MU-NLPC/Calc-aqua_rat huggingface dataset:
In a group of 90 students, 36 are taking History, and 30 are taking Statistics. If 59 students are taking History or Statistics or both, then how many students are taking History but not Statistics? Select
A) 9
B) 19
C) 23
D) 27
E) 29

Solution: Number of students taking history =H=36   Number of students taking statistics =S= 30   Total number of students =T= 90   Number of students taking History or Statistics or both =B= 59   Number of students taking neither history nor statistics =N= 90-59= 
90-59 = 31
31   LetXbe the number of students taking both history and statistics.   Then   T= H + S + N - X   or 90 = 36 + 30 +31 - X   or X = 7   Now,   Number of students taking only history will be   H-X   or  36-7= 
 36-7 = 29
29   Answer:- 29
Answer: E
If k and y are integers, and 10k + y is odd , which of the following must be true?	Choose the correct choice from the following answers:
A) k is odd
B) k is even
C) y is odd integer
D) y is even
E) both k and y are odd

Solution: 10k will be always even as 10 has 2 as one of its factors   if 10k+y is odd, then the only possible explanation is that y is odd   correct answer y is odd integer
Answer: C
Which of the following is equal to (y+1)!/y!?
Options.
A) y-1	B) 1+(1/y)	C) 1	D) y+1	E) y

Solution: (y + 1)! = (y + 1) * x!   (y + 1)!/y! = y + 1   Answer: y+1
Answer: D
A tiger is 50 of its own leaps behind a deer. The tiger takes 5 leaps per minutes to deer’s 4. If the tiger and the deer cover 8 m and 5 m per leap respectively, what distance will the tiger have to run before it catches the deer ?	Choose the correct option.
A) 600m
B) 700m
C) 800m
D) 1000m
E) 1200m

Solution: Tiger takes 5 leaps /m and Deer takes 4 leaps/ m   Thus, tiger runs at the speed of 5 x 8 = 40 m/min   and deer runs at the speed of 4 x 5 = 20 m/min   Tiger is 50 leaps behind,which is 50 x 8 = 400 m   Relative speed of tiger and deer is = 20 m/min   Thus, 400/20 = 20 m   Thus,the tiger will catch deer = 20 x 40 =800 m   ANSWER:800m
Answer: C
A number is doubled and 9 is added. If resultant is trebled, it becomes 75. What is that number
Options.
A) 8
B) 10
C) 12
D) 14
E) 15

Solution: Explanation:   => 3(2x+9) = 75   => 2x+9 = 25   => x = 8   8nswer: Option 8
Answer: A
An event manager has ten patterns of chairs and eight patterns of tables.In how many ways can he make a pair of table and chair?
Select the correct option:	A) 70	B) 60	C) 100	D) 80	E) 90

Solution: He has 10 patterns of chairs and 8 patterns of tables.   Hence,A chair can be arranged in 10 ways   A table can be arranged in 8 ways   Hence one chair and one table can be arranged=(10*8)= 
(10*8) = 80
80 ways   Answer is option 80
Answer: D
If there are 4 pairs of twins, and a committee will be formed with 3 members. In how many ways this committee formed in a way that no siblings in a group? Choose the correct choice from the following options:
A) 32  B) 24  C) 56  D) 44  E) 40

Solution: The first member can be anybody, so 8 possibilities.   The second member cannot be the sibling of the previous member, therefore 6 possibilities (anybody from the remaining 3 pairs).   Finally, the third member, can be chosen from the remaining 2 pairs, so 4 possibilities.   This would give us 8*6*4 possibilities, but in this case we don't care about the order in which we choose them, we have to divide the product we obtained by 6(=3!), which is the number of possibilities we can chose the same three distinct members, say ABC (it can be BAC, CAB,...). You can count those possibilities for such a small number as 3, but why avoid permutations? Is it better to start listing the possibilities instead of just accepting the already proven result?   So, the correct answer is   8*4= 
  8*4 = 32
32.   32nswer 32.
Answer: A
Two trains of lengths 156.62 and 100 meters are running on parallel lines with respective speeds of 30 km/hr and 36 km/hr. The time of crossing each other, if they run in the opposite direction is  Select the correct option: A) 322 sec B) 14 sec C) 11sec D) 13 sec E) 34 sec

