MU-NLPC/Calc-aqua_rat huggingface dataset:
The “connection” between any two positive integers a and b is the ratio of the smallest common multiple of a and b to the product of a and b. For instance, the smallest common multiple of 8 and 12 is 24, and the product of 8 and 12 is 96, so the connection between 8 and 12 is 24/96 = 1/4
The positive integer y is less than 20 and the connection between y and 6 is equal to 1/1. How many possible values of y are there?  Options.
A) 7  B) 8  C) 9  D) 10  E) 11

Solution: Since “connection” between y and 6 is 1/1 then LCM(6, y)=6y, which means that 6 and y are co-prime (they do not share any common factor but 1), because if the had any common factor but 1 then LCM(6, y) would be less than 6y.   So, we should check how many integers less than 20 are co-prime with 6, which can be rephrased as how many integers less than 20 are not divisible by 2 or 3 (6=2*3).   There are  (18-2)/2+1= 
 (18-2)/2+1 = 9
9 multiples of 2 in the range from 0 to 20, not inclusive;   There are  (18-3)/3+1= 
 (18-3)/3+1 = 6
6 multiples of 3 in the range from 0 to 20, not inclusive;   There are 3 multiples of 6 in the range from 0 to 20, not inclusive (6, 12, 18) - overlap of the above two sets;   Total multiples of 2 or 6 in the range from 0 to 20, not inclusive is 9+6-3= 
9+6-3 = 12
12;   Total integers in the range from 0 to 20, not inclusive is 19;   Hence, there are total of   19-12= 
  19-12 = 7
7 numbers which have no common factor with 6 other than 1: 1, 5, 7, 11, 13, 17 and 19.   7nswer: 7.
Answer: A
Mrs. Rodger got a weekly raise of $135. If she gets paid every other week, write an integer describing how the raise will affect her paycheck.
Choose the correct answer:  A) $ 145.  B) $ 146  C) $ 135  D) $ 148  E) None

Solution: Solution:   Let the 1st paycheck be x (integer).   Mrs. Rodger got a weekly raise of $ 135.   So after completing the 1st week she will get $ (x+135).   Similarly after completing the 2nd week she will get $ (x + 135) + $ 135.   = $ (x + 135 + 135)   = $ (x + 270)   So in this way end of every week her salary will increase by $ 135.   Answer $ 135
Answer: C
How many revolutions will it take for a circular wheel of 1.95 m radius make in traveling a distance of 1 km?	Choose the most appropriate option
A) 14557.1 B) 24257.1 C) 11257.1 D) 12257.1 E) 12567.1

Solution: 2 * 22/7 * 1.95 * x = 12257.1   x = 1000   Answer: 12257.1
Answer: D
A customer pays 50 dollars for a coffee maker after a discount of 20 dollars
What is the original price of the coffe maker?  Pick.
A) $50  B) $60  C) $70  D) $80  E) $90

Solution: Let x be the original price.   x - 20 = 50   x - 20 + 20 = 50 + 20   x + 0 = 70   x = 70   correct answer is $70)$70
Answer: C
The sum of the present ages of two persons A and B is 60. If the age of A is twice that of B, find the sum of their ages 5 years hence?  Choose the correct choice from the following options:  A) 22  B) 25  C) 70  D) 27  E) 21

Solution: A + B = 60, A = 2B   2B + B = 60 => B = 20 then A = 40.   5 years, their ages will be 45 and 25.   Sum of their ages = 45 + 25= 
45 + 25 = 70
70.Answer:70
Answer: C
Ms. Harris invested in Fund X and Fund B. The total amount she invested, in both funds combined, was $100,000. In one year, Fund X paid 23% and Fund B paid 17%. The interest earned in Fund B was exactly $200 greater than the interest earned in Fund X. How much did Ms. Morris invest in Fund X?  Options:  A) $32,000  B) $36,000  C) $40,000  D) $42,000  E) $45,000

Solution: 0.17B-0.23X = 200 | * 100   17B-23X=20,000   X+B=100,000   B=100,000 - X   17(100,000 - X) - 23X = 20,000   1,700,000 - 17X - 23X = 20,000   1,680,000 = 40X   divide by 40   first two digits: 42...so answer is $42,000.
Answer: D
The speed of a boat in still water is 60kmph and the speed of the current is 20kmph. Find the speed downstream and upstream?	Select.
A) 35, 25 kmph B) 80, 40 kmph C) 40, 60 kmph D) 50, 55 kmph E) 50, 65 kmph

