MU-NLPC/Calc-aqua_rat huggingface dataset:
In the following question, a matrix of certain characters is given.These characters follow a certain trend, row-wise or column wise.Find out this trend and choose the missing character accordingly.
Answers
A) 12	B) 372	C) 38	D) 37	E) 39

Solution: Explanation:   In the first row, 72 ÷ (24/2) = 72 ÷ 12 = 6.   In the second row, 96 ÷ (16/2) = 96 ÷ 8 = 12.   Let the missing number in the third row be y.   Then, 108 ÷ (y/2) = 18 or y/2 = 108/18= 
108/18 = 6
6 or y= 12.   12nswer: 12) 12
Answer: A
A man swims downstream 36 km and upstream 26 km taking 2 hours each time, what is the speed of the man in still water? Pick:  A) 9  B) 18.4  C) 15.5  D) 16.7  E) 13.4

Solution: 36 --- 2 DS = 18   ? ---- 1   26 ---- 2 US = 13   ? ---- 1 M = ?   M = (18 + 13)/2= 
(18 + 13)/2 = 31/2 = around 15.5
15.5   Answer: 15.5
Answer: C
Three persons invested Rs.9000 in a joint business. The second person invested Rs.1000 more than the first and the third Rs.1000 more than second. After two years, they gained Rs.6300. How much third person will get?
Select the correct option.
A) 2400 B) 2429 C) 2980 D) 2707 E) 2800

Solution: First persons investment = x   Second persons investment = x + 1000   Third persons investments = x + 2000   x + x + 1000 + x + 2000 = 9000   3x = 6000   x = 2000   Ratio = 2000 : 3000 : 4000   2:3:4   4/9 * 6300= 
4/9 * 6300 = 2_800
2800   Answer:2800
Answer: E
A local club has between 24 and 57 members. The members of the club can be separated into groups of which all but the final group, which will have 3 members, will have 4 members. The members can also be separated into groups so that all groups but the final group, which will have 3 members, will have 5 members. If the members are separated into as many groups of 6 as possible, how many members will be in the final group? (Source: Bell Curves)	Choose the correct answer:	A) 6	B) 5	C) 3	D) 2	E) 1

Solution: Case 1: Final group = 3; Rest of the group = 4A; Number of members = 4A + 3   Case 2: Final group = 3; Rest of the group = 5B; Number of members = 5B + 3   4A + 3 = 5B + 3   4A = 5B --> Possible values = 20, 40, 60, ........ --> But only 40 satisfies the given conditions   Number of members = 40 + 3= 
40 + 3 = 43
43   When divided into groups of 6, final group will have 1 member (6*7 + 1).   Answer: 1
Answer: E
In a partnership between A, B and C. A's capital is Rs.5000. If his share of a profit of Rs.800 is Rs.200 and C's share is Rs.130, what is B's capital?  Choose the correct option:
A) 22772
B) 20982
C) 26882
D) 11750
E) 28812

Solution: 200 + 130= 
200 + 130 = 330
330   800 - 330= 
800 - 330 = 470
470   200 ---- 5000   470 ---- ?=> 11750.Answer: 11750
Answer: D
A cake shop has a surplus of cupcakes and prices them at 15% below the wholesale price of $3. A customer comes in with a coupon for 10% off a dozen cupcakes. How much does that customer pay for a dozen cupcakes? Choose the correct choice from the following answers
A) $27.56 B) $28.52 C) $30.60 D) $27 E) $27.54

Solution: Wholesale cost of cupcakes = $3   Cupcakes were priced at 15% below $3 = $2.55   Cost of a dozen cupcakes = 12 * 2.55= 
12 * 2.55 = 30.6
$30.60   % discount given by coupon= 10%   Customer paid = .9 * 30.6= 
.9 * 30.6 = 27.54
$27.54   Answer $27.54
Answer: E
Jill invests $10000 in an account that pays an annual rate of 3.96%, compounding semi-annually. Approximately how much R does she have in her account after two years?
Choose the correct choice from the following answers:
A) $10079.44  B) R=$10815.83  C) $12652.61  D) $14232.14  E) $20598.11