Solution: Explanation:   Total distance to be covered = 156.62 + 100= 
156.62 + 100 = 256.62
256.62 m   Trains are running in opposite directions, hence   Relative speed= 30 + 36= 
30 + 36 = 66
66 km/hr= 18.33 m/sec   Time = Distance / Relative Speed   = 256.62 /18.33= 
256.62 /18.33 = 14
14 sec   Therefore, the time of crossing each other in the opposite direction is 14 seconds.   ANSWER: 14 sec
Answer: B
James can eat 25 marshmallows is 20 minutes. Dylan can eat 25 in one hour. In how much time will the two eat 150 marshmallows?	Answers
A) 40 minutes.	B) 1 hour and 30 minutes.	C) 1 hour	D) 1 hour and 40 minutes.	E) 2 hours and 15 minutes

Solution: Rate =Output/Time   James Rate=25/20=5/4   Dylan Rate=25/60=5/12   Combined rate = 5/4+5/12= 20/12   Combined Rate*Combined Time= Combined Output   20/12*t=150   t=90 mins => 1 hr 30 min   ANSWER:1 hour and 30 minutes.
Answer: B
How many positive integers will divide evenly into 560?	Select the correct option:
A) 8
B) 12
C) 16
D) 18
E) 20

Solution: 520 = 10*13*4 = 8*5*13 = 2^3*5*13   We need to positive integers will divide evenly into 520 or simply the factors of 520   If a number is of the form 2^a*3^b*5^c,   Total factors = (a+1)(b+1)(c+1)   Therefore, number of factors of 520 = (3+1)*(1+1)*(1+1) = 4*2*2 = 20   Option 20
Answer: E
George takes 30 days to do a piece of work and Mark takes 45 days for the same work. For the first 15 days only George works. Then Mark also joins him. Find the time taken to complete the entire work. Choices: A) 24 days B) 25 days C) 26 days D) 27 days E) 28 days

Solution: George 1 day work= 1/30   Mark 1 day work= 1/45   George 15 day work= 15*1/30 =1/2   Work remaining= 1-1/2 =1/2   George + Mark 1 day work= 1/30 + 1/45 =1/18   Number of day required to complete 1/2 work= (1/2)/(1/18)= 
(1/2)/(1/18) = 9
9 days   So total days required to complete the work is  15+9= 
 15+9 = 24
24 days.   24 daysNSWER:24 days
Answer: A
What is the probability of rolling a total of 5 with a single roll of two fair six-sided dice, each with the distinct numbers 1 through 6 on each side?
Choose the correct choice from the following answers:	A) 1/12	B) 1/6	C) 2/7	D) 1/3	E) 1/9

Solution: Totalsample spacefrom two fair six-sided dice is 36.   There are six possible ways to be 5 i.e. (1+4), (2+3), (3+2), (4+1)   So, total probability is 4/36 or 1/9.   Answer is 1/9.
Answer: E
The number of meters in WB is equal to the square root of the number of centimeters in WB. What is the length of WB (1 meter=100 centimeters)?	Choose one:
A) 100 meters  B) 10 meters  C) 100 centimeters  D) 10 centimeter  E) 1 centimeter

Solution: I'd plug in the options for this question.   Check option A: if the number of meters in WB is 100, then the number of centimeters is 100*100. The square root of 100*100 is 100: 100 = 100.   100 metersnswer: 100 meters.
Answer: A
There are 10 teams in a certain league and each team plays each of the other teams exactly twice. If each game is played by 2 teams, what is the total number of games played?	Choose the correct choice from the following.
A) 15	B) 16	C) 28	D) 56	E) 90

