MU-NLPC/Calc-aqua_rat huggingface dataset:
Look at this series: 49, 46, 51, 48, 53, 50, ... What number should come next? Options: A) 54 B) 58 C) 45 D) 55 E) 58

Solution: Explanation:   In this simple alternating subtraction and addition series; 3 is subtracted, then 5 is added, and so on.   Answer: Option 55
Answer: D
The data A and B are equal to the data subtracted C; The data B is three times the data A; If the data A is equal to 12 What is the sum of the data A, B and C?	Select the correct option.
A) 86 B) 92 C) 84 D) 102 E) 96

Solution: The equations raised.   A + B = C   B = 3A   A = 12 then   B = 36 and C = 48   A + B + C = 96   Answer: 96
Answer: E
P can finish a work in 18 days. Q can finish the same work in 15 days. Q worked for 10 days and left the job. how many days does P alone need to finish the remaining work?  Choose one:
A) 2 B) 3 C) 4 D) 5 E) 6

Solution: Work done by P in 1 day = 1/18   Work done by Q in 1 day = 1/15   Work done by Q in 10 days = 10/15 = 2/3   Remaining work = 1 – 2/3 = 1/3   Number of days in which P can finish the remaining work = (1/3) / (1/18)= 
(1/3) / (1/18) = 6
6   Answer is 6.
Answer: E
Which of the following leads to the correct mathematical solution for the number of ways that the letters of the word DATA could be arranged to create a four-letter code? Choose one:	A) 4!/2!	B) 6! − (3! + 2!)	C) 6! − (3! × 2!)	D) 6!/(3! + 2!)	E) 6!/(3! × 2!)

Solution: Number of letters in word 'DATA' = 4.   The letters 'A' appear 2 times in the word 'DATA'.   Therefore the mathematical solution for number of ways that the letters of the word D4!/2!T4!/2! can be arranged to create four-letter code   = 4!/2!   4!/2!nswer:4!/2!
Answer: A
If each of 4 digit code is formed of integers from 1 to 10, inclusively, and each of the digits are different, how many possible codes are there? Pick one.
A) 6,040	B) 6,840	C) 6,240	D) 5,040	E) 4,069

Solution: Code consists of 4 digits and no digit is repeated.   First digit of the code can have 10 possibilities   Second digit can have 9 possibilities   Third digit can have 8 possibilities   Total number of possible codes = 10*9*8*7= 
10*9*8*7 = 5_040
5040   Answer: 5,040
Answer: D
If * stands for /, / stands for -, + stands for * and - stands for +, then
9/15*9+2-9 = ?	Select the correct option:
A) 14.7 B) 15.3 C) 14.1 D) 16.2 E) 17.2

Solution: 9/15*9+2-9 is changed to 9-15/9*2+9   resolve it like (9)-(15*2)/9+(9)   => 18-30/9   =>18-10/3 => (54-10)/3   => 44/3= 
44/3 = 44/3 = around 14.666667
14.6666666666666666666   implies 14.7   14.7NSWER:14.7
Answer: A
Simple interest on a certain sum of money for 3 years at 8% per annum is half the compound interest on Rs. 4000 for 2 years at 10% per annum. The sum placed on simple interest is:	Choose the correct choice from the following answers.
A) Rs.1550	B) Rs.1650	C) Rs.1750	D) Rs.2000	E) Rs.3000

Solution: C.I = 4000 * (1+10/100)2 –4000   = 4000 *11/10 + 11/10 –4000 = Rs.840   :. Sum = Rs.(420 * 100)/ (3 *8) = Rs.1750   ANSWER:Rs.1750
Answer: C
Find the compound interest on $500 in 5years at 5% per annum, the interest being compounded yearly? Choose the correct choice from the following:	A) $138.14	B) $150.12	C) $142.65	D) $152	E) $164.12

Solution: Principle = $500   Rate = 5% yearly   Amount = 500*(1 + 5/100)^5 = 500 * 21/20 * 21/20 * 21/20 * 21/20 * 21/20   = $638.14   C.I. = 638.14-500= 
638.14-500 = 138.14
$138.14   $138.14nswer is $138.14
Answer: A
A case of 12 rolls of paper towels sells for $9. The cost of one roll sold individually is $1.What is the percent T of savings per roll for the 12-roll package over the cost of 12 rolls purchased individually?	Choices:
A) 9%
B) 11%
C) 15%
D) 25%
E) 90%

