MU-NLPC/Calc-aqua_rat huggingface dataset:
If a sequence of 8 consecutive odd integers with increasing values has 3 as its 7th term, what is the sum of the terms of the sequence?  Answers:  A) -16  B) -8  C) -4  D) 4  E) 8

Solution: Let x be the first term.   Then x + 12 = 3 and x = -9   The sum is: x + (x+2) +...+ (x+14) =   8x + 2(1+2+...+7) = 8x + 2(7)(8) / 2 = 8(-9) + 56 = -16   The answer is -16.
Answer: A
A and B can do a work in 18 day, B and C in 30 days, A and C in 22 (1/2) days. In how many days can A,B and C individually do the work? Choose the most appropriate option: A) 30,45,90 B) 30,45,60 C) 30,45,40 D) 30,43,60 E) 30,44,60

Solution: (A+B+C)'s two days work = 1/18 + 1/30 + 2/45   = (5 + 3 + 4)/90 = 2/15   (A+B+C)'s one day work = 2/15 * 1/2 = 1/15   A's one day's work = 1/15 - 1/30 = 1/30   B's one day's work = 1/15 - 2/45 = 1/45   C's one day's work = 1/15 - 1/18= 1/90   So, A,B and C can individually do the work in 30, 45 and 90 days.   30,45,90nswer:30,45,90
Answer: A
If points A and B are (8-3) units apart, which of the following can have only one possible value?
I. The area of a square region with side AB
II. The circumference of a circle passing through points A and B
III. The area of a rectangular region with diagonal AB
Choose the correct option:
A) I only
B) II only
C) III only
D) I and II only
E) I and III only

Solution: I. The area of a square region with side AB --> side=AB=(8-3) or 5 --> the area of a square is 5^2=25, so only one possible value;   II. The circumference of a circle passing through points A and B --> circle is not defined by only two points, hence the circumference of a circle passing through points A and B can take infinitely many values. For example consider when AB=diameter and when points A and B are not the endpoints of the diameter;   III. The area of a rectangular region with diagonal AB --> consider the case when AB is the diagonal of a square (the area is 25/2) and the case when AB is the diagonal of a rectangle with the sides equal to 3 and 4 (the area 12).   I onlynswer: I only.
Answer: A
If six persons sit in a row, then the probability that three particular persons are always together is? Choose the most appropriate option
A) 1/9  B) 1/3  C) 1/5  D) 1/1  E) 1/2

Solution: Six persons can be arranged in a row in 6! ways. Treat the three persons to sit together as one unit then there four persons and they can be arranged in 4! ways. Again three persons can be arranged among them selves in 3! ways. Favourable outcomes = 3!4! Required probability = 3!4!/6! = 1/5   Answer:1/5
Answer: C
The product Z of two prime numbers is between 20 and 60. If one of the prime numbers is greater than 2 but less than 6 and the other is greater than 18 but less than 36 then what is Z?  Choose the correct choice from the following answers:	A) 21	B) 35	C) 39	D) 51	E) 57

Solution: The smallest possible product is 57 which is 3*19.   All other products are too big.   The answer is 57.
Answer: E
If there are 156 laborers in a crew, and on a certain day, 70 were present. Calculate the percentage that showed up for work? (round to the nearest tenth).	Options:	A) 45.9%	B) 43.9%	C) 42.9%	D) 41.9%	E) 44.9%

Solution: 70/156*100=44.87   44.9%   correct answer 44.9%
Answer: E
In a friendship gang Andrew has 8 gang, in how many ways can he invite one or more of the gang to his house?  Choices:
A) 245
B) 255
C) 260
D) 267
E) 278

Solution: Andrew can select one or more than one of his 8 gang.   => Required number of ways = 28 – 1= 255.   255
Answer: B
The smallest 2 digit prime number is?	Choices.
A) A)11
B) B)13
C) C)19
D) D)113
E) E)None