Solution: Every team plays with 9 teams...so total no of matches = 10 x 9 = 90.   Now, each match is played twice => 90 x 2   But 2 teams play a match => 90 x 2 /2 = 90.   Answer: 90
Answer: E
Four of the following five are alike in a certain way and hence form a group. Which one does not belong to the group? Choose one
A) 70	B) 80	C) 52	D) 48	E) 68

Solution: 70   70ll the numbers are multiple of 4, except 70.
Answer: A
A father said to his son, "I was as old as you are at present at the time of your birth." If the father's age is 26 years now, the son's age five years back was?	Answers.
A) 8 years B) 14 years C) 18 years D) 19 years E) 15 years

Solution: Let the son's present age be x years.   Then, (26 - x) = x   2x = 26 => x = 13   Son's age 5 years back = (13 - 5)= 
(13 - 5) = 8
8 years.   8 yearsnswer: 8 years
Answer: A
a certain no. of men can finish a piece f work in 10 days.If however there were 10 men less it will take 10 days more for the work to be finished.How many men were there originally	Choose the most appropriate option
A) 100
B) 110
C) 120
D) 130
E) none of these

Solution: 20 men will do work in 10 day   but 10 i.e. (20-10) will complete work in 20i.e. (10+10) days.   ANSWnone of theseR:none of these
Answer: E
Three 6 faced dice are thrown together. The probability that exactly two dice show the same number on them is ?  Choose the correct choice:  A) 5/11  B) 5/12  C) 5/16  D) 5/10  E) 5/13

Solution: Explanation:   Using question number 11 and 12, we get the probability as   1 - (1/36 + 5/9) = 5/12   Answer:5/12
Answer: B
I bought two books; for Rs.480. I sold one at a loss of 15% and other at a gain of 19% and then I found each book was sold at the same price. Find the cost of the book sold at a loss?	Answers.
A) 299 B) 280 C) 288 D) 271 E) 212

Solution: x*(85/100) = (480 - x)119/100   x = 280   Answer: 280
Answer: B
Cost is expressed by the formula tb^4. If b is doubled, the new cost E is what percent of the original cost?
Choose the correct option.
A) E=200 B) E=600 C) E=800 D) E=1600 E) 50

Solution: Original Cost E, C1=t1*b1^4   New Cost C2= t2*b2^4....only b is doubled so t2=t1 and b2=2b1   C2=t2*(2b1)^4   =16(t1*b1^4)   =16C1   16 times C1=>1600% of C1   Ans E=1600=1600
Answer: D
Let the number which when multiplied by 16 is increased by 375.
Choose the correct choice from the following answers:
A) 14
B) 20
C) 26
D) 25
E) 30

Solution: Solution   Let the number be x .   Then, 16x - x = 375   ‹=›15x = 375   x ‹=› 25.   Answer 25
Answer: D
How many two-element subsets of <1, 2,3,4,5,6,7> are there that do not contain the pair of elements 2 and 4?	Pick
A) 11  B) 12  C) 14  D) 15  E) 20

Solution: 7C2 - 1 = 20 Answer is 20
Answer: E
If E=x^4 + y^4 = 100, then the greatest possible value of x is between  Choose the most appropriate option.
A) 0 and 3	B) 3 and 6	C) 6 and 9	D) 9 and 12	E) 12 and 15

Solution: My attempt:   If E=x^4+y^4=100, then the greatest possible value of x would be when y is minimum.   Let y^4 be 0. Now x^4 = 100. x should be definitely greater than 3 but less than 4. The only option that fits this range is 3 and 6   Hence answer is --   b) 3 and 6.
Answer: B
If the number 517*324 is completely divisible by 9, then the smallest whole number in the place of * will be:	Choose the correct answer:  A) 3  B) 1  C) 5  D) 4  E) 2