Solution: Cost of 12 paper towels individually = 1*12= 
1*12 = 12
12   Cost of a set of 12 paper towels= 9   Cost of one roll = 9/12 = 3/4= 
3/4 = 3/4 = around 0.75
0.75   Savings per roll= 1-.75= 
1-.75 = 0.25
0.25   % of savings is T= .25/ 1 *100= 
.25/ 1 *100 = 25
25% 25% is the answer.
Answer: D
A man can row a boat at 20 kmph in still water. If the speed of the stream is 4 kmph, what is the time taken to row a distance of 60 km downstream? Choose the correct choice from the following:
A) 30/18 B) 30/29 C) 30/12 D) 30/13 E) 30/12

Solution: Speed downstream = 20 + 4= 
20 + 4 = 24
24 kmph.   Time required to cover 60 km downstream= d/s = 60/24   = 30/12 hours.   Answer:30/12
Answer: E
What is the place value of 3 in the numeral 3259  Choose one:
A) 2700
B) 2800
C) 2900
D) 2980
E) 3000

Solution: 3 * 1000= 
3 * 1000 = 3_000
3000   3000
Answer: E
The area of a rectangular field is equal to 300 square meters. Its perimeter is equal to 70 meters. Find the length of this rectangle.	Select the correct option:
A) 40
B) 70
C) 20
D) 80
E) 60

Solution: L * W = 300 : area , L is the length and W is the width.   2 L + 2 W = 70 : perimeter   L = 35 - w : solve for L   (35 - W) * W = 300 : substitute in the area equation   W = 15 and L = 20 : solve for W and find L using L = 35 - w.   correct answer 20
Answer: C
What is the sum of the integers from -190 to 192 inclusive?	Choose the correct choice from the following options:
A) 0
B) 5
C) 383
D) 875
E) 965

Solution: sum/n= average.   sum=(average)(n)   average=a+b/2=190+192/2=1   number of items(n)=B-A+1=192-(-190)+1=192+191= 
192+191 = 383
383.   sum=average*n=1*383= 
1*383 = 383
383.   answer is 383
Answer: C
What is the units digit of (147^25)^49 ?  Options
A) 1
B) 3
C) 5
D) 7
E) 9

Solution: The units digit of the exponents of 7 repeat in a cycle of four, which is {7,9,3,1}. The number 25 has the form 4n+1 so the units digit is 7 inside the bracket. The exponent 49 has the form 4n+1, so the units digit is 7. The answer is 7.
Answer: D
A certain cube floating in a bucket of water has between 60 and 85 percent of its volume below the surface of the water. If between 9 and 26 cubic centimeters of the cube's volume is above the surface of the water, then the length of a side of the cube is approximately
Select the correct option: A) 4 B) 5 C) 7 D) 8 E) 9

Solution: If sides are 7, vol=7^3=343   60%= 205.8, 85%=291.55   so vol above water, between 137.2 and 51.45 -->too big   If side are 4, vol = 64   60%=38.4, 85%=54.4   vol above water between 25.6 and 9.6   So 4 should be the answer.   Check option C,   If sides are 5, vol = 125   60%= 75, .85%=106.25   vol above water between 18.75-50   (Sides are 4 cubic centimeters)   4
Answer: A
In a kilometer race, A beats B by 80 meters or 10 seconds. What time does A take to complete the race?  Choose the correct option:
A) 167 sec B) 190 sec C) 176 sec D) 115 sec E) 123 sec

Solution: Time taken by B run 1000 meters   = (1000 * 10)/80= 
(1000 * 10)/80 = 125
125 sec.   Time taken by A= 125 - 10= 
125 - 10 = 115
115 sec.   Answer:115 sec
Answer: D
Two pipes P and Q can fill a cistern in 10 and 15 minutes respectively. Both are opened together, but at the end of 2 minutes the first is turned off. How many more minutes will it take for the cistern to fill after the first pipe is turned off?	Select:
A) 6  B) 7  C) 8  D) 9  E) 10