Solution: The smallest 3-digit number is 10, which is divisible by 2.   10 is not a prime number.   11 is a prime number.   Hence 11 is the smallest 2-digit prime number.   11)
Answer: A
A can do a piece of work in 90 days & Y can do it in 80 days. They began working together but A leaves after some days and then B completed the remaining work in 46 days. The number of days after which A left the work was?	Choices:
A) 12 days
B) 18 days
C) 16 days
D) 19 days
E) 21 days

Solution: A and B did the work for some days.   After that , B completed the remaining work in 46 days .   In 46 days, word done by B =   1   80   x 46 =   23   45   Remaining work = 1 – 23/45   = 17/45   Remaining work is done by both A and B together =   17/45x 90 x 80/90 + 80   = 16 days   16 days
Answer: C
If grapes are 92% water and raisins are 20% water, then how much did a quantity of raisins, which currently weighs 11 pounds, weigh when all the raisins were grapes? (Assume that the only difference between their raisin-weight and their grape-weight is water that evaporated during their transformation.)
Choose the correct option:
A) 25 pounds	B) 46 pounds	C) 92 pounds	D) 110 pounds	E) 146 pounds

Solution: Since only water evaporates, then the weight of pulp (non-water) in grapes and raisins is the same. Thus 0.08*{weight of grapes}=0.8*{weight of raisins} --> 0.08x = 0.8*11 --> x = 110.   Answer: 110 pounds.
Answer: D
A furniture store owner decided to drop the price of her recliners by 20% to spur business. By the end of the week she had sold 50% more recliners. What is the percentage increase of the gross? Choose the correct answer
A) 10%
B) 15%
C) 20%
D) 25%
E) 50%

Solution: Say a recliner is actually worth $100   If she sells 100 recliners then she earns $10000   After the discount of 20%, she will earn $80 per recliner and she sells 50% more ie.,150 recliners   Hence her sales yields 150*80= 
150*80 = 12_000
$12000   Increase in sales=12000-10000= 
12000-10000 = 2_000
$2000   So% increase= 2000*100/10000= 
2000*100/10000 = 20
20%   20% is the answer
Answer: C
Of the final grades received by the students in a certain math course, 1/5 are A's, 1/4 are B's, 1/2 are C's, and the remaining 5 grades are D's. What is the number of students in the course?
Pick one
A) 80
B) 110
C) 160
D) 100
E) 400

Solution: We start by creating a variable for the total number of students in the math course. We can say:   T = Total number of students in the math course   Next, we can use variable T in an equation that we translate from the given information. We are given that, of the final grades received by the students in a certain math course, 1/5 are A's, 1/4 are B's, 1/2 are C's, and the remaining 5 grades are D's. Since this represents all the grades in the class, it represents all the students in the class. Thus we know:   #A’s + #B’s + #C’s + #D’s = Total number of students in the class   1/5(T) + ¼(T) + ½(T) + 5 = T   We can multiply the entire equation by 20 to cancel out the denominators of the fractions and we have:   4T + 5T + 10T + 100 = 20T   19T + 100 = 20T   100 = T   There are a total of 100 students in the math class.   Answer is 100.
Answer: D
After decreasing 15% in the price of an article costs Rs.915. Find the actual cost of an article?	Choose the correct choice from the following choices:
A) 915	B) 1000	C) 1076	D) 1067	E) 1760

Solution: 1076P* (85/100) = 915   1076P= 10.76 * 100= 
10.76 * 100 = 1_076
> 1076P= 1076   Answer:1076
Answer: C
In a recent election, James received 1.5 percent of the 2,000 votes cast. To win the election, a candidate needed to receive more than 50 percent of the vote. How many additional votes would James have needed to win the election?	Choose the most appropriate option:
A) 901 B) 989 C) 990 D) 971 E) 1,001