Solution: PS. I guess one can use simple interest to solve cause the answer choices are quite spread between you can easily arrive at something near 8%   Hence R=$10815.83 the answer
Answer: B
What is the ratio whose terms differ by 40 and the measure of which is 2⁄7?
Select:
A) 16 : 56	B) 14 : 56	C) 15 : 56	D) 16 : 72	E) None of these

Solution: Let the ratio be x: (x + 40).Then,   x/(x+40)=2/7 ⇒ 2x + 80 ⇒ x = 16.   ∴ Required ratio = 16 : 56.   16 : 56nswer 16 : 56
Answer: A
A group of boy scouts and girls scouts is going on a rafting trip. 52% of the scouts arrived with signed permission slips. If 40% of the scouts were boy scouts and 62.5% of the boy scouts arrived with signed permission slips, then what percentage of the children were girl scouts who arrived with signed permission slips? Pick one
A) 27
B) 28
C) 29
D) 30
E) 31

Solution: We don't know how many scouts went on the trip, so let's assume 100 scouts went on the trip (since we only are concerned with percents in the answer)   40% were boy scouts so 40% of 100 = 40 were boy scouts   62.5% of the boy scouts brought their permission slips signed, so  .625*40= 
 .625*40 = 25
25 boy scouts had signed slips   15 boy scouts did not   52% of all the scouts had signed slips, so  .52*100= 
 .52*100 = 52
52 in total had signed slips   thus  52 - 25= 
 52 - 25 = 27
27 girl scouts had signed slips   thus the percentage of scouts who were girl scouts arriving with signed permission slips is  27/100= 
 27/100 = 27/100 = around 0.27
.27= 27%   27
Answer: A
A and B can together finish a work in 30 days. They worked at it for 20 days and then B let. The remaining work was done by A alone in 20 more days. B alone can do the entire work in Choose the correct choice from the following answers:
A) 48 days	B) 50 days	C) 54 days	D) 60 days	E) 67 days

Solution: A+B 's 1 day work = 1/30   A+B's 20 days work = 20*1/30 = 2/3   Remaining work left = 1-2/3 = 1/3   A does 1/3 work in ---> 20 days   A does 1 work in ---> x days   x = 3*20= 
3*20 = 60
60 days   A ll take 60 days to complete the whole work   A's 1 day work= 1/60   Therefore B's 1 day work = (A+B)'s 1 day work - A's 1 day work   => 1/30 - 1/60   =1/60   So B's 1 day work = 1/60   B ll complete the entire work alone in 60 days   ANSWER:60 days
Answer: D
A, B and C enter into a partnership. They invest Rs. 40,000, 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? Choose the correct choice from the following answers:  A) 3:4:9  B) 3:4:7  C) 3:4:5  D) 3:4:1  E) 3:4:2

Solution: A:3:4:7:C = (40000 * 36) : (80000 * 12 + 40000 * 24) : (120000 * 24 + 40000 * 12)   = 144:192:336   = 3:4:7   Answer:3:4:7
Answer: B
Three pipes, A, B, & C are attached to a tank. A & B can fill it in 20 & 30 minutes respectively while C can empty it in 15 minutes. If A, B & C are kept open successively for 4 minute each, how soon will the tank be filled?
Choose the correct choice from the following options.
A) 2 hours
B) 12 hours
C) 3 hours
D) 5 hours
E) 6 hours

Solution: in three minute 1/20+1/30-1/15=1/60 part is filled   12 min--------1/60 parts   x min--------- 1 part(full)   x=720 min =12 hours   ANSWER:12 hours
Answer: B
A person was asked to state his age in years. His reply was , "Take my age 3 years hence, multiply it by 3 and subtract 3 times my age 3 years ago and you will know how old I am." What was the age of the person ?  Choose the correct answer:  A) 18  B) 92  C) 27  D) 26  E) 19