Solution: Let x be the total time it takes for the cistern to fill.   2/10 + x/15 = 1   x/15 = 4/5   x = 12   After the first pipe is turned off, it takes 10 more minutes to fill the cistern.   The answer is 10.
Answer: E
An employee may claim Rs. 7.00 for each km when he travels by taxi and Rs. 6.00 for each km if he drives his own car. If in one week he claimed Rs. 595 for traveling 90 km. How many kms did he travel by taxi ?
Choose the correct choice from the following options.
A) 55 kms B) 85 kms C) 65 kms D) 15 kms E) 25 kms

Solution: Explanation:   Let x and y be the respective km's travelled by man via taxi and by his own car.   Given x + y = 90 => x = 90 - y   But according to the question,   7x + 6y = 595   7(90-y) + 6y = 595   => 630 - 7y + 6y = 595   => y = 630 - 595= 
630 - 595 = 35
35=> x = 90 - 35= 
90 - 35 = 55
55   Therefore, the distance travelled by taxi is 55 kms.   55 kmsnswer: 55 kms
Answer: A
Three runners Bob, Mary and James start running around a circular track of length 15m from the same point simultaneously in the same direction at speeds of 1.5 m/s, 2.5 m/s and 4.5 m/s respectively. When will they meet for the first time after they started moving? Choose the correct choice:
A) 90 seconds  B) 120 seconds  C) 30 seconds  D) 15 seconds  E) 35 seconds

Solution: If they all meet after T seconds, it means they covered the distances 1.5T, 2.5T, and 4.5T respectively.   Since they all arrive to the same spot, it means that the differences taken pairwise between the distances must be positive integer multiples of the length of the track, which is 15m. So, 1T, 2T, and 3T must all be multiples of 15. 1T multiple of 15 means T multiple of 15. The smallest T with this property is 15 and is on the list of answers.   Answer 15 seconds.
Answer: D
A man can row a boat at 24 kmph in still water. If the speed of the stream is 16 kmph, what is the time taken to row a distance of 70 km downstream?
Choose the most appropriate option:
A) 7/4 hours
B) 3/4 hours
C) 8/13 hours
D) 4/13 hours
E) 10/13 hours

Solution: Speed downstream = 24 + 16= 
24 + 16 = 40
40 kmph.   Time required to cover 70 km downstream= d/s = 70/40 = 7/4 hours.7/4 hoursnswer:7/4 hours
Answer: A
Which of the following is non-negative number?  Choose the correct option
A) (a-0.9)(a-1)  B) (a+1)(a-1)  C) (a+0.9)(a+1)  D) (a-0.6)(a-0.6)  E) a(a+1)

Solution: 5-sec approach:   D. (a-0.6)(a-0.6) = (a-0.6)^2. The square of a number is always non-negative.   Answer: (a-0.6)(a-0.6).
Answer: D
Assume that f(1)=0 and f(m+n)=f(m)+f(n)+4(9mn-1). For all natural numbers (Integers>0)m and n. What is the value of f(17)? Choose the correct choice from the following answers:
A) 4832  B) 4855  C) 4825  D) 4895  E) 4862

Solution: Explanation:   f(1) = 0   f(2) = f(1+1) = f(1)+f(1)+4(9×1×1 – 1) = 0+0+4×8 = 32   f(4) = f(2+2) = f(2)+f(2)+4(9×2×2 – 1) = 32+32+4×35 = 204   f(8) = f(4+4) = f(4)+f(4)+4(9×4×4 – 1) = 204+204+4×143 = 980   f(16) = f(8+8) = f(8)+f(8)+4(9×8×8 – 1) = 980+980+4×575 = 4260   f(17) = f(1+16) = f(16)+f(1)+4(9×16×1 –1) = 4260+0+ 4×143 = 4832   4832nswer:4832
Answer: A
If |y + 7| = 12, what is the sum of all the possible values of y? Answers:
A) -14  B) -12  C) -8  D) 8  E) 12

Solution: There will be two cases   y+7 = 12 or y+7 = -12   => y = 5 or y = -19   sum of both the values will be -19 + 5 = -14   -14nswer: -14
Answer: A
What is the probability of getting a number less than 4 when a die is rolled?	Select the correct option
A) 1/2
B) 4/7
C) 1/6
D) 4/7
E) 5/12

Solution: Total number of outcomes possible when a die is rolled=6   1/2ny one face out of the 6 face n(s)=6   e=getting a number less than 4={1,2,3}   Hence,n(e)=3   p(e)=n(e)/n(s)   =3/6   =1/2   Option 1/2
Answer: A
How many two digit numbers of distinct digits can be formed by using digits 1, 2, 3, 4, 5, 6 and 7 such that the numbers are divisible by 4?  Pick.
A) 7	B) 8	C) 9	D) 10	E) 11