Solution: Speed downstream = 60 + 20= 
60 + 20 = 80
80 kmph   Speed upstream= 60 - 20= 
60 - 20 = 40
40 kmph   ANSWER:80, 40 kmph
Answer: B
Working together, Tim and Tom can type 15 pages in one hour. If they would be able to type 18 pages in one hour if Tom increases his typing speed by 60%, what is the ratio of Tom's normal typing speed to that of Tim?	Choose the correct choice
A) 1/2  B) 1/3  C) 1/4  D) 1/5  E) 1/6

Solution: Lets say Tim types x pages an hour and Tom types y pages an hour.   We know that x+y=15   Tom increase speed by 60% means he will type 1.6 y pages an hour.   So we get x+1.6 y=18   We need to know the ratio of Tom's speed to Tim's speed. This is going to be proportional to the number of pages each can type in an hour, hence (y/x).   Subtracting both : 0.6 y=3 so y=5 ... so x=10   (y/x)=5/10 =1/2   1/2nswer is (1/2)
Answer: A
Bob finishes the first half of an exam in two-sixth the time it takes him to finish the second half. If the whole exam takes him an hour, how many minutes does he spend on the first half of the exam?
Select
A) 15
B) 24
C) 27
D) 36
E) 40

Solution: Many times, it is easiest to think of problems like this conceptually (as opposed to formulaically). Conceptually, if the first half of the exam takes 2/6's the time of the second half (6/6's), we can see that the hour the entire exam took to finish can be broken down into eight's. (Another way to look at this problem is via ratio's - first half is 2:8 and the second half is 6:8). With each sixth of an hour being 15/2 minutes (60/8), the first half of the exam would have taken 15 minutes. Correct answer is 15.
Answer: A
Find the prodect of the local value and absolute value of 4 in 23468
Choices:  A) 400  B) 1600  C) 1200  D) 80  E) 70

Solution: Explanation:   Local value of 4 = 4 x 100 = 400   Place value of 4 = 4   There fore = 4 x 400 = 1600   Answer: Option 1600
Answer: B
How many kg of salt at 42 paise per kg must a man mix with 25 kg of salt at 24 paise per kg so that he may, on selling the mixture at 40 paise per kg gain 25% on the outlay? Choose the correct choice from the following options
A) 15 kg
B) 18 kg
C) 20 kg
D) 24 kg
E) None of these

Solution: Here, cost price of mixture = 100×100/100+25 = 32 paise   ∴q1q2=32−24/42−32=810=45   and hence q1 = 4⁄5 × 25 = 20 kg   Answer 20 kg
Answer: C
At what rate percent per annum will the simple interest on a sum of money be 2/5 of the amount in 10 years?  Answers:  A) 5%  B) 4%  C) 2%  D) 6%  E) 7%

Solution: Let sum = x. Then, S.I. = 2x/5, Time = 20 years.   Rate = (100 * 2x) / (x * 5 * 20) = 2%   ANSWER:2%
Answer: C
In how many different ways can the letters of the word ‘ARMOUM’ be arranged?  Choose the correct choice from the following options.
A) 200	B) 210	C) 220	D) 240	E) 360

Solution: ARMOUR = 6 letter whereas R repeated twice 6! 6xSx4x3x2x1 => 360   360
Answer: E
There are 200 female managers in a certain company. Find the total number R of female employees in the company, if 2/5 of all the employees are managers and 2/5 of all male employees are managers.	Select the correct option.
A) R=300	B) R=400	C) R=500	D) 600	E) None of these

Solution: {Managers} = {Female Managers} + {Male Managers};   We are told that the total number of managers in the company is 2/5 of all the employees , thus{Managers} = 2/5 (M + F), where M and F are number of female and male employees, respectively.   Also, we know that 2/5 of all male employees are managers:{Male Managers} = 2/5 * Mas well as there are total of 200 female managers:{Female Managers} = 200;   Thus:2/5 (M + F) = 200 + 2/5 * M-->F = 500.   Answer: R=500.
Answer: C
The wages of 24 men and 16 women amounts to Rs.11600 per day. Half the number of men and 37 women earn the same amount per day. What is the daily wage of a man?	Options.
A) 2378
B) 277
C) 208
D) 270
E) 350

Solution: Let the wage of a man is m and woman be w.   24m+16w=11600   12m+37w = 11600   Solving we get m = 350   Answer:350
Answer: E
A committee of 6 people is to be selected from 8 people. How many different committees are possible?  Select:  A) 28  B) 40  C) 56  D) D.168  E) 336