Solution: Explanation:   Let the present age of person be x years.   Then, 3(x + 3) - 3(x - 3 ) = x <=> (3x + 9) - (3x - 9) = x <=> x = 18..   18nswer: 18) 18
Answer: A
A, B, C enter into a partnership investing Rs. 35,000, Rs. 45,000 and Rs. 55,000 respectively. The respective shares of A, B, C in annual profit of Rs. 40,500 are:  Choose the correct choice
A) Rs. 10,500, Rs. 13,500, Rs. 16,500	B) Rs. 10,500, Rs. 13,500, Rs. 16,508	C) Rs. 10,500, Rs. 13,500, Rs. 16,56	D) Rs. 10,500, Rs. 13,500, Rs. 16,57	E) Rs. 10,500, Rs. 13,500, Rs. 16,502

Solution: A:B:C = 35000 : 45000 : 55000 = 7:9:11   A's share = 40500 * 7/27 = Rs. 10500   B's share = 40500 * 9/27 = Rs. 13500   C's share = 40500 * 11/27 = Rs. 16500   nual profit of Rs. 40,500 are:   Rs. 10,500, Rs. 13,500, Rs. 16,500nswer:Rs. 10,500, Rs. 13,500, Rs. 16,500
Answer: A
A student committee on academic integrity has 90 ways to select a president and vice president from a group of candidates. The same person cannot be both president and vice president. How many candidates are there?
Choose the most appropriate option
A) 7
B) 8
C) 9
D) 10
E) 11

Solution: Let the number of people to choose from = n   No of people to be chosen = 2   The number of ways 2 people can be chosen from n people=nC2   Now, the two people selected can be arranged in 2! ways   Hence nC2*2!=90 which gives n=10   ANSWER:10
Answer: D
If a man lost 4% by selling oranges at the rate of 12 a rupee at how many a rupee must he sell them to gain 44%?  Select:
A) 1 B) 8 C) 7 D) 5 E) 4

Solution: 96% ---- 12   144% ---- ?     96/144 * 12= 
  96/144 * 12 = 8
8   Answer: 8
Answer: B
A, B and C's age is in ratio 2:5:7. Find their ages if the sum of their age is 70 years.
Pick one:
A) 10 , 25 and 35	B) 5, 20 and 35	C) 8, 20 and 32	D) 11, 23 and 27	E) 10, 20 and 30

Solution: Let the age of A, B and C be 2x, 5x and 7x.   2x + 5x + 7x = 70   14x = 70   x = 5   The ages are 10, 25 and 35.   10 , 25 and 35nswer : 10 , 25 and 35
Answer: A
The price of 24 apples is equal to that of 28 oranges. The price of 45 apples and 60 oranges together is Rs.1350. The total price of 30 apples and 40 oranges is	Options.
A) 850 B) 900 C) 750 D) 950 E) 800

Solution: Let the price of one apple = a and price of one orange = b   Price of 24 apples is equal to that of 28 oranges   24a = 28b   => 6a = 7b   ⇒b=6a/7 -----(Equation 1)   price of 45 apples and 60 oranges together is Rs.1350   => 45a + 60b = 1350   => 3a + 4b = 90   ⇒3a+4(6a)/7=90 (∵ Substituted the value of b from equation 1)   ⇒a+4(2a)/7=30   => 7a + 8a = 30 × 7 = 210   => 15a = 210   ⇒a=21015=423=14   b=6a7=(6×14)/7=6×2=12   Total price of 30 apples and 40 oranges   = 30a + 45b = (30 × 14) + (40 × 12) = 420 + 480= 
420 + 480 = 900
900   Answer is 900.
Answer: B
Two water pumps, working simultaneously at their respective constant rates, took exactly nine hours to fill a certain swimming pool. If the constant rate of one pump was 1.5 times the constant rate of the other, how many hours would it have taken the faster pump to fill the pool if it had worked alone at its constant rate? Choose the correct answer
A) 12  B) 14  C) 15  D) 16  E) 18