Solution: Counting the different combinations possible is the easiest method as the options tell you that the correct number is a relatively small number.   The total cases possible are:   12   16   24   32   36   44 (not counted as we need distinct digits)   52   56   64   72   76   Edit: Total: 10   10 is the correct answer.
Answer: D
A courtyard is 25 meter long and 15 meter board is to be paved with bricks of dimensions 20 cm by 10 cm. The total number of bricks required is?
Choose the correct choice from the following answers
A) 22877  B) 27778  C) 18750  D) 27999  E) 17799

Solution: Number of bricks =18750ourtyard area/1 brick area   =(2500×1500/20×10)=18750   Answer: 18750
Answer: C
The cost of Type 1 rice is Rs.15 per kg and Type 2 rice is Rs.20 per kg. If both Type 1 and Type 2 are mixed in the ratio of 2 : 3, then the price per kg of the mixed variety of rice is
Answers:
A) Rs.19.50  B) Rs.19  C) Rs.18  D) Rs.18.50  E) None

Solution: Let the price of the mixed variety be Rs. x per kg. By the rule of alligation, we have :   (20-x)/(x-15) = 2/3 =› 60 - 3x = 2x - 30   =› 5x = 90 =› x = 18.   so, price of the mixture is Rs. 18 per kg.   Answer Rs.18
Answer: C
How many factors does 49^2 have?	Choose the most appropriate option:
A) 2  B) 8  C) 24  D) 25  E) 36

Solution: 36^2 = 6*6*6*6 = 2^4*3^4   Total factors = (4+1)*(4+1) = 6*6= 
6*6 = 36
36   Answer 36.
Answer: E
A code is to be made by arranging 9 letters. five of the letters used will be the letter A, two of the letters used will be the letter B, one of the letters used will be the letter C, and one of the letters used will be the letter D. If there is only one way to present each letter, how many different codes are possible? Pick:
A) 42
B) 210
C) 46820
D) 84002
E) 90720

Solution: we have 9 letters out of which 2 are of one kind, 2 are of another kind..   so total ways = 9!/2!2!=90720   ans 90720
Answer: E
In a race, A beats B by 15 metres and C by 29 metres. If B and C run over the course together, B wins by 15 metres. What is the length of the course?  Select the correct option
A) 225m	B) 229m	C) 222m	D) 221m	E) 226m

Solution: Explanation:   Let X be the length of the course   according to the question,   A beats B by 15 metres and C by 29 metres   Applying this,   If A runs X metres, B runs (X-15) and C runs ( X-29) metres.   B and C together run, B runs X metres and C runs (X-15)   => If B runs 1 metre, C runs X-15/X   => B runs X-15 m, C runs (X-15/x) * (X-15)   APPLYING THIS,   X-29 = (X-15)(X-15) / X   Solving,   X2 -29X= X2 – 30 X + 225= 
+ 225 = 225
225   Thus, length of the course is 225 metres.   225mNSWER: 225m
Answer: A
Find the value of x from the equation:
x^2−7x+10=0 Choose the correct option.
A) 5 or 2 B) 4 or 1 C) 4 or 2 D) 6 or 1 E) 7 or 4

Solution: Here we need to find out a and b such that a + b = -7 and ab = +10   a = -5 and b = -2 satisfies the above condition.   Hence   x   2   −   7   x   +   10   =   (   x   −   5   )   (   x   −   2   )   x2−7x+10=(x−5)(x−2)   x   2   −   7   x   +   10   =   0   ⇒   (   x   −   5   )   (   x   −   2   )   =   0   x2−7x+10=0⇒(x−5)(x−2)=0   Step 3: Equate each factor to 0 and solve the equations   (   x   −   5   )   (   x   −   2   )   =   0   ⇒   (   x   −   5   )   =   0   or   (   x   −   2   )   =   0   ⇒   x   = 5 or 2   5 or 2
Answer: A
If a company allocates 10 percent of its budget to advertising, 10 percent to capital improvements, and 72 percent to salaries, what fraction of its budget remains for other allocations?	Choose the correct option:
A) 4/5
B) 2/25
C) 3/10
D) 1/5
E) 1/10