Solution: Because the order does not matter in selecting 6 people for the committee, this is a combination question.   The number of ways to select 6 people from 8 = 8C6 = 8!/6!*2! = 28. Hence 28.
Answer: A
A student has 7 trousers and 10 shirts. In how many different ways can the student select a trouser and a shirt?
Choose the correct choice from the following choices:
A) 52 B) 58 C) 64 D) 70 E) 76

Solution: The student can select one trouser in 7 ways.   The student can select one shirt in 10 ways.   The number of ways to select one trouser and one shirt is  7 * 10= 
 7 * 10 = 70
70 ways   The answer is 70.
Answer: D
The average mark obtained by 22 candidates in an examination is 47. The average of the first ten is 55 while the last eleven is 40 .The marks obtained by the 11th candidate is ?	Choices
A) 22	B) 44	C) 49	D) 68	E) 76

Solution: It is clear that 22 x 47 = 10 x 55 + K + 11 x 40 ⇒⇒ K = 44   Answer:44
Answer: B
Out of three numbers, the first is twice the second and is half of the third. If the average of the three numbers is 63, the three numbers in order are?  Choose the most appropriate option.
A) 27, 54, and 108	B) 54, 27, and 108	C) 108, 27, and 54	D) 108, 54, and 27	E) 54, 108, and 27

Solution: Let the numbers be 2x, x and 4x   (2x + x + 4x)/3 = 63   7x/3 = 63   x = 27   The numbers in order are 54, 27, and 108   The answer is 54, 27, and 108.
Answer: B
A’s speed is 51/44 times that of B. If A and B run a race, what part of the length of the race should A give B as a head start, so that the race ends in a dead heat?  Choose the correct choice.
A) 1/51	B) 4/51	C) 7/51	D) 3/44	E) 7/44

Solution: We have the ratio of A’s speed and B’s speed. This means, we know how much distance A covers compared with B in the same time.   This is what the beginning of the race will look like:   (Start) A_________B______________________________   If A covers 51 meters, B covers 44 meters in that time. So if the race is 51 meters long, when A reaches the finish line, B would be 7 meters behind him. If we want the race to end in a dead heat, we want B to be at the finish line too at the same time. This means B should get a head start of 7 meters so that he doesn’t need to cover that. In that case, the time required by A (to cover 51 meters) would be the same as the time required by B (to cover 44 meters) to reach the finish line.   So B should get a head start of 7/51th of the race.   Answer (7/51)
Answer: C
Andrea and Zach are both waiting for an
appointment with a guidance counselor.
When they arrived, each received a card
from the secretary, telling the hour and
minute of his or her arrival. Two minutes
ago, Andrea had been waiting exactly as
many minutes as Zach. Three minutes from
now, Andrea will have been waiting exactly
2/3 as long as Zach. If the time is now 11:30,
at what time did Andrea arrive?
Choose the correct answer
A) 11:16  B) 11:18  C) 11:20  D) 11:23  E) 11:25

Solution: Let a equal the number of minutes that Andrea had been waiting two minutes ago. At   that time, Zach had been waiting for twice as long as Andrea, so he had been waiting for   2a minutes. Three minutes from now, both Andrea and Zach will each have been waiting   for 5 minutes longer:   Two minutes ago Three minutes from now   Andrea a a + 5   Zach 2a 2a + 5   Three minutes from now, Andrea will have been waiting for 23   as long as Zach, so make an equtation as follows:   a+5=2/3(2a+5)   3a+15=2(2a+5)   3a+15=4a+10   3a+5=4a   5=a   Thus, two minutes ago, at 11:28, Andrea had been waiting for 5 minutes. So she arrived at 11:23.   correct answer 11:23)11.23
Answer: D
A question paper consists of five problems, each problem having three internal choices. In how many ways can a candidate attempt one or more problems? Choose the correct choice from the following:
A) 63
B) 511
C) 1023
D) 15
E) 31

Solution: Given that, the question paper consists of five problems. For each problem, one or two or three or none of the choices can be attempted.   Hence, the required number of ways = 45 - 1.   = 210 - 1 = 1024 - 1= 
1024 - 1 = 1_023
1023   ANSWER:1023
Answer: C
A committee of 7 is chosen from 8 men and 5 women so as to contain at least 2 men and 3 women. How many different committees could be formed?	Options:  A) 308  B) 700  C) 1404  D) 2620  E) 3510