Solution: Let x be the rate of the slower pump. Then 1.5x is the rate of the faster pump.   Both pumps together can fill 1/6 of the pool each hour.   2.5x = 1/9   x = 1/22.5   1.5x = 1.5/22.5 = 1/15   The faster pump could fill the pool in 15 hours.   The answer is 15.
Answer: C
(1/5)^f * (1/4)^18 = 1/(2(10)^35). What is f?  Choose the most appropriate option.
A) 17
B) 18
C) 34
D) 35
E) 36

Solution: We need to arrive at a common base. -->   (5)^(-f) * 2^(-36) = 2^(-36)*5^(-35)   5^(-f)=5^(-35)   -f=-35   f=35=35
Answer: D
The average of 17 numbers is 59. Average of the first 9 of them is 56 and that of the last 9 is 63. Find the 9th number? Pick one
A) 64	B) 68	C) 65	D) 66	E) 67

Solution: Sum of all the 17 numbers = 17 * 59 = 1,003Sum of the first 9 of them = 9 * 56= 
9 * 56 = 504
504Sum of the last 9 of them= 9 * 63= 
9 * 63 = 567
567So, the 8th number= 504 + 567 - 1,003= 68.Answer: 68
Answer: B
A grocer has a sales of Euro 6435, Euro 6927, Euro 6855, Euro 7230 and Euro 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Euro 6500?  Select
A) Euro 4691	B) Euro 4591	C) Euro 3591	D) Euro 7791	E) Euro 4991

Solution: E   Euro 4991   Total sale for 5 months = Euro (6435 + 6927 + 6855 + 7230 + 6562)= 
(6435 + 6927 + 6855 + 7230 + 6562) = 34_009
Euro 34009.   Required sale= Euro 4991uro [ (6500 x 6) - 34009 ]   = Euro 4991uro  (39000 - 34009)= 
 (39000 - 34009) = 4_991
Euro 4991uro 4991.
Answer: E
The ratio between the perimeter and the breadth of a rectangle is 5 : 1. If the area of the rectangle is 216 sq. cm, what is the length of the rectangle?
Select.
A) 18 cm
B) 20 cm
C) 22 cm
D) 24 cm
E) 25 cm

Solution: 2(l + b) = 5   b 1   2l + 2b = 5b   3b = 2l   b = 2 l   3   Then, Area = 216 cm2   l x b = 216   l x 2 l = 216   3   l2 = 324   l = 18 cm.   18 cm
Answer: A
A room contains 100 people, 20 percent of whom are women. A group of people, 30 percent of whom are women, leaves the room. Of the people remaining in the room, 10 percent are women. How many people left the room?  Options:
A) 50	B) 40	C) 30	D) 20	E) 10

Solution: (1) 100 total = 20% women ~ 20 women   (2) x left = 30% x women   (3) 100-x left in the room = 10%(100-x) women   --> (1)=(2) + (3)   --> 30% x + 10%(100-x) = 20   --> 20% x = 10   --> x = 50   50nswer is 50
Answer: A
Prakash has 3 pairs of shoes; each pair is a different color. If Prakash randomly selects 2 shoes without replacement from the 6 shoes, what is the probability that she will select 2 shoes of the same color?
Answers:
A) 2/5	B) 1/5	C) 1/9	D) 1/10	E) 1/25

Solution: Can be tackled in this way as well: Probability of selecting any 1 out of 6 shoes = 6/6= 
6/6 = 1
1   Probability of selecting the next shoe (out of 6 available) having the same color= 1/5 (as after selecting the 1st one, there is only 1 another shoe left with the same color).   Thus the total probability = 1*1/5=1/5.   1/5 is the correct answer.
Answer: B
In an exam, B scored 60 percent, C scored 40 percent and D 59 percent. The maximum score awarded in the exam is 600. Find the average mark scored by all the three candidates?	Choose the correct answer.
A) 316	B) 318	C) 320	D) 322	E) 324

