MU-NLPC/Calc-aqua_rat huggingface dataset:
During a trip, Francine traveled x percent of the total distance at an average speed of 20 miles per hour and the rest of the distance at an average speed of 80 miles per hour. In terms of x, what was Francineâ€™s average speed for the entire trip?  Choose the correct answer:	A) (180-x)/2	B) (x+60)/4	C) (300-x)/5	D) 600/(115-x)	E) 8,000/(400-4x)

Solution: E....   X% traveeled at 80 mph   100-X% traveeled at 20 mph   total timt taken = x/80 +(100-x)/20 = (400-4x)/80   Total distance = x+(100-x) = 100   Av speed = Tot Dis/Time Taken which is 8,000/(400-4x)
Answer: E
Which of the following describes all values of x for which 2–x^2 >= 0? Choose the correct choice from the following answers:	A) x >= 1	B) x <= –1	C) 0 <= x <= 2	D) x <= –1 or x >= 1	E) –2 <= x <= 2

Solution: Which of the following describes all values of x for which 2–x^2 >= 0?   (A) x >= 1   Plugged in 2. 2–(3)^2 >= 0 -7>=0? NO. Wrong   (B) x <= –1   Plugged in -3. 2–(-3)^2 >= 0 -7>=0? NO. Wrong   (C) 0 <= x <= 2   Plugged in 0, 1, and 2. All of them work. But E is better because it describes all the values of x   (D) x <= –1 or x >= 1   A and B answer this. Wrong.   (E) –2 <= x <= 2   X is a positive or negative fraction or a zero.   x = -2 x = 2 x = 0   Plug all of them. They work.   Answer is –2 <= x <= 2.
Answer: E
A man buys an item at Rs. 800 and sells it at the loss of 20 percent. Then what is the selling price of that item
Choices
A) Rs. 640	B) Rs. 760	C) Rs. 860	D) Rs. 960	E) None of these

Solution: Explanation:   Here always remember, when ever x% loss,   it means S.P. = (100 - x)% of C.P   when ever x% profit,   it means S.P. = (100 + x)% of C.P   So here will be (100 - x)% of C.P.   = 80% of 800   = 80/100 * 800= 
80/100 * 800 = 640
640   Option Rs. 640
Answer: A
A freight elevator can carry a maximum load of 1200 pounds. Sean, who weighs 200 pounds, is in the elevator with two packages weighing 150 pounds and 280 pounds. If he needs to fit three more packages in the elevator that weigh as much as possible without exceeding the elevator limit, what is the difference between their average and the average of the two packages already in the elevator?	Choose the correct choice from the following answers:
A) 25
B) 85
C) 190
D) 215
E) 210

Solution: The average of existing 2 package is (150 + 280)/2 = 430/2= 
430/2 = 215
215   Remaining allowed weight= 1200 - 200 - 430= 
1200 - 200 - 430 = 570
570   .   allowed per package= 570 / 3= 
570 / 3 = 190
190   So difference in average of existing and allowable= 215 - 190= 
215 - 190 = 25
25   Hence 25
Answer: A
A bag contains five white and four red balls. Two balls are picked at random from the bag. What is the probability that they both are different color?	Choose the correct choice from the following:
A) 5/7 B) 5/9 C) 5/1 D) 5/2 E) 5/5

Solution: Two balls can be picked from nine balls in ⁹C₂ ways.   We select one white ball and one red ball from five white balls and four red balls. This can be done ⁵C₁ . ⁴C₁ ways.   The required probability   = (5 * 4)/⁹C₂ = 20/36 = 5/9   Answer:5/9
Answer: B
Sujit incurred a loss of 45% on selling an article for Rs.3410/-. What was the cost price of the article?  Choose one:
A) Rs.6200/- B) Rs.5080/- C) Rs.6250/- D) Rs.6750/- E) None of these