Solution: James = (1.5/100)*2000= 
(1.5/100)*2000 = 30
30   Votes to win= (50/100)*Total Votes +1 = (50/100)*2000 +1= 
(50/100)*2000 +1 = 1_001
1001   Remaining Voted needed to win election= 1001 - 30= 
1001 - 30 = 971
971   Answer: option 971
Answer: D
Victor's job requires him to complete a series of identical jobs. If Victor is supervised at work, he finishes each job three days faster than if he is unsupervised. If Victor works for 144 days and is supervised for half the time, he will finish a total of 36 jobs. How long R would it take Victor to complete 10 jobs without any supervision?  Pick
A) 34
B) 52
C) 60
D) 70
E) 92

Solution: Rate when supervised = (job)/(time) = 1/t.   Rate when unsupervised = (job)/(time) = 1/(t+3).   For  144/2= 
 144/2 = 72
72 days he is supervised and for  144/2= 
 144/2 = 72
72 days he is unsupervised and does 36 jobs:   72/t + 72/(t+3)= 36 --> t=3 days --> t+3 = 6 days.   Victor to complete 10 jobs without any supervision will need R 10(t + 3) = 60 days.   Answer: 60.
Answer: C
If Tim had lunch at $50.50 and he gave 10% tip, how much did he spend?  Choose the correct answer.
A) $30.60
B) $60.60
C) $70.60
D) $55.55
E) $50.60

Solution: The tip is 20% of what he paid for lunch. Hence   tip = 20% of 50.50 = (10/100)*50.50= 
(10/100)*50.50 = 5.05
$5.05   Total spent     50.50 + 5.05= 
  50.50 + 5.05 = 55.55
$55.55   correct answer $55.55
Answer: D
If two integers x, y (x>y) are selected from -10 to 10 (inclusive), how many possible cases are there?
Choose the correct choice from the following answers: A) 150 B) 180 C) 190 D) 210 E) 240

Solution: If two integers x, y (x>y) are selected from -10 to 9 (inclusive), how many possible cases are there?   A. 150   B. 180   C. 190   D. 210   E. 240   --> 21C2=21*20/2= 
21*20/2 = 210
210. Therefore, the answer is 210
Answer: D
When all the students in a school are made to stand in rows of 60, 35 such rows are formed. If the students are made to stand in rows of 25, how many such rows will be formed ?	Choose the correct choice.
A) 31
B) 84
C) 78
D) 19
E) 21

Solution: Explanation:   Total number of students = 60 x 35   When arranged in rows of 25, number of rows formed are,   = 84.   Answer: 84
Answer: B
A train 360 m long runs with a speed of 45 km/hr. What time will it take to pass a platform of 140 m long?	Choose one.
A) 38 sec  B) 35 sec  C) 44 sec  D) 40 sec  E) 48 sec

Solution: train length= 360m   platform length = 140m   time= ?   length = speed * time   total length =360+140= 
360+140 = 500
500m   speed= 45 km/hr =45 * (5/18) (m/sec) =12.5 m/sec   time = length/speed = 500/12.5= 
500/12.5 = 40
40sec   ANSWER:40 sec
Answer: D
A can finish a work in 21 days and B can do the same work in 15 days. B worked for 10 days and left the job. In how many days, A alone can finish the remaining work?  Pick one:  A) 6  B) 5  C) 5.5  D) 7  E) 8

Solution: B's 10 day's work = ( 1 x 10 ) = 2 .   15 3   Remaining work = ( 1 - 2 ) = 1 .   3 3   Now, 1 work is done by A in 1 day.   21   Therefore 1 work is done by A in ( 21 x 1 ) = 7 days.   7
Answer: D
A double decked bus can accomodate 120 passengers,50 in the upper deck and 70 in the lower deck.In how many ways can the passengers be accomodated if 15 refuse to be in the upper deck while 10 others refuse to be in the lower deck? Choose the correct answer:  A) 1. 95!/40!55!  B) 2. 85!/40!45!  C) 3. 110!/50!60!  D) 4. 110!50!60!/40!45!  E) 5. 110!/40!45!