Solution: Sum of digits = (5 + 1 + 7 + x + 3 + 2 + 4) = (22 + x), which must be divisible by 9.   x = 5.   5
Answer: C
Rahul's Mathematics test had 70 problems, 10 arithmetic, 30 algebra, 35 geometry problems.
Although he answered 70% of arithmetic, 40% of arithmetic and 60% of geometry problems correctly,
still he got less than 60% problems right. How many more questions he would have to answer more to get
passed  Pick one:
A) 5 B) 6 C) 2 D) 8 E) 9

Solution: Explanation:   Number of questions attempted correctly = (70% of 10 + 40% of 30 + 60% of 35)   = 7 + 12 + 21= 
7 + 12 + 21 = 40
40.   Questions to be answered correctly for 60%= 60% of total quations   = 60 % of 70 = 45.   He would have to answer 42 - 40= 
42 - 40 = 2
2   Answer: Option 2
Answer: C
The manager of a theater noted that for every 10 admissions tickets sold, the theater sells 3 bags of popcorn at 2.25 $ each, 4 sodas at 1.70 $ each and 2 candy bars at 1.00$ each. To the nearest cent, what is the average (arithmetic mean) amount of these snacks sales per ticket sold?  Pick
A) 1.48$
B) 1.56$
C) 1.60$
D) 1.64$
E) 1.70$

Solution: For every 10 tickets amount of snacks sold is  3*2.25+4*1.7+2*1= 
 3*2.25+4*1.7+2*1 = 15.55
$15.55, hence amount of the snacks sales per ticket is $15.55/10=~$1.56.   Answer: 1.56$.
Answer: B
If x+y=20, x-y=36, for integers of x and y, x=?  Pick one:	A) 20	B) 25	C) 28	D) 20	E) 42

Solution: x+y = 20   x-y = 36   2x =56   x = 28   Answer is 28
Answer: C
When the number 72y6139 is exactly divisible by 11, then the smallest whole number that can replace y is?
Options.
A) 1  B) 3  C) 5  D) 6  E) 9

Solution: The given number =72y6139   Sum of the odd places =9+1+y+7   Sum of the even places = 3+6+2= 
3+6+2 = 11
11   (Sum of the odd places)- (Sum of even places)= Number (exactly divisible by 11)   (16+y)-(11) = divisible by 11   y � 5 = divisible by 11.   Y must be 6, to make given number divisible by 11.   6
Answer: D
List F consists of 12 consecutive integers. If -4 is the least integer in list F, what is the range of positive integers in list F? Options:
A) 5
B) 6
C) 7
D) 11
E) 12

Solution: Since -4 is the least integer in list F, then 7 is the largest integer in that list. Thus the range of the positive integers in the list is   7-1= 
  7-1 = 6
6.   Answer: 6.
Answer: B
A car covers a distance of 624 km in 8 hours. Find its speed? Choose the most appropriate option
A) 78	B) 277	C) 298	D) 269	E) 213

Solution: 624/8= 
624/8 = 78
78 kmph   78nswer:78
Answer: A
Two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 16 kmph and 21 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is?	Choose the correct choice from the following
A) 217
B) 444
C) 728
D) 278
E) 268

Solution: 1h ----- 5   ? ------ 60   12 h   RS = 16 + 21= 
16 + 21 = 37
37   T= 12   D = 37 * 12= 
37 * 12 = 444
444   Answer: 444
Answer: B
A speed of 11 metres per second is the same as :  Choose one:
A) 50.4 km/hr B) 55 km/hr C) 60 km/hr D) 68.5 km/hr E) 39.6 km/hr

Solution: Sol.   11 m/sec = [11 * 18/5] km/hr = 39.6 km/hr.   Answer 39.6 km/hr
Answer: E
A, B and C have Rs.700 between them, A and C together have Rs.300 and B and C Rs.600. How much does C have?  Select the correct option:
A) 200	B) 250	C) 300	D) 350	E) 400