Solution: Explanation:   45% loss means SP of Rs.3410/- is 55% of CP   :. CP = 3410x100/55 = Rs.6200/-   Rs.6200/-nswer: Option Rs.6200/-
Answer: A
Find the least number must be subtracted from 5474827 so that remaining no.is divisible by 12?	Choose the correct choice from the following answers:
A) 3	B) 5	C) 4	D) 7	E) 2

Solution: On dividing 5474827 by 12 we get the remainder 7, so 7 should be subtracted   7
Answer: D
Tap 'A' can fill the tank completely in 6 hrs while tap 'B' can empty it by 12 hrs. By mistake, the person forgot to close the tap 'B', As a result, both the taps, remained open. After 7 hrs, the person realized the mistake and immediately closed the tap 'B'. In how much time now onwards, would the tank be full?  Choose the correct choice from the following answers
A) 2.5 hours	B) 4.5 hours	C) 5.5 hours	D) 1.5 hour	E) None of these

Solution: Explanation :   Tap A can fill the tank completely in 6 hours   => In 1 hour, Tap A can fill 1⁄6 of the tank   Tap B can empty the tank completely in 12 hours   => In 1 hour, Tap B can empty 1⁄12 of the tank   i.e., In one hour, Tank A and B together can effectively fill 1⁄6 - 1⁄12 = 1⁄12 of the tank   => In 7 hours, Tank A and B can effectively fill 1⁄12 × 7 = 7/12 of the tank.   Time taken to fill the remaining 1−(7/12) = 5/12 of the tank = (5/12)/(1/6)= 
(5/12)/(1/6) = 5/2 = around 2.5
2.5 hours. 2.5 hoursnswer : Option 2.5 hours
Answer: A
Among 250 viewers interviewed who watch at least one of the three TV channels namely A, BC. 116 watch A, 127 watch C, while 107 watch B. If 60 watch exactly two channels. How many watch exactly one channel?  Pick
A) 185 B) 180 C) 170 D) 190 E) 195

Solution: 250 = n(Exactly 1 channel) + n(Exactly 2 channels) + n(Exactly 3 channels)   250 = n(Exactly 1 channel) + 60 + n(Exactly 3 channels)   Let's find the value of n(Exactly 3 channels) = x   250 = n(A) + n(B) + n(C) - n(A and B) - n(B and C) - n(C and A) + n(A and B and C)   Note that each of n(A and B) is the sum of 'number of people watching exactly two channels A and B' and 'number of people watching all three channels'.   250 = 116 + 127 + 107 - n(Exactly 2 channels) - 3x + x   250 = 116 + 127 + 107 - 60 - 2x   x = 25   250 = n(Exactly 1 channel) + 60 + 25   n(Exactly 1 channel) = 170   Answer (170)
Answer: C
In a dairy farm, 40 cows eat 40 bags of husk in 40 days. In how many days one cow will eat one bag of husk?	Choices.
A) 32 B) 36 C) 38 D) 40 E) 50

Solution: Assume that in x days, one cow will eat one bag of husk.   More cows, less days (Indirect proportion)   More bags, more days (direct proportion)   Hence we can write as   (cows)40:1   (bags)1:40   x:40   =40×1×40=1×40×x   =x=40   ANSWER : 40
Answer: D
A grocer has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6500?	Choose the correct option:
A) Rs. 4991 B) Rs. 5991 C) Rs. 6001 D) Rs. 6991 E) Rs. 7991

Solution: Total sale for 5 months = Rs. (6435 + 6927 + 6855 + 7230 + 6562) = Rs. 34009.   Required sale = Rs. [ (6500 x 6) - 34009 ]   = Rs. (39000 - 34009)   = Rs. 4991.   Rs. 4991NSWER:Rs. 4991
Answer: A
If the wages of 6 men for 15 days be Rs.2100, then find the wages of
for 12 days.  Choose the correct choice: A) Rs. 2530 B) Rs. 2520 C) Rs. 2500 D) Rs. 1520 E) Rs. 3520