Solution: 120 passengers,50 in the upper deck and 70 in the lower deck.   25 passengers have issues as 15 refuse to be in the upper deck while 10 others refuse to be in the lower deck   So those 15 will be put in lower deck and 10 will be in upper deck   So from the rest 95 passengers(120-25), we need to find 40 people to put into upper deck and the rest go to lower deck   So the ways are: C(95,40) = 95!/40!55! . 1. 95!/40!55!nswer 1. 95!/40!55!
Answer: A
A student has 8 trousers and 11 shirts. In how many different ways can the student select a trouser and a shirt? Choose the correct answer.
A) 76  B) 88  C) 100  D) 112  E) 124

Solution: The student can select one trouser in 8 ways.   The student can select one shirt in 11 ways.   The number of ways to select one trouser and one shirt is  8 * 11= 
 8 * 11 = 88
88 ways   The answer is 88.
Answer: B
At what time between 5 and 6 o' clock are the hands of a 3 minutes apart ?  Choose the correct choice from the following:
A) 24min
B) 12min
C) 13min
D) 14min
E) 15min

Solution: n this type of problems the formuae is   (5*x+ or - t)*12/11   Here x is replaced by the first interval of given time. Here x is 5.   t is spaces apart   Case 1 : (5*x + t) * 12/11   (5*5 + 3) * 12/11   28 * 12/11 = 336/11= min   therefore the hands will be 3 min apart at 31 5/11 min past 5.   Case 2 : (5*x - t) * 12/11   (5*5 -3 ) * 12/11   22 *12/11= 
22 *12/11 = 24
24 min   therefore the hands will be 3 min apart at 24 min past 5 24minnswer: 24min
Answer: A
A, B, C hired a car for Rs. 720 and used it for 9, 10 and 13 hours respectively. Hire charges paid by B are:
Choose the correct choice from the following options
A) Rs 220
B) Rs.225
C) Rs.230
D) Rs.235
E) Rs.255

Solution: A : B : C = 9 : 10 : 13.   Hire charges paid by B = Rs. 720 * 10/32   = Rs. 225.   ANSWER:Rs.225
Answer: B
10 machines, each working at the same constant rate, together can complete a certain job in 12 days. How many additional machines, each working at the same constant rate, will be needed to complete the Job in 8 days?  Choices:  A) 2  B) 3  C) 4  D) 5  E) 8

Solution: Another solution which is faster is Since each machine works at a constant rate. The time needs to bought down from 12 to 8. So the new time is 2/3 of the original time. Thus to achieve this we need the rate to be 3/2 of original.   So 3/2* 10= 
3/2* 10 = 15
15   So we need   15-10= 
  15-10 = 5
5 more machines.   Answer : 5
Answer: D
A man can place 6 large boxes or 9 boxes inside a carton. Can you calculate in how many cartons can he place 66 boxes ? Choose the correct choice from the following options:
A) 9  B) 10  C) 11  D) 12  E) 13

Solution: 9   5 cartons for large boxes = 5 * 6= 
5 * 6 = 30
30 boxes   4 cartons for small boxes= 4 * 9= 
4 * 9 = 36
36 boxes   He will need 9 cartons to place 66 boxes.
Answer: A
The price of a cycle is reduced by 25 per cent. The new price is reduced by a further 20 per cent. The two reductions together are equal to a single reduction of	Choose the correct choice from the following choices:
A) 33 B) 40 C) 99 D) 28 E) 72

Solution: Explanation:   Let the original price of the cycle be 100. After the first reduction the price will be 75.   This new price is then reduced by 20% = 0.8 x 75 = 60   60 represents a reduction of 40 percent on the original.   Answer: 40) 40%
Answer: B
The sum of three consecutive even numbers is 63. Find the middle number of the three? Choices
A) 14
B) 23
C) 25
D) 29
E) 21