Solution: 200+B+C = 700   200+C = 300   B+C =600   --------------   200+B+2C = 900   200+B+C = 700   ----------------   C = 200   200NSWER:200
Answer: A
If the average of e, b, c, 14 and 15 is 12. What is the average value of e, b, c and 29 Options:
A) 12
B) 13
C) 14
D) 15
E) 16

Solution: e+b+c+14+15 = 12*5= 
12*5 = 60
60=>e+b+c = 60-29= 
60-29 = 31
31   e+b+c+29= 31+29= 
31+29 = 60
60   Average= 60/4= 
60/4 = 15
15   Answer 15
Answer: D
The diagonals of a rhombus are 30 cm and 12 cm. Find its area? Options.
A) 176  B) 190  C) 180  D) 278  E) 292

Solution: 1/2 * 30 * 12= 
1/2 * 30 * 12 = 180
180   Answer:180
Answer: C
Three years ago the average age of a class of six members was 22 years. A boy have been added, the average age of the class is the same today. What is the age of the boy?	Choose the correct choice from the following answers: A) A)1 B) B)2 C) C)3 D) D)4 E) E)5

Solution: 6 * 25= 
6 * 25 = 150
150   7 * 22= 
7 * 22 = 154
154   `4   4
Answer: D
Consider a lady took a loan from a bank at the rate of 12% p.a. simple interest. After 3 years she had to pay Rs. 5400 interest only for the period. The principal amount borrowed by her was Choose the correct choice from the following answers:	A) Rs. 2000	B) Rs. 10000	C) Rs. 15000	D) Rs. 20000	E) None of these

Solution: Explanation :   Principal = Rs. (100×5400 / 12×3)   => Rs. 15,000.   Answer : Rs. 15000
Answer: C
A, B and C enter into a partnership. They invest Rs. 1,20,000, Rs. 80,000 and Rs. 1,20,000 respectively. At the end of the first year, B withdraws Rs. 40,000, while at the end of the second year, C withdraws Rs. 80,000. In what ratio will the profit be shared at the end of 3 years ?  Choices
A) 9 : 4 : 8
B) 9 : 4 : 7
C) 3 : 4 : 2
D) 3 : 4 : 1
E) 9 : 4 : 5

Solution: A : B : C = (120000 x 36) : (80000 x 12 + 40000 x 24) : (120000 x 24 + 40000 x 12)   = 432 : 192 : 336   = 9 : 4 : 7.   Answer: 9 : 4 : 7
Answer: B
If w is the square of a positive integer, which of the following must be equal to the square of the next positive integer?
Choose the correct choice from the following options:  A) √n + 1  B) n + 1  C) n^2 + 1  D) w + 2√w + 1  E) n^2 + 2n + 1

Solution: If w is the square of a positive integer, which of the following must be equal to the square of the next positive integer?   w = (x)^2 where x is a positive integer   To calculate -   (x+1)^2 = x^2 + 2x + 1   root(w) = x   Ans - w + 2 root(w) + 1   This should bew + 2√w + 1
Answer: D
Apple costs X rupees per kilogram for first 30 kgs and Y rupees per kilogram for each additional kilogram. If the price of 40 kilograms is 420 and for 50 kgs of Apples is 540 then the cost of first 10 kgs of Apples is
Pick
A) 100
B) 3.66
C) 3.6
D) 3.62
E) 3.61

Solution: 100ns: By framing equations we get   30X+10Y=420   30X+20Y=540   Eliminate Q by multiplying the first equation by 2 and subtracting second equation from the first   60x+20y = 840 -   30x+20y = 540   => 30x = 300 => x = 10   Then we get X = 10   Cost of 10 kgs of apples = 10x 10 = 100   100nswer:100
Answer: A
There are 50 employees in the office of ABC Company. Of these, 22 have taken an accounting course, 14 have taken a course in finance and 15 have taken a marketing course. Nine of the employees have taken exactly two of the courses and 3 employee has taken all three of the courses. How many of the 50 employees have taken none of the courses? Pick:
A) 4
B) 9
C) 8
D) 5
E) 14