Solution: Average mark scored by all the three boys   = [60/100 (600) + 40/100 (600) + 59/100 (600)] / 3   = 318   Answer: 318
Answer: B
Nitin's age was equal to square of some number last year and the following year it would be cube of a number. If again Nitin's age has to be equal to the cube of some number, then for how long he will have to wait? Choose the correct answer: A) 10 years B) 38 years C) 39 years D) 64 years E) 44 years

Solution: current age = 26 years because Nitin's age was equal to square of some number ( 25= 5^2) last year and the following year it would be cube of a number (27= 3^3).   Next cube age will be 64 =4^3 which will come after   64-26= 
  64-26 = 38
38 years.   ANSWER:38 years
Answer: B
Akhil purchased 70kg vegetable at Rs. 420, then sold them at the rate of Rs. 6.50 per kg, find the profit percent. Choose one:  A) 8 1/3%  B) 7 1/3%  C) 6 1/3%  D) 5 1/3%  E) 4 1/3%

Solution: Explanation:   Please note in this type of questions, get the value of 1 kg to solve this question, lets solve it.   C.P. of 1 Kg = 420/70 = Rs. 6   Selling Price = 6.50   Gain = Rs. 0.50   Gain%=.50/6∗100=8 1/3%   Option 8 1/3%
Answer: A
If a, b, c are consecutive positive integers and a<b<c, which of the following must be true?
I. c-a=2
II. -abc is positive integer
III. (a+b+c)/3 is an integer Choose the correct choice from the following options:
A) I & III only  B) II  C) I and II  D) II and III  E) I, II and III

Solution: If a, b, c are consequitive positive integers and a<b<c, which of the following must be true?   1. c-a=2   2. abc is an even integer   3. (a+b+c) /3 is an integer   1.   a=a   b=a+1   c=a+2   c-a=a+2-a=2.   Correct   2. -abc is positive integer.   positive * negative = negative   False.   3. (a+b+c) /3 is an integer   Again;   a=a   b=a+1   c=a+2   a+b+c=(a+a+1+a+2)=3a+3   3a is always divisible by 3   3 is divisible by 3.   Thus3a+3is also divisible by 3.   Rule:   if integer x is divisible by n   and   integer y is divisible by n   then; x+y must be divisible by n   Correct.   I & III onlyns :I & III only( + +1+ +2)= 
( + +1+ +2) = 3
3a+3   3a is always divisible by 3   3 is divisible by 3.   Thus3a+3is also divisible by 3.   Rule:   if integer x is divisible by n   and   integer y is divisible by n   then; x+y must be divisible by n   Correct.   I & III onlyns :I & III only
Answer: A
What is the remainder when 263251 is divided by 9?
Select.
A) 2
B) 8
C) 7
D) 1
E) 9

Solution: Explanation:   If the sum of the digits of a number is divisible by 9, the number will be divisible by 9.   2 + 6 + 3 + 2 + 5 + 1= 
2 + 6 + 3 + 2 + 5 + 1 = 19
19   The nearest multiple of 9 is 18.   19 - 18= 
19 - 18 = 1
1.   Answer: 1
Answer: D
In a village there are 150 men and 90 women in present time.if in next year population will be P=(a^2 +b^2)^1/2 , and in every year men are reduces 5%.what is population of after 2 year. Choose the most appropriate option: A) 140 B) 141 C) 142 D) 143 E) 146

Solution: next year total population=[150^2+90^2]^.5=174.92=175   man decreased by 5% so total man =150*.95= 
150*.95 = 142.5
142.5   women will be= 175-142.5= 
175-142.5 = 32.5
32.5   so population after two years= [135^2+32.5^2]^.5=146.15=146   so population after two year= 146   ANSW146R:146
Answer: E
On a game show, a contestant is given three keys, each of which opens exactly one of three identical boxes. The first box contains $2, the second $200, and the third $2000. The contestant assigns each key to one of the boxes and wins the amount of money contained in any box that is opened by the key assigned to it. What is the probability that a contestant will win more than $2000?	Choose the correct choice from the following choices:
A) 1/9
B) 1/8
C) 1/3
D) 1/6
E) 1/2