Solution: Let the required wages be Rs. x.   More men, More wages	(Direct Proportion)   Less days, Less wages	(Direct Proportion)   Men 6: 9 : :2100:x   Days 15:12   Therefore (6x15 x x)=(9x12x2100) <=> x=(9x12x2100)/(6x15) =2520   Hence the required wages are Rs. 2520.   Answer is Rs. 2520.
Answer: B
what is the smallest integer that is multiple of 5,7,11 Pick one:	A) A)70	B) B)35	C) C)385	D) D)280	E) E)140

Solution: It is the lcm of 5, 7 and 11 which is 385.   The answer is 385.
Answer: C
A and B together can complete one-ninth of a job in a day. What is the difference between the maximum and minimum number of days A could take to complete the job alone, if A and B take whole number of days to complete the job alone?
Options:  A) 45  B) B.60  C) C.80  D) D.90  E) be determined

Solution: A and B together can complete one-ninth of a job in a day means that AB together does one whole work in 9 days.   1/A +1/B = 1/9   The minimum value A can take is 10 days (Anything less than 10 days is not possible because in other case, no of days taken by B will become negative, which is not possible practically)   When A takes least time (10Days) then B would take the Max time (90 days) to complete the work alone.   In order to find the Max time taken by A, find out the min time taken by B as we did earlier.   The minimum value B can take is 10 days (Anything less than 10days is not possible because in other case, no of days taken by A will become negative, which is not possible practically)   When B takes least time (10Days) then A would take the Max time (90 days) to complete the work alone.   So the required difference = Max Time taken-Min Time taken   = 90 - 10= 
90 - 10 = 80
80 Days   Option C.80
Answer: C
What is the rate percent when the simple interest on Rs.910 amount to Rs.260 in 4 Years?  Choose the correct choice:  A) 7.14  B) 6.14  C) 5.14  D) 3.14  E) 2.14

Solution: 260 = (910*4*R)/100   R = 7.14%   7.14nswer: 7.14
Answer: A
Evaluate permutation
8P8 Pick:
A) 40290  B) 40300  C) 40310  D) 40320  E) 40330

Solution: Explanation:   nPn=n!   8P8=8*7*6*5∗4∗3∗2∗1=40320   Option 40320
Answer: D
1. If the product of 6 integers is negative, at most how many of the integers can be negative? Pick
A) 2 B) 3 C) 4 D) 5 E) 6

Solution: We're told that the product of 6 numbers is negative (the fact that they're integers is actually irrelevant). We're asked for the MAXIMUM number of those 6 that COULD be negative. We'll start with the largest and work our way down..   6 are negative: (-1)(-1)(-1)(-1)(-1)(-1) = + 1...which is NOT a negative product   5 are negative: (-1)(-1)(-1)(-1)(-1)(+1) = -1...which IS a negative product   5
Answer: D
The ratio of the incomes of Rajan and Balan is 7:6 and the ratio of their expenditure is 6:5. If at the end of the year, each saves $1000 then the income of Rajan is?	Choose the correct choice from the following options
A) $7600
B) $7000
C) $8000
D) $9000
E) $5000

Solution: Let the income of Rajan and $7000alan be $7x and $6x   Let their expenditures be $6y and $5y   7x-6y = 1000-------1)   6x-5y = 1000-------2)   From 1) and 2)   x = 1000   Rajan's income = 7x = 7*1000= 
7*1000 = 7_000
$7000   Answer is $7000
Answer: B
In a apartment, 30% of the people speak English, 20% speak Hindi and 10% speak both. If a people is selected at random, what is the probability that he has speak English or Hindi?	Choose the correct option
A) 1/3 B) 2/3 C) 2/5 D) 2/9 E) 3/7

Solution: P (E) = 30 / 100 = 3 / 10 , P (H) = 20 / 100 = 1 / 5 and P (E ∩ H) = 10 / 100 = 1 / 10   P (E or H) = P (E U H)   = P (E) + P (H) - P (E ∩ H)   = (3 / 10) + (1 / 5) - (1 / 10) = 4 / 10 = 2/5   2/5
Answer: C
If a and b are integers and (a*b)^5 = 128y, y could be: Choose the correct choice from the following answers.
A) 1
B) 2
C) 4
D) 8
E) 16