Solution: 50 Employees. Counting every different attendand to the courses we have:   Accounting: 22   Finance: 14   Marketing: 15   Which would add up to 51 different attendands, which is not possible.   Now 9 have taken exactly 2 courses, which means that there are 9 less different attendands. Say that 9 of the Finance attentands also attended Accounting.   51-9= 
51-9 = 42
42   3 Person has taken all three courses. As above, we subtract him from the number of different attendands. Since this time the person took all three courses, we have to substract him two times.   42-6= 
42-6 = 36
36.   Answer : 14
Answer: E
A cricket player whose bowling average was 24.85 runs per wicket, takes 5 wicket for 52 runs in a match. Due to this his average decreases by 0.85. What will be the number of wickets taken by him till the last match? Choose the correct choice from the following answers:
A) 64  B) 72  C) 85  D) 96  E) 108

Solution: Average = Total Runs / Total wickets   Total runs after last match = 24.85w + 52   Total wickets after last match = w + 5   (24.85w + 52) / (w + 5) = 24.85 - 0.85= 
24.85 - 0.85 = 24
24   w= 80   so total wickets aftr last match = w+5 = 85   ANSWER:85
Answer: C
A box contains ten bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that at least one bulb is good?  Select:
A) 1/6  B) 16/625  C) 609/625  D) 5/6  E) 18/263

Solution: Required probability   = 1 - 16/625   = 609/625   Answer: 609/625
Answer: C
A bag contains 10 balls numbered from 0 to 9. the balls are such that the person picking a ball out of the bag is equally likely to pick anyone of them. A person picked a ball and replaced it in the bag after noting its number. He repeated this process 2 more times. What is the probability that the ball picked first is numbered higher than the ball picked second and the ball picked second is numbered higher than the ball picked third?  Choose the correct choice from the following answers:	A) 72/100	B) 3/25	C) 4/5	D) 1/6	E) 1/9

Solution: Explanation :   Let, the number of the ball picked first =a, second =b and third =c and these three numbers a, b and c are distinct.   Three distinct ball can be picked in (10×9×8) ways.   The order of a, b and c can be as follows:-   (i) a>b>c.   (ii) a>c>b.   (iii) b>c>a.   (iv) b>a>c.   (v) c>a>b.   (vi) c>b>a.   They will occur equal number of times. So, the number of ways in which (a>b>c) are :-   =>1/6 x 10 x 9 x 8.   =>120.   Hence, the required probability is :-   =>120 / (10x10x10).   =>3/25.   Answer : 3/25
Answer: B
In a certain pond, 100 fish were caught, tagged, and returned to the pond. A few days later, 100 fish were caught again, of which 2 were found to have been tagged. If the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond, what is the approximate number of fish in the pond?
Choose the correct choice from the following answers:	A) 400	B) 625	C) 1,250	D) 2,500	E) 10,000

Solution: total fish = x   percentage of second catch = (2/100)*100= 
(2/100)*100 = 2
2%   so, x * 2%= 50   x = 2500 ans. 2,500
Answer: D
P has $21 more than what Q and R together would have had if both B and C had 1/5 of what P has. How much does P have?	Options.
A) $35	B) $36	C) $37	D) $38	E) $39

Solution: P = (2/5)*P+21   (3/5)*P=21   P=35   The answer is $35.
Answer: A
A circle graph shows how the MegaTech corporation allocates its Research and Development budget: 14% microphotonics; 24% home electronics; 10% food additives; 29% genetically modified microorganisms; 8% industrial lubricants; and the remainder for basic astrophysics. If the arc of each sector of the graph is proportional to the percentage of the budget it represents, how many degrees of the circle are used to represent basic astrophysics research?	Choose the correct choice from the following answers
A) 8°	B) 10°	C) 18°	D) 54°	E) 52°

