (Passed in Math) + (Passed in French) - (Students who passed Math or French) = 35+65-78= 
35+65-78 = 22
22%   22%NSWER:22%
Answer: A
The probability that a man will be alive for 10more yrs is 1/4 & the probability that his wife will alive for 10 more yrs is 1/3. The probability that none of them will be alive for 10 more yrs, is	Select:  A) 1/2  B) 1  C) 2/3  D) 3/4  E) 4/5

Solution: Sol. Required probability = Pg.) x P(B) = (1— D x(1 —I) =: x 1=1/2   1/2ns.(1/2)
Answer: A
Some articles were bought at 6 articles for Rs. 5 and sold at 5 articles for Rs. 6. Gain percent is:  Choose the correct choice from the following choices
A) 30%
B) 32%
C) 34%
D) 35%
E) 44%

Solution: Suppose, number of articles bought = L.C.M. of 6 and 5 = 30.   C.P. of 30 articles = Rs.5/6x30= Rs. 25.   S.P. of 30 articles = Rs.6/5x 30= Rs. 36.   Gain % =	11/25x 100% = 44%.   Answer is 44%.
Answer: E
The speed of a car is 100 km in the first hour and 60 km in the second hour. What is the average speed of the car?
Select the correct option.
A) 50 kmph
B) 65 kmph
C) 75 kmph
D) 80 kmph
E) 90 kmph

Solution: Explanation:   S = (100 + 60)/2= 
(100 + 60)/2 = 80
80 kmph   80 kmph)
Answer: D
((-1.9)(0.6) – (2.6)(1.2))/2.0 = ?
Select:
A) -0.71	B) 1.0	C) 1.07	D) 1.71	E) -2.13

Solution: Dove straight into calculation but quickly realized that the sum of two negatives is a negative so there is only one option.   -2.13   Answer -2.13
Answer: E
When the no.7y86038 is exactly divisible by 11, then the smallest whole no.in place of y? Choose the correct choice from the following options:
A) 2
B) 3
C) 5
D) 7
E) 8

Solution: The given number =7y86038   Sum of the odd places =8+0+8+7= 
8+0+8+7 = 23
23   Sum of the even places= 3+6+y   (Sum of the odd places)- (Sum of even places) = Number (exactly divisible by 11)   23-(9+y) = divisible by 11   14 � y = divisible by 11.   Y must be 3, to make given number divisible by 11.   3
Answer: B