Solution: Distribute the exponent.   a^5 * b^5 = 128 y   Find the prime factorization of 96. This is 2^5 *2^2.   We need 2^3 (or some other power of 2 that will give us a multiple of 2^5 as our second term).   2^3 = 8   The answer is 8.
Answer: D
A car rental company charges for mileage as follows: 10 dollars per mile for the first n miles and 11 dollars per mile for each mile over n miles. How much will the mileage charge be, in dollars, for a journey of d miles, where d > n ? Choose one.
A) 7d-n
B) 5d-n
C) 3*11d-n
D) 11d-n
E) 4d-n

Solution: Total Distance in miles = d   Millage Charge = 10n + (d-n) 11   10n --> For the first n Miles   (d-n)11--> Total no of miles after traveling the first n miles is d-n and the rate after n miles is 11 .   If we solve the equation , We will get 11d-n   Answer : 11d-n
Answer: D
On dividing a number by 357, we get 39 as remainder.On dividing the same number by 17, what will be the remainder ?	Choose the correct choice from the following answers:  A) 4  B) 5  C) 8  D) 7  E) 2

Solution: Let x be the number and y be the quotient.Then,   x=357*y+39   =(17*21*y)+(17*2)+5   =17*(21y+2)+5.   Required number =5.   Answer is 5
Answer: B
The variables m and n are positive integers. When m is divided by 4, there is a remainder of 5, and when n is divided by 3, there is a remainder of 4. Which of the following are possible values of m + n?
I. 50
II. 70
III. 92  Choices
A) I only B) III only C) I and II D) I​ and III E) II and III

Solution: m = 4k + 5 --> Values are 5, 9, 13, 17   n = 3k + 4 --> Values are 4, 7, 10, 13   I. 16 --> 9 + 7 --> Possible   II. 24 --> Not possible   III. 29 --> Not possible   I onlynswer: I only
Answer: A
If 34 men completed 2/5th of a work in 8 days working 9 hours a day. How many more man should be engaged to finish the rest of the work in 6 days working 9 hours a day?
Choose the correct answer
A) 100 B) 102 C) 104 D) 106 E) 108

Solution: Using the chain rule,   M1 x T1 = M2 x T2   Thus, (34 x 8 x 9) / 2/5 = (M2 x 6 x 9) / 3/5   M2 = 68.   Therefore, required number of men = (68 + 34)= 
(68 + 34) = 102
102   ANSWER:102
Answer: B
March 11, 2003 is a Tuesday. What will be the day on which march 11 2004 comes??	Select:
A) Thursday  B) Friday  C) Saturday  D) Sunday  E) Monday

Solution: 2004 is a leap year that means 29 days in feb.   so march 11,2003 to march 11, 2004 will be 366 days.   366/7=52 weeks + 2 days. Hence Thursday   ThursdayNSWER:Thursday
Answer: A
Two electronic musical instruments were purchased for 8000. The first was sold at a profit of 40% and the second at loss of 40%. If the sale price was the same in both the cases, what was the cost price of two electronic musical instruments?	Pick:
A) 2000, 5000
B) 2200, 5500
C) 2400, 5000
D) 2400, 5600
E) None of these

Solution: Here, SP1 = SP2   ⇒ 140 CP1 = 60CP2 ⇒ CP1/CP2=6/14=3/7   ∴ CP1 = 3(3+7)×8000=24003(3+7)×8000=2400   and CP2 = 8000 – 2400 = 5600   Answer 2400, 5600
Answer: D
What is the average of first 21 multiples of 7 ?
Choose the correct answer
A) 49  B) 77  C) 66  D) 57  E) 50