Solution: 14% microphotonics;   24% home electronics;   10% food additives;   29% genetically modified microorganisms;   8% industrial lubricants;   100-(14+24+10+29+8)= 
100-(14+24+10+29+8) = 15
15% basic astrophysics.   15% of 360° is 54°.   Answer: 54°.
Answer: D
If x = 147, which of the following numbers could be subtracted from x to create a sum that is divisible by 6?
Choose the correct choice from the following choices:	A) 1	B) 2	C) 3	D) 4	E) 5

Solution: Divisibility rule of 6: A number is divisible by 6 if it is divisible by both 2 and 3   Divisibility rule of 3: A number is divisible by 3 if the sum of the digits is divisible by 3   x = 147. We need to make this number even in order for it to be divisible by 2.   Hence we need to subtract an odd number from it.   Hence left over options are A, C, and E   147 - 1= 
147 - 1 = 146
146. Sum of digits= 11.   This is not divisible by 3.   147 - 3= 
147 - 3 = 144
144. Sum of digits= 9   This is divisible by 3.   Hence 3 should be subtracted from 147 to make the resultant a multiple of 6.   3orrect Option: 3
Answer: C
If the integer x is rounded to the nearest hundred, the result represents a 66 2/3 % increase over the value obtained when x is rounded to the nearest ten. which of the following is a possible value of x?  Select:	A) 64	B) 67	C) 99	D) 133	E) 147

Solution: 100= (x-y) + 2/3(x-y)   300=5(x-y)   x-y =60   64 rounded to nearest tenth will result in 60.   64nswer 64
Answer: A
How many numbers between 1 and 100 are divisible by 7 ?
Choices
A) 9	B) 11	C) 17	D) 14	E) 12

Solution: No. of divisible by 7 7, 14 --------- 98, n = a + (N - 1)d   98 = 7 + (N - 1) 7, 98 = 7 + 7N - 7   98/7= N = 14   Answer:14
Answer: D
A sum of money is to be divided among Ann, Bob and Chloe. First, Ann receives $4 plus one-half of what remains. Next, Bob receives $4 plus one-third of what remains. Finally, Chloe receives the remaining $32. How much money N did Bob receive?	Select:
A) 20
B) 22
C) 24
D) 26
E) 52

Solution: Notice that we need not consider Ann's portion in the solution. We can just let K = the money REMAINING after Ann has received her portion and go from there.   Our equation will use the fact that, once we remove Bob's portion, we have $32 for Chloe.   So, we getK - Bob's $ = 32   Bob received 4 dollars plus one-third of what remained   Once Bob receives $4, the amount remaining is K-4 dollars. So, Bob gets a 1/3 of that as well.   1/3 of K-4 is (K-4)/3   So ALTOGETHER, 22ob receives4 + (K-4)/3   So, our equation becomes:K -[4 + (K-4)/3 ]= 32   Simplify to get: K - 4 - (K-4)/3 = 32   Multiply both sides by 3 to get: 3K - 12 - K + 4 = 96   Simplify: 2K - 8 = 96   Solve: K = 52   Plug this K-value intoK - 22ob's $ = 32to get: 52 - 22ob's $ = 32   So, 22ob's $ N= 20   Answer:   22
Answer: B
If d is a positive even integer, and n and m are consecutive integers, then (n - m)^d/(m - n)d =
Choose the correct choice from the following answers
A) -2	B) -1	C) 0	D) 1	E) 2

Solution: d= +ve even integer   Since,n and m are consecutive integers , their difference will be 1   ((n-m)^d)/((m-n)d)= ((n-m)/(m-n))^d = (-1)^d   Since we are raising the difference of n and m to power d , which is even , the answer will be 1 .   Answer 1
Answer: D