Solution: Let's call the boxes that contain $2, $200, and $2000, respectively, Box A, Box B, Box C. These are opened, respectively, by Key A, Key B, and Key C.   We want to know the probability of winning more than $2000. Notice that if the distribution of keys is:   Box A = Key B   Box B = Key A   Box C = Key C   then the contestant wins exactly $2000, not more than $2000. The only configuration that leads to winning more than $2000 is:   Box A = Key A   Box B = Key B   Box C = Key C   i.e., getting all three keys correct. That's the only way to be more than $2000. So, really, the question can be rephrased: what is the probability of guessing the order of keys so that each key matches the correct box?   Well, for a set of three items, the number of possible permutations is 3! = 3*2*1= 
3*2*1 = 6
6.   Of those 6 possible permutations, only one of them leads to all three keys being paired with the right box. So, the answer is   Probability= 1/6,   Answer = 1/6
Answer: D
Given 3^n, for any real integer of n, which of the following is NOT a possible resultant? Choose the correct choice from the following answers:	A) 19,683	B) 17,7147	C) 6,561	D) 1,594,332	E) 59,049

Solution: Given that the answers have different last digits, there are several ways to solve this, but the most straight forward way is to check the algorithm. 3^n has a cycle of 4.   3^1 = 3   3^2 = 9   3^3 = 27   3^4 = 81   3^5 = 243   Observe that the last digit of the resultant of 3^1 and 3^5 is 3. If we continue 3^n, the last digit follows the pattern 3, 9, 7, 1, 3, 9, 7, 1, 3, .... So, all we need look for is the last digit in the pattern.   The answer with last digit 2.   Answer: 1,594,332
Answer: D
A person spent Rs. 8,550 from his salary on food and 8,640 on house rent. After that he was left with 40% of his monthly salary. What is his monthly salary ?  Pick:
A) 38,650	B) 28,650	C) 48,650	D) 68,650	E) 18,650

Solution: Total money spent on food and house rent = 8,550+8,640 = 17,190   Which is 100 - 40= 
100 - 40 = 60
60% of his monthly salary   ∴ His salary= 17190x100/60 = 28650   Answer : 28,650
Answer: B
In a class, there are 18 boys who are over 160 cm tall. If these constitute three-fourths of the boys and the total number of boys is two-thirds of the total number of students in the class, what is the number of girls in the class ?	Choose the correct choice:
A) 11
B) 12
C) 28
D) 27
E) 19

Solution: Let the number of boys be x. Then, (3/4)x = 18 or x = 18 x(4/3) = 24.   If total number of students is y, then (2/3) y = 24 or y = 24 x (3/2) = 36.   Therefore Number of girls in the class = (36 - 24)= 
(36 - 24) = 12
12.   Answer: 12
Answer: B
In a class of 35 students, 2 students did not borrow any books from the library, 12 students each borrowed 1 book, 10 students each borrowed 2 books, and the rest borrowed at least 3 books. If the average number of books per student was 2, what is the maximum number of books any single student could have borrowed?
Pick one:  A) 3  B) 5  C) 8  D) 13  E) 15

Solution: Total # of students = 35   Avg # of books per student = 2   Total # of books = 35*2= 
35*2 = 70
70   # of student borrowed at least 3 books= 35-2-12-10= 
35-2-12-10 = 11
11   # of books borrowed by above 11 students= 70-(12*1)+(10*2) = 38   8onsidering that 10 out of above 11 students borrowed only 3 books, # of books borrowed = 10*3= 
10*3 = 30
30   So maximum # of books borrowed by any single student= 38-30= 
38-30 = 8
8   Option 8
Answer: C
A car traveled the first quarter of a certain distance at four times the speed it traveled the remaining distance. What proportion of the total time traveled, was the time taken to travel the first quarter of the distance?  Choose the correct choice from the following answers
A) 1/4 B) 1/5 C) 1/6 D) 1/7 E) 1/13