Solution: Middle no=63/3= 
63/3 = 21
21   Ans 21
Answer: E
A "digital word" is defined as a four-letter combination of the digits 1 and 0 only. How many "digital words" are there?
Choose the correct option:
A) 2  B) 4  C) 6  D) 8  E) 16

Solution: only digits allowed are 1 and 0 so for a 4 digit number the possibilities are   1111-> 4!/4! ->1   0000-> 4!/3! ->1   1000-> 4!/3! ->4   1100->4!/2!2! ->6   1110->4!/3! ->4   Total 1+1+4+6+4= 
1+1+4+6+4 = 16
16 is possible..   16 is the answer
Answer: E
If 2 is the remainder when m is divided by 5, what is the remainder when 3m is divided by 5?
Answers
A) 0 B) 1 C) 2 D) 3 E) 4

Solution: Let's find a number which when divided by 5 leaves remainder 2 = 5+2= 
5+2 = 7
7   i.e. one possible value of m= 7   value of 3m = 3*7= 
3*7 = 21
21   when em is divided by 5 then remainder= Rem (21/5) = 1   Answer: option 1
Answer: B
How many positive integers less than 254 are multiple of 4 but NOT multiples of 6?
Choose the correct choice from the following options:
A) 20 B) 31 C) 42 D) 43 E) 64

Solution: 252/4= 
252/4 = 63
63   Multiples of 4 which are a multiple of 6 will be of the form 2*2*3= 
2*2*3 = 12
12n where n>0   240/12= 
240/12 = 20
20   63-20= 
63-20 = 43
43   Answer: 43
Answer: D
In how many ways can you sit 8 people on a bench if 5 of them must sit together?	Options
A) 720
B) 2,160
C) 2,880
D) 4,320
E) 40,320

Solution: In such questions, always tie the person that have to sit together. So we have effectively 3+1= 
3+1 = 4
4 persons to arrange.   They can be arranged in 4! ways.   Now the 5 persons can themselves be arranged in 5! ways.   Total ways: 4!*5!= 2880.   2,880 is the answer.
Answer: C
Amit and Ananthu can do a work in 15 days and 25 days respectively. Amit started the work and left after 3 days. Ananthu took over and completed the work. In how many days was the total work completed?
Answers:  A) 28 days  B) 20 days  C) 23 days  D) 25 days  E) 27 days

Solution: 28 daysmit’s one day’s work= 1/15   28 daysmit’s 3 day’s work = 1/15 *3 = 1/5   Work left= 1-1/5 = 4/5   28 daysnanthu’s one day’s work= 1/25   28 daysnanthu can do work in = 4/5 *25= 
4/5 *25 = 20
20/1 days   So total days= 25+3= 
25+3 = 28
28 days   28 daysNSWER:28 days
Answer: A
How many 4 digit numbers that do not contain the digit 2 are there?
Choices.
A) 5832 B) 4332 C) 6444 D) 5854 E) 7296

Solution: Applying combinations....8 * 9 * 9 * 9 = 5832...   8 for first digit...cant be 0 or 2   9 and 9 for 2nd and 3rd....cant be 2   9 for fourth digit cannot be 2   5832NSWER: 5832
Answer: A
If an article is sold at 19% profit instead of 12% profit, then the profit would be Rs. 105 more. What is the cost price? Choose the correct choice from the following
A) 1890  B) 2790  C) 1990  D) 1500  E) 1701

Solution: Let the cost price of an article be Rs. x.   (19% of x) - (12% of x) = 105   19x/100 - 12x/100 = 105 => 7x = 105 * 100   => x = 1500   1990ost price = Rs.1500   Answer: 1990
Answer: C
The difference between the compound interest and the simple interest accrued on an amount of Rs. 18,000 in 2 years was Rs. 405. What was the rate of interest p.c.p.a. ?	Pick.
A) 33  B) 38  C) 37  D) 15  E) 28