Solution: Required average = 7(1+2+....+21) / 21   (7/21)X ( (21x22) / 2 ) (because sum of first 21 natural numbers)   = 77   ANSWER IS 77
Answer: B
A recipe for a large batch of fruit juice at a factory calls for 10% oranges, 20% lemons, and 70% limes. if 200 lemons are used, how many limes are needed? Choose the correct choice from the following answers:
A) 100	B) 200	C) 300	D) 700	E) 1400

Solution: 20%= 200 fruit   100%=1000 fruit   70% of 1000 fruit=700 fruit   700 limes   ANSWER:700
Answer: D
What is the compound interest paid on a sum of Rs.4500 for the period of 2 years at 10% per annum.
Choose the correct choice from the following answers.
A) 945 B) 620 C) 610 D) 600 E) None of these

Solution: Solution= Interest % for 1st year= 10   Interest % for 2nd year= 10+ 10% of 10= 10+ 10 *10/100= 
10+ 10 *10/100 = 11
11   Total % of interest= 10 + 11= 
10 + 11 = 21
21   Total interest= 21 % 4500 = 4500* (21/100)= 
4500* (21/100) = 945
945   945nswer 945
Answer: A
Combine terms: 8a + 26b -4b – 16a.	Choose the correct choice.
A) 4a + 22b B) -28a + 30b C) -8a + 22b D) 28a + 30b E) 5a + 30b

Solution: Solution:   8a + 26b -4b – 16a.   = 8a – 16a + 26b – 4b.   = -8a + 22b.   Answer: (-8a + 22b)
Answer: C
8 cups of milk are to be poured into a 4-cup bottle and a 8-cup bottle. If each bottle is to be filled to the same fraction of its capacity, how many cups of milk should be poured into the 8-cup bottle?
Choose the correct choice from the following answers:
A) 16/3
B) 7/3
C) 5/2
D) 4/3
E) 3

Solution: Let x be the # of cups going into the 8 cup bottle.   so.... x/8 = ((8-x)/4)   64 - 8x = 4x   64 = 12x   x = 16/3.   16/3nswer : 16/3
Answer: A
Which number should replace both the asterisks in (* /20) x (*/80) = 1 ? Choices:	A) 20	B) 40	C) 60	D) 80	E) 120

Solution: Let (y/20) x (y/80) = 1   y^2 = 20 x 80 = 20 x 20 x 4   y = (20 x 2) = 40   The answer is 40.
Answer: B
Mrs. Rodger got a weekly raise of $148. If she gets paid every other week, write an integer describing how the raise will affect her paycheck.
Choose the most appropriate option:
A) $140
B) $141
C) $142
D) $148
E) $145

Solution: Let the 1st paycheck be x (integer).   Mrs. Rodger got a weekly raise of $ 148.   So after completing the 1st week she will get $ (x+148).   Similarly after completing the 2nd week she will get $ (x + 148) + $ 148.   = $ (x + 148 + 148)   = $ (x + 296)   So in this way end of every week her salary will increase by $ 148.   correct answer $148)$148
Answer: D
In a class there are 20 boys and 24 girls. In how many ways can a boy and a girl be selected?  Choose the correct option
A) 508  B) 480  C) 800  D) 570  E) 503

Solution: We can select one boy from 20 boys in 20 ways.   We select one girl from 24 girls in 24 ways   We select a boy and girl in 20 * 24 ways i.e., = 480 ways.   Answer:480
Answer: B
The average temperature in Lincoln in July is 85 degrees. Last
Wednesday, it was 90 degrees. Today it was 15 degrees cooler than
last Wednesday. What was the temperature today?	Choose the correct choice from the following
A) 15 degrees B) 25 degrees C) 75 degrees D) 45 degrees E) 55 degrees

Solution: The July temperature is extra information. 90 – 15 = 75   It was 75 degrees today.   correct answer 75 degrees
Answer: C
Boys and girls in a class are writing letters. There are twice as many girls as boys in the class, and each girl writes 3 more letters than each boy. If boys write 24 of the 90 total letters written by the class, how many letters does each boy write?
Choose the correct option
A) 3	B) 4	C) 6	D) 8	E) 12