Solution: These problems can be solved through algebra or sly number picking. Being a big fan of solving problems with numbers, let's pick a total distance divisible by 4 (say 40) so we can break it up into quarters, and a speed that can easily be one fourth, say 10. Each quarter is thus 10 kilometers (or miles or feet or angstroms for all it matters), and the runner's speed is 10 km/h for the first quarter and 5/2 km/h for the remaining quarters.   He'll take 1 hour to do the first quarter and then 4 hours for the second quarter, 4 hours for the third and 4 hours for the fourth. On total he will take 13 hours to complete this race, of which 1 hour was spent on the first quarter. So 1/13. Answer 1/13.
Answer: E
Robert purchased $4000 worth of US saving bonds. If bonds are sold in $50 or $100 denominations only, which of the following CANNOT be the number of US saving bonds that Robert purchased? Choose the correct choice: A) 20 B) 47 C) 50 D) 80 E) 90

Solution: I started off with looking at the answer choices... 20-47-50 are in a tight range, so my guess was to look and rule out the bigger numbers.   The total amount is $4000. So with 90 bonds, each $50 = $4500 , we already exceed the $4000 limit. Hence E is the answer.   90 remains.
Answer: E
Find the perimeter and area of the rectangle of length 11 cm and breadth 9 cm. Answers:
A) 71 cm2
B) 99 cm2
C) 141 cm2
D) 171 cm2
E) 221 cm2

Solution: length = 11 cm, breadth = 9 cm   Perimeter of rectangle = 2 (length + breadth)   = 2 (11 + 9) cm   = 2 × 20 cm   = 40 cm   We know that the area of rectangle = length × breadth   = (11 × 9) cm22   = 99 cm2   ANSWER : 99 cm2
Answer: B
What is the least number to be added to 1480 to make it a perfect square?	Choose the correct option
A) 105 B) 160 C) 200 D) 71 E) 120

Solution: The numbers greater than 1480 and are square of number is 1600.   The least number that should be added 1480 to make it perfect square = 1600 - 1480= 
1600 - 1480 = 120
120.   ANSW120R:120
Answer: E
8 liters are drawn from a cask full of wine and is then filled with water. This operation is performed three more times . The ratio of the quantity of wine now left in cask to that of the water is 16:65. How much wine did the cask hold originally?
Pick:
A) 12  B) 24  C) 36  D) 42  E) 56

Solution: Let the quantity of wine in the cask originally be x liters   quantity of wine left in cask after 4 operations = x(1 - 8/x)^4 liters   x(1 - 8/x)^4 /x = 16/81   (1-8/x)^4 = (2/3)^4   x = 24   Answer is 24
Answer: B
In an effort to plan out expenses, the Roberts family is representing its annual budget as a circle graph. Each sector of the graph is proportional to the amount of the budget it represents. If “clothes and shoes” takes up 72° of the chart, how much of the Roberts’s $20,000 annual budget is dedicated to clothes and shoes? Pick one:
A) $1,500
B) $3,000
C) $4,000
D) $5,000
E) $5,400

Solution: Given for clothes and shoes” takes up 72° of the circular chart.   Then clothes and shoes = 72/360 * 20000.= 
72/360 * 20000. = 4_000
> 4000.   IMO option $4,000 is correct answer...
Answer: C
If f is a function defined for all k by f(k) = k^5 /16, what is f(3k) in terms of f(k)?
Choose the correct choice from the following answers
A) 1/8 f(k)	B) 5/8 f(k)	C) 244 f(k)	D) 243 f(k)	E) 323 f(k)

Solution: f(k) = k^5 /16   f(3k) = (3k)^5/16 = 243 * k^5 /16 = 243 * (k^5 /16) = 243 f(k).   So answer is 243 f(k).
Answer: D