Solution: Explanation:   Let the rate be R% p.a. Then,   Rate = 15%.   Answer: 15) 15%
Answer: D
Look at this series: 664, 332, 340, 170, ____, 89, ... What number should fill the blank?  Choose the correct choice from the following:  A) 85  B) 97  C) 109  D) 178  E) 184

Solution: 664/2= 
664/2 = 332
332   340/2= 
340/2 = 170
170   x/2=89 so x=2*89= 
2*89 = 178
178   ANSWER:178
Answer: D
What is the remainder when 9^381 is divided by 5 ?  Pick:
A) 0
B) 1
C) 2
D) 3
E) 4

Solution: I also agree that the remainder is '4' (using the last digit of the powers of 7). Could we have the official answer please?4
Answer: E
The avg weight of A,B & C is 84 kg. If D joins the group, the avg weight of the group becomes 80 kg.If another man E who weights is 3 kg more than D Replaces A, Then the avgof B,C,D&E becomes 79 kg. What is the weight of A?  Choose the most appropriate option.
A) 45  B) 65  C) 75  D) 89  E) 90

Solution: A + B + C = 3 *84= 
3 *84 = 252
252   A + B + C + D= 4 * 80= 
4 * 80 = 320
320 ---- (i)   So, D= 68& E = 68 + 3= 
68 + 3 = 71
71   B + C + D +E= 79 * 4= 
79 * 4 = 316
316 --- (ii)   From Eq. (i) & (ii)   A-E= 320 – 316 = 4   A = E +4 = 71 + 4= 
71 + 4 = 75
75   75
Answer: C
Of the 5 distinguishable wires that lead into an apartment, 2 are for cable television service, and 3 are for telephone service. Using these wires, how many distinct combinations of 3 wires are there such that at least 1 of the wires is for cable television?  Choose the correct answer
A) 6  B) 7  C) 8  D) 9  E) 10

Solution: In these Q, where at least is used, the best is to find none and then subtract from total..   here total ways= 5C3=5!/3!2!=10..   ways where no cable television is used=3c3=1..   therefore ways containing at least one wire of cable tele=10-1=9..   Ans: 9
Answer: D
P is 30% more efficient than Q. P can complete a work in 23 days. If P and Q work together, how much time will it take to complete the same work?	Choose the correct choice from the following options:  A) 9  B) 10  C) 11  D) 13  E) 15

Solution: Work done by P in 1 day = 1/23   Let work done by Q in 1 day = q   q × (130/100) = 1/23   => q = 100/(23×130) = 10/(23×13)   Work done by P and Q in 1 day = 1/23 + 10/(23×13) = 23/(23×13)= 1/13   => P and Q together can do the work in 13 days   Option 13
Answer: D
In what time will a railway train 20 m long moving at the rate of 36 kmph pass a telegraph post on its way? Choose the most appropriate option
A) 6 sec B) 7 sec C) 8 sec D) 9 sec E) 2 sec

Solution: T = 60/36 * 18/5   = 2 sec   Answer:2 sec
Answer: E
A group of students decided to collect as many paise from each member of group as is the number of members. If the total collection amounts to Rs. 59.29, the number of the member is the group is Pick one
A) 57
B) 67
C) 77
D) 87
E) 97

Solution: Money collected = (59.29 x 100) paise = 5929 paise.   Number of members = 5929 = 77.   ANSWER :77
Answer: C
What is the total cost of 2 sandwiches at $2.49 each and 4 sodas at $1.87 each?  Choose the correct option
A) $3.36  B) $6.85  C) $8.46  D) $10.08  E) $12.46