Solution: 10 + 10 + 72= 
10 + 10 + 72 = 92
92% 100 - 92= 8% to all others   2/25
Answer: B
The sum of ages of 5 children born 3 years different each is 70 yrs. What is the age of the Elder child? Answers.
A) 17
B) 19
C) 16
D) 18
E) 20

Solution: Let the ages of children be x, (x + 3), (x + 6), (x + 9) and (x + 12) years.   Then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 70   5x = 40   x = 8.   x+12= 8+12= 
8+12 = 20
20   20
Answer: E
A person can swim in still water at 12 km/h. If the speed of water 2 km/h, how many hours will the man take to swim back against the current for 10km? Choose the correct choice from the following answers
A) 1  B) 4  C) 5  D) 6  E) 7

Solution: M = 12   S = 2   US = 12 - 2= 
12 - 2 = 10
10   D= 10   T = 10/10= 
10/10 = 1
1 1nswer:1
Answer: A
Murali travelled from city A to city B at a speed of 20 kmph and from city B to city C at 80 kmph. What is the average speed of Murali from A to C given that the ratio of distances between A to B and B to C is 2 : 3?
Choose the correct choice from the following:
A) kmph  B) kmph  C) kmph  D) kmph  E) kmph

Solution: Let the distances between city A to B and B to C be 2x km and 3x km respectively.   Total time taken to cover from A to C   = (2x)/20 + (3x)/80   = (8x + 3x)/80 = 11x/80   = (2x + 3x)/(11x/80) = 36.4 kmph.   Answer: kmph
Answer: B
By selling 50 meters of cloth. I gain the selling price of 16 meters. Find the gain percent? Choose the most appropriate option:
A) 44 1/17%	B) 42 5/8%	C) 42 6/4%	D) 42 6/8%	E) 42 1/7%

Solution: SP = CP + g   50 SP = 50 CP + 16 SP   34 SP = 50 CP   34 --- 16 CP gain   100 --- ? => 47 1/17%   44 1/17%nswer: 44 1/17%
Answer: A
A can do a piece of work in 30 days. He works at it for 5 days and then B finishes it in 20 days. In what time can A and B together it?  Choose the most appropriate option
A) 13 1/7 days B) 13 1/3 days C) 13 1/8 days D) 13 8/3 days E) 12 1/3 days

Solution: 5/30 + 20/x = 1   x = 24   1/30 + 1/24 = 3/40   40/3 = 13 1/3 days   Answer:13 1/3 days
Answer: B
Vicky's salary is 75% more than Ashu's. Vicky got a raise of 40% on his salary while Ashu got a raise of 25% on his salary. By what percent is Vicky's salary more than Ashu's?	Choose the correct choice:
A) 96%
B) 51.1%
C) 90%
D) 52.1%
E) None of these

Solution: Solution: Let Ashu's salary = 100; Ashu's salary after rise = 125.   Then Vicky's salary = 175.   Vicky's salary after rise of 40% = 245.   [As 10% of Vicky's salary is 17.5 then 40% = 17.5*4= 
17.5*4 = 70
70] .   Difference between Vicky's salary and Ashu's salary= 245-125= 
245-125 = 120
120; .   % more Vicky's salary than Ashu's= 120*100/125= 
120*100/125 = 96
96%.   96%nswer: Option 96%
Answer: A
25% of all students in a class commute by public transportation. If 10% of the students aspire to be scientists, which of the following can be the percentage of students who do not commute by public transportation and do not aspire to be scientists?
I.	10%
II.	70%
III.	90% Choose the correct answer:
A) I ONLY  B) II ONLY  C) III ONLY  D) I AND II  E) I AND III

Solution: 25% Students use public transportation. This means 75% students do not use public transportation. 10% students aspire to be scientists means even if all these students use public transportation, minimum 75% - 10% = 65% students do not use public transportation and do not aspire to be scientists.This means correct answer is between 65% and 75%   Answer : II ONLY.75  - 10= 
75  - 10 = 65
65% students do not use public transportation and do not aspire to be scientists.This means correct answer is between 65% and 75%   Answer : II ONLY.
Answer: B
If the average marks of three batches of 50, 60 and 45 students respectively is 50, 55 and 60, then the average marks of all the students is Select
A) 53.33  B) 54.83  C) 55  D) 57  E) None