Solution: There are twice as many girls as boys in the class --> g = 2b.   Each girl writes 3 more letters than each boy --> boys write x letters, girls write x+3 letters.   Boys write 24 letters --> bx = 24.   Girls write 90-24= 
90-24 = 66
66 letters --> (2b)(x+3)= 66 --> 2bx + 6b = 66 --> 2*24 + 6b = 66 --> b = 3.   bx = 24 --> 3x = 24 --> x = 8.   Answer: 8.
Answer: D
In how many different orders can the people Alice, benjamin Charlene, David, Elaine, Frederick, Gale, and Harold be standing on line if each of Alice, David, Charlene must be on the line before each of Frederick, Gale, and Harold? Pick one.
A) 2016	B) 1,296	C) 1,512	D) 2,018	E) 2,268

Solution: Place B and E first: 8 options for B, 7 options for E.   We are left with 6 empty places. A, D and C must take first 3 places and F, G, H must take the remaining three. A, D and C can be arranged in their places in 3! ways. The same for F, G, and H.   Total = 8*7*3!*3! = 2,016.   2016nswer: 2016
Answer: A
Deby normally drives to work in 45 minutes at an average speed of 40 miles per hour. This week, however, she plans to bike to work along a route that decreases the total distance she usually travels when driving by 20% . If Deby averages between 12 and 16 miles per hour when biking, how many minutes earlier will she need to leave in the morning in order to ensure she arrives at work at the same time as when she drives?  Choose one
A) 135	B) 105	C) 95	D) 75	E) 45

Solution: 75eby normally drives to work in 45 minutes at an average speed of 40 miles per hour.Use formula 75 = RT   Car:   T1: 45 min   R1: 40 mph   751: [(40*45)/60= 
(40*45)/60 = 30
30 miles   Bike:   T1:?   R2: 12 - 16 mph   752: 08*751= 24 miles   T1: [(24*60)/12= 
(24*60)/12 = 120
120 min (Only 12 mph speed yields an answer given in the choices)   Therefore, 75eb has to leave 120 min - 45 min= 75 min early   ANSWER: 75
Answer: D
In a 100 m race, A runs at 8km per hour. If A gives B a start of 4 m and still him by 15 seconds, what is the speed of B ?
Answers
A) 5.56 km/hr.	B) 5.06 km/hr.	C) 5.76 km/hr.	D) 6.76 km/hr.	E) 5.72 km/hr.

Solution: Time taken by A to cover 100 m =(60 X 60 / 8000)	x 100 sec = 45 sec.   B covers (100 - 4)= 
(100 - 4) = 96
96 m in (45 + 15)= 
(45 + 15) = 60
60 sec.   B's speed= (96 x 60 x 60)/(60 x 1000)km/hr = 5.76 km/hr.   Answer is 5.76 km/hr.
Answer: C
A boat running up stram takes 4 hours to cover a certain distance, while it takes 8 hours to cover the same distance running down stream. what is the ratio between the speed of the boat and the speed of water current respectively?	Choose the correct option
A) 2 : 3
B) 5 : 6
C) 4 : 5
D) 3 : 1
E) 8 : 1

Solution: Explanation:   Let speed of boat is x km/h and speed stream is y km/hr   4(x+y) = 8(x-y)   4x+4y = 8x-8y   12y 4 +4= 
4 +4 = 8
8x-8y   12y= 4x   3y = x   x/y = 3/1   3 : 1   Answer: Option 3 : 1
Answer: D
Jane received an assorted bouquet of 25 flowers which included 8 white flowers,7 lavender flowers and 9 purple flowers.
She closed her eyes a pulled one flower from the bouquet. She opened her eyes, noticed that it was white and placed it aside. She closed her eyes and pulled a 2nd flower from the bouquet. What is the probability that the 2nd flower will also be white?  Choose the correct choice
A) 8/25  B) 7/24  C) 7/25  D) 8/25  E) 9/15