Solution: Answer = $12.46   2 * 2.49 + 4 * 1.87   = 2 (2.50 - 0.01) + 4 (2.00 - 0.13)   = 5 + 8 - 0.02 - 0.52   = 13 - 0.54= 
13 - 0.54 = 12.46
12.46
Answer: E
The ratio of red, yellow, and green jelly beans in a jar is 2:4:5. If the number of jelly beans is increased by 60%, 50%, and 40% respectively, what will be the new ratio?
Choose the correct choice:
A) 10:18:27
B) 12:25:30
C) 14:27:32
D) 16:30:35
E) 18:34:39

Solution: The new ratio will be 3.2:6:7=32:60:70=16:30:35.   The answer is 16:30:35.
Answer: D
If the mean of weight of students in a class of weight 38, 50, 70, 88 and 110 is 71.5 kg, what is the mean of the class if student of weight 50 kg left the class?  Options.
A) 72 kg B) 75 kg C) 68.5 kg D) 76.5 kg E) 80.5 kg

Solution: Mean = (Sum of all weights in class)/(no. students)   M1 = (38+70+88+110)/(4)= 
(38+70+88+110)/(4) = 153/2 = around 76.5
76.5 kg   Answer=76.5 kg
Answer: D
If A speaks the truth 70% of the times, B speaks the truth 60% of the times. What is the probability that they tell the truth at the same time
Answers:  A) 0.49  B) 0.48  C) 0.41  D) 0.42  E) 0.411

Solution: Explanation:   Probability that A speaks truth is 70/100= 
70/100 = 7/10 = around 0.7
0.7   Probability that B speaks truth is   60/100= 
  60/100 = 3/5 = around 0.6
0.6   Since both A and B are independent of each other   So probability of A intersection B is P(A) × P(B)=0.7× 0.6 = 0.42   Answer: 0.42
Answer: D
Convert the following into a fraction:1.0%  Choose the most appropriate option.
A) 1/1
B) 10/1
C) 1/10
D) 1/100
E) None of the Above

Solution: 1.0% =1/1   1/1nswer is 1/1.
Answer: A
If four coins are tossed, the probability of getting two heads and two tails is ?  Choose the correct choice from the following answers:	A) 3/8	B) 3/6	C) 3/1	D) 3/2	E) 3/4

Solution: Since four coins are tossed, sample space = 24   Getting two heads and two tails can happen in six ways.   n(E) = six ways   p(E) = 6/24 = 3/8   3/8nswer: 3/8
Answer: A
The speed of a car is 90 km in the first hour and 60 km in the second hour. What is the average speed of the car?  Choose one:
A) 12  B) 75  C) 88  D) 54  E) 15

Solution: S = (90 + 60)/2= 
(90 + 60)/2 = 75
75 kmph   Answer: 75
Answer: B
A young girl counted in the following way on the fingers of her left hand. She started collang the thumb 1, the index finger 2, the middle finger 3, the ring finger 4, the little finger 5, then reversed direction calling the ring finger 6, the the middle finger 7, the index finger 8, the thumb 9 then back to the index finger for 10, the middel finger for 11, and so on. She counted up to 1993. She ended on her  Choose the correct option.
A) a) thumb	B) b) the index finger	C) c) the middle finger	D) d) the ring finger	E) e) the little finger

Solution: Notice the pattern. The thumb lansd up at numbers 1,9,17,25,33,... so every 8th number   By this patter the thumb is also at number 1993 (multiple of 8 + 1)   Hence 1993 has to be thumb   a) thumbnswer is (a) thumb)
Answer: A
At an examination in which full marks were 500. A got 10% less than B, B got 25% more than C and C got 20% less than D. If A got 360marks, what percentage of full marks was obtained by D?	Choose the correct choice from the following answers.
A) 88% B) 90% C) 80% D) 87% E) 20%

Solution: A B 80% D   90 100 80 100   A D   90 ----- 100   360 ------ ? = 400   500 ------ 400   100 ------- ? => 80%   Answer:80%
Answer: C