Solution: The only cases possible are :   1. 2 men and 5 women : 8C2 * 5C5 = 28   2. 4 men and 3 women: 8C4*5C3 = 280   Rest of the cases will either have 1 or 0 men (not allowed) or will have 1 or 2 or 0 women (not allowed)   Total possible combinations = 28+280= 
28+280 = 308
308. Thus 308 is the correct answer.
Answer: A
Two taps can separately fill a cistern 10 minutes and 15 minutes respectively and when the waste pipe is open, they can together fill it in 20 minutes. The waste pipe can empty the full cistern in?
Choose the correct choice:
A) 2.8 B) 8 C) 6 D) 9 E) 5

Solution: 1/10 + 1/15 - 1/x = 1/20   x = 20/7 = 2.8   2.8nswer: 2.8
Answer: A
A survey of n people in the town of Eros found that 50% of them preferred Brand A. Another survey of 125 people in the town of Angie found that 60% preferred Brand A. In total, 55% of all the people surveyed together preferred Brand A. What is the total number of people surveyed?  Choose the correct answer
A) 50	B) 100	C) 150	D) 200	E) 250

Solution: It is simply a weighted average question. Since the given average of 50% and 60% is 55% (right in the middle), it means the number of people surveyed in Eros (n) is same as the number of people surveyed in Angie.   So n = 125   Total = 125 + 125= 
125 + 125 = 250
250   Answer (250)
Answer: E
There were totally 100 men.85 are married.75 have T.V, 85 have radio,70 have A.C. How many men have T.V, radio, A.C and also married? Pick one:
A) 11
B) 12
C) 13
D) 14
E) 15

Solution: 100-(100-85)-(100-75)-(100-85)-(100-70)= 100-15-25-15-30=100-85= 
100-85 = 15
15   ANSW15R:15
Answer: E
If x is divisible by 9, 108, and 36, which of the following must be the least multiple of x?  Choose the correct answer:
A) 108
B) 36
C) 9
D) 324
E) 120

Solution: If x is divisible by 9, 108, and 36, then x must be a multiple of 9,4 and 3.   Hence,the least multiple of x will be   9*4*3= 
  9*4*3 = 108
108.   108NSWER:108
Answer: A
If q and b are positive numbers, and q^3 + b^3 = 75, then the greatest possible value of q is between:
Choose the correct answer
A) 0 and 3
B) 3 and 5
C) 4 and 5
D) 5 and 7
E) 6 and 9

Solution: Yes the question is ambiguous, and the answer is certainly not C between 4 and 5 .   The question stated: q and b are positive numbers but not positive integers.   so fractions are allowed to be a part of calculation.   So if the answer is C then the value 4.5 = 9/2 must comply the equation.   (9/2)^3 + b^3 = 75   so, b^3 = -129/8 , which is not possible according to the question.   Moreover the question didn't mentioninclusive or not, so we can't assume that b is 4 .   hi asif,   question is correct IMO.   Sincemaximumvalues areuniqueso you cant take any value and make it satisfy with equation   question is asking that maximum value ofa(means that unique value ofa) is between...   its not saying all value of that range will satisfy.
Answer: C
A farmer wishes to start a 100 square metres rectangular vegetable garden. Since he has only 30 m barbed wire, he fences three sides of the garden letting his house compound wall act as the fourth side fencing. The dimension of the garden is:  Pick:
A) 15 m × 6.67 m	B) 20 m × 5 m	C) 30 m × 3.33 m	D) 40 m × 2.5 m	E) None of these

Solution: We have : 2b + l = 30 ⇒ l = 30 – 2b.   Area = 100 m2 ⇒ l × b = 100 ⇒ b(30 – 2b) = 100   ⇒ b2 – 15b + 50 = 0 ⇒ (b – 10)(b – 5) = 0   ⇒ b = 10 or b = 5.   When b = 10, l = 10 and when b = 5, l = 20.   Since the garden is rectangular,   so its dimension is 20 m × 5 m.   Answer 20 m × 5 m
Answer: B
Two trains starting at the same time from two stations 200 km apart and going in opposite directions cross each other at a distance of 110 km from one of the stations. What is the ratio of their speeds ? Choices:
A) 11:9
B) 11:20
C) 9:20
D) 11:8
E) None of these