Solution: Solution: Initially, there are 25 flowers total. After the first white flower is removed, 7 white flowers remain and a total of 24 flowers overall are left in the bouquet.   Probability = Favorable outcomes / Total out comes   Therefore, probability = 7/24   Answer Option: 7/24
Answer: B
A man travelled from the village to the post-office at the rate of 25 kmph and walked back at the rate of 4 kmph. If the whole journey took 5 hours 48 minutes, find the distance of the post-office from the village Answers.
A) 20
B) 87
C) 276
D) 198
E) 171

Solution: Explanation:   Average speed = (2 ×a × b)/(a + b) here a = 25 b = 4   Average speed = 2 × 25 × 4/(25 + 4) = 200/29 kmph.   Distance covered in 5 hours 48 minutes = Speed × time   Distance = (200/29) × (29/5) = 40 kms   Distance covered in 5 hours 48 minutes = 40 kms   Distance of the post office from the village = (40/2)= 
(40/2) = 20
20 km.   20nswer: 20
Answer: A
The mean of 50 observations is 200. But later he found that there is decrements of 15 from each observations. what is the the updated mean is ?	Choose the correct choice from the following options:
A) 165
B) 185
C) 198
D) 221
E) 240

Solution: 185   Answer is 185
Answer: B
Let R1 and R2 respectively denote the maximum and minimum possible remainders when (276)n is divided by 91 for any natural number n,n>= 144. Find R1+R2.  Pick one:
A) 89
B) 90
C) 91
D) 92
E) 93

Solution: But the least value for n can be= 144 (as given in question, n>=144)   So, 3n/91= 3*144/91= 68   now, the highest remainder can be when it reaches  68+3+3+3+3+3+3+3= 
 68+3+3+3+3+3+3+3 = 89
89   (as each time we increment n by 1 the remainder increases by 3,   3*145/91= 71- remiander   3*146/91= 74   3*147/91=77   ... so on and so far upto 89 after which it becomes 89+3= 
89+3 = 92
92 which means it crosses 91)   Hence least remainder would be  92 -91= 
 92 -91 = 1
1   and highest remainder= 89   R1+ R2= 89+1= 
89+1 = 90
90   ANSWER:90
Answer: B
Set A contains all the even numbers between 12 and 60 inclusive. Set B contains all the even numbers between 62 and 110 inclusive. What is the difference between the sum of elements of set B and the sum of the elements of set A?
Choose the correct choice
A) 850	B) 1250	C) 1650	D) 2050	E) 2450

Solution: Each term in set B is 50 more than the corresponding term in set A.   The difference of the sums = 25 * 50= 
25 * 50 = 1_250
1250.   The answer is 1250.
Answer: B
The average (arithmetic mean) of four different positive integers is 10. If the first of these integers in 3 times the second integer and the second integer is 2 less than the third integer, what is the least possible value of the fourth integer?	Options.
A) 5	B) 4	C) 3	D) 2	E) 0

Solution: Let the second integer be x and the fourth be a.   Then [3x + x + (x+2) + a]/4 = 10   => 5x + 2 + a = 40   => 5x + a = 40   => a = 40 - 5x   From the above equation we can see that a is minimum when x is maximum, provided both are positive   The maximum value that x can take in the above equation while still keeping a positive is x=8   This gives us a= 40 - 40= 
40 - 40 = 0
0   Therefore the minimum value that the fourth integer can have is 0. Option 0.
Answer: E
38, 85, 22,75, 31,47, 13, 82
Which of the following numbers is greater than three-fourth of the numbers but less than one-fourth of the numbers in the list above? Choose the correct choice from the following answers:
A) a- 56
B) b- 68
C) c- 69
D) d- 71
E) e- 78.5

Solution: Important:- Arrange the numbers in ascending order first.   13, 22, 31, 38, 47, 75, 82, 85   3/4th of the number list represents- 75 (6th number)   remaining 1/4th list represents 82 (7 th number)   78.5 fits in between above 2   Answer:- e- 78.5
Answer: E