Solution: Explanation :   In the same time, they cover 110 km and 90 km respectively.   => Ratio of their speeds = 110 : 90 = 11 : 9   11:9nswer : 11:9
Answer: A
Oil is poured in a cylindrical barrel at a rate of 5 cubic meters per hour, the level of oil in the tank rises at a rate of 1 meters per hour. Which of the following best approximates the radius of the tank in meters?	Choose the most appropriate option:
A) √35/22
B) √10/3
C) 4
D) 5
E) 10

Solution: Here's my re-worked solution:   volume = 5 = pi (r^2)(1)   5 = 22/7 (1)(r^2)   35/22 = r^2   r = sqrt(35/22)   √35/22ns: √35/22
Answer: A
A tank is filled in 10 hours by three pipes A, B and C. The pipe C is twice as fast as B and B is twice as fast as A. How much time will pipe A alone take to fill the tank? Choose the correct option:
A) 70 hours  B) 30 hours  C) 35 hours  D) 50 hours  E) 60 hours

Solution: 1/A + 1/B + 1/C = 1/10 ( a, b and c 1 hour work)   given.. 1/B= 2/A and 1/C = 2/B = 4/A   hence 1/A + 2/A + 4/A = 1/10   on solving.... we get 1/70 hours = 1/70 ( work done by 70 hours in 1 hour)   therefore time taken by 70 hours is 70 hours to finish the whole work   70 hoursNSWER:70 hours
Answer: A
In a sports club with 30 members, 17 play badminton and 17 play tennis and 2 do not play either. How many members play both badminton and tennis?  Select:
A) 4 B) 8 C) 9 D) 10 E) 11

Solution: Let x play both badminton and tennis so 17-x play only badminton and 19-x play only tennis. 2 play none and there are total 30 students. hence,   (17-x)+(17-x)+x+2=30   34-2x+x=30   34-x=30   x=4   So 4 members play both badminton and tennis.   4
Answer: A
A train 146 m long is running at a speed of 98 kmph. How long does it take to pass a man who is running at 12 kmph in the same direction as the train?	Choose the correct choice from the following choices:
A) 6 sec
B) 9 sec
C) 12 sec
D) 18 sec
E) 15 sec

Solution: Answer : A.   Speed of the train relative to man = (98 - 12) kmph   = (86* 5/18) m/sec = (215/9)m/sec   Time taken by the train to cross the man   = Time taken by It to cover 146 m at 219/9 m / sec = 146 *9/ 219= 
146 *9/ 219 = 6
6sec
Answer: A
The length of a rectangular landscape is 4times its breadth. There is a playground in it whose area is 1200 square mtr & which is 1/3rd of the total landscape. What is the length of the landscape?
Choose the correct choice from the following choices:
A) 100	B) 110	C) 120	D) 140	E) 160

Solution: Sol. x * 4x = 3 * 1200   x = 30   Length = 4 * 30= 
4 * 30 = 120
120   120
Answer: C
A circular box kept around a circular place. If the difference between the circumference of the outer circle and the inner circle is 44m, find the width of the box?  Choose the correct choice from the following answers.
A) 6 m B) 9 m C) 10 m D) 7 m E) 11 m

Solution: Let radius of the outer circle be R and radius of the inner circle be r.   Circumference of the outer circle =   Circumference of the inner circle =   But,   or, R - r =   Thus, width of the road = 7 m   7 m
Answer: D
The soldiers of Ghost platoon want to call in some mortars on Taliban fighters shooting at them from a mud compound. The compound is 300m away at 5 deg (compass heading). Firebase Darvishan is 10 kilometers away at 290 deg from Ghost platoon. If the mortar shells are landing 100m directly east of the compound, how should Ghost platoon tell the gunnser at Firebase Darvishan to make corrections on their shots?  Options:
A) Drop 100.1M Right .27 deg
B) Drop 106.771M Right 3 deg
C) Drom 91.501M, Left .34 deg
D) Drop 99.918M Right .24deg
E) Drop 85.345M Right 1.28 deg

Solution: Drop 99.918M Right .24degrop 99.918M Right .24deg
Answer: D
The sum of the first 40 positive even integers is 2,550. What is the sum of the odd integers from 101 to 200, inclusive?
Choose the correct choice from the following answers
A) 6,500 B) 7,500 C) 10,500 D) 15,000 E) 19,600

Solution: 101+103+.......199   If we remove 100 from each of these it will be sum of 1st 100 odd numbers.   so 101+103+.......199 = 40 * 100 + (1+3+5+7+......)   sum of 1st 100 natural numbers = (100 * 101) / 2= 
(100 * 101) / 2 = 5_050
5050   Sum of 1st 40 positive even integers= 2550   sum of 1st 100 odd numbers = 5050 - 2550= 
5050 - 2550 = 2_500
2500   so 101+103+.......199= 40 * 100 + (1+3+5+7+......) = 4000 + 2500= 
4000 + 2500 = 6_500
6500   6,500 is the answer.
Answer: A
It was calculated that 50 men could complete a piece of work in 10 days. When work was scheduled to commence, it was found necessary to send 25 men to another project. How much longer will it take to complete the work?  Pick one.
A) 20 days.
B) 15 days.
C) 22 days.
D) 30 days.
E) 18 days.

Solution: One day work = 1 / 10   One man’s one day work = 1 / ( 10 * 50)   Now:   No. Of workers = 25   One day work = 25 * 1 / ( 10 * 50)   The total no. of days required to complete the work = (50 * 10) / 25= 
(50 * 10) / 25 = 20
20   20 days.nswer:20 days.
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 25 percent employee discount to the retail price to buy the recorder, how much did the employee pay for the recorder?  Choose the correct choice from the following:  A) $198  B) $216  C) $220  D) $180  E) $240

Solution: Wholesale cost of video recorder = 200 $   Video recorder was priced at 20 percent above 200 = 240 $   % discount given by store employee = 25   Emlpoyee paid = .75 * 240= 
.75 * 240 = 180
180 $   Answer $180
Answer: D
A room 5m 55cm long and 3m 74 cm broad is to be paved with square tiles. Find the least number of square tiles required to cover the floor Choose the correct choice:
A) 176 B) 170 C) 160 D) 179 E) 174

Solution: Let x and y be the sides of the rectangle. Then, Correct area = xy.   Area of the room = (544 x 374) cm2.   Size of largest square tile = H.C.F. of 544 cm and 374 cm = 34 cm.   Area of 1 tile = (34 x 34) cm2.   Number of tiles required =(544*374)/(34*34)= 
(544*374)/(34*34) = 176
176   176NSWER 176 176
Answer: A
Suppose that 25% of all the wise people are nice and half of all the nice
people are wise. Suppose further that 25% of all the people are neither
wise nor nice. What percent of all the people are both wise and nice?	Choose the correct choice from the following.
A) 10%
B) 15%
C) 20%
D) 25%
E) 30%

Solution: Let k be the number of all the people who are both nice and wise. Then, the   number of wise people is 4k and the number of nice people is 2k. The number of people   who are either wise or nice or both is 4k + 2k − k = 5k. If the number of all people is   x, then x − 0.25x = 5k, so x = 20k/3.   correct answer 15%
Answer: B
A firm has 4 senior partners and 4 junior partners. How many different groups of 3 partners can be formed in which at least one member of the group is a senior partner. (2 groups are considered different if at least one group member is different)  Pick
A) 40  B) 44  C) 48  D) 52  E) 56

Solution: The total number of ways to form a group of 3 is 8C3 = 56   The number of groups without a senior partner is 4C3 = 4   The number of groups which include a senior partner is  56-4= 
 56-4 = 52
52   The answer is 52.
Answer: D
The average of 15 result is 55. Average of the first 7 of them is 57 and that of the last 7 is 61. Find the 8th result?
Choose the correct choice from the following answers
A) 760 B) 720 C) 700 D) 786 E) 797

Solution: Sum of all the 13 results = 15 * 55= 
15 * 55 = 825
825   Sum of the first 7 of them= 7 * 57= 
7 * 57 = 399
399   Sum of the last 7 of them= 7 * 61= 
7 * 61 = 427
427   So, the 8th number= 825 + 399 - 427= 
825 + 399 - 427 = 797
797.   797
Answer: E
If you wanted to plant a certain number of flowers, but knew that 1 in 5 would not grow, how many flowers would you need to plant if you want a total of 20?  Choose the correct choice from the following answers
A) 20
B) 30
C) 28
D) 25
E) 32

Solution: 20 / (5-1)= 
20 / (5-1) = 5
5   5 * 5= 
5 * 5 = 25
25   25 - (5-1)= 20   The correct answer is 25
Answer: D
The average of 10 numbers is calculated as 15. It is discovered later on that while calculating the average, one number namely 36 was wrongly read as 26. The correct average is?  Choose the correct choice:
A) 10 B) 13 C) 16 D) 18 E) 22

Solution: Explanation:   10 * 15 + 36 – 26 = 160/10= 
160/10 = 16
16   16)
Answer: C