Solution: Sol.   Required average = [50x50 + 60x55 + 45x60 / 50 + 60 + 45]   = [2500 + 3300 + 2700 / 155]   = 8500 / 155 = 54.83.   Answer 54.83
Answer: B
A train 540 meters long is running with a speed of 54 kmph. The time taken by it to cross a tunnel 120 meters long is? Pick one.
A) 29  B) 44  C) 54  D) 99  E) 11

Solution: D = 540 + 120= 
540 + 120 = 660
660   S= 54 * 5/18= 
54 * 5/18 = 15
15 mps   T= 660/15= 
660/15 = 44
44 sec   Answer: 44
Answer: B
Amal borrowed a sum of money with simple interest as per the following rate structure:
(a) 6 p.c. p.a. for the first three years
(b) 8 p.c. p.a. for the next five years
(c) 12 p.c. p.a. for the next eight years
If he paid a total of 5,040 as interest at the end of twelve years, how much money did he borrow?  Choose one:
A) 8,000
B) 10,000
C) 12,000
D) 6,000
E) None of these

Solution: Let x be the amount Amal borrowed.   ∴ 18% of x + 40% of x + 48% of x = 5040   or, 106% of x = 5040   ∴ x = 5040⁄106 × 100 = 4754.71   Answer None of these
Answer: E
How many consonants are present between the first and second vowel in the sequence of English alphabet ?	Select the correct option
A) 3 B) 13 C) 11 D) 10 E) None of these

Solution: Explanation:   Ref : A B C D E F G H I J K L M N O P Q R S T U V W X Y Z   The first and second vowels are A and E respectively. There are 3 letters between A and E; there are no vowels in between. Thus, there are 3 consonants between A and E.   3NSWER 3
Answer: A
If q > a and L < a, which of the following cannot be true?  Choose the correct choice from the following options.
A) d + L = 14  B) d - L = 7  C) d - L = 1  D) a - q = 9  E) a + d = 9

Solution: Is the answer D?   If q>a, then q-a>0 (always positive). The converse would be a-q<0 (always negative). Option a - q = 9 states that a-q=9, which can never be true.
Answer: D
Which of the following best approximates the percent by which the distance from A to C along a diagonal of square ABCD reduces the distance from A to C around the edge of square ABCD? Select the correct option:
A) 30%
B) 43%
C) 45%
D) 50%
E) 70%

Solution: let the sides be 2 units.   original distance=2+2= 
2+2 = 4
4 units   changed distance=2sq.root2   %change=change dist.-original dist./original dist.   =(2sq.root 2-4)/4==-.2955   reduced by ~30%   30%ns 30%
Answer: A
Irin, Ingrid and Nell bake chocolate chip cookies in the ratio of 9.18: 5.17: 2.05. If altogether they baked a batch of 170 cookies, what percent of the cookies did Irin bake?  Select the correct option:
A) 0.125%
B) 1.25%
C) 12.5%
D) 53.5%
E) 0.152%

Solution: 9.18x+5.17x+2.05x = 16.4x 9.18 +5.17 +2.05= 
9.18 +5.17 +2.05 = 16.4
16.4x= 170 cookies   x= 170/16.4 = 10 (approx)   So, Irin baked 10*9.18 cookies or 91 cookies (approx)   % share = 91/170= 53.5 approx   Hence, answer is 53.5%.
Answer: D
A credit card number has 6 digits (between 1 to 9). The first two digits are 12 in that order, the third digit is bigger than 6, the forth is divisible by 3 and the fifth digit is 3 times the sixth. How many different credit card numbers exist? Pick one
A) 27	B) 36	C) 72	D) 112	E) 422

Solution: {1}{2}{greater than 6}{divisible by 3}{3x}{x}:   The third digit can take 3 values: 7, 8, or 9.   The fourth digit can take 3 values: 3, 6, or 9.   The fifth and sixth digits can take 3 values: 31, 62, or 93.   Total = 3*3*3= 
3*3*3 = 27
27.   27nswer: 27.
Answer: A
The population of a village is 7800. It increases annually at the rate of 18% p.a. What will be its population after 2 years?	Options.
A) 10000 B) 12000 C) 13000 D) 10860 E) 14400

Solution: Formula :   ( After =100 denominator   Ago = 100 numerator)   7800 × 118/100 × 118/100 = 10860   10860
Answer: D
Find the fourth proportional to 2.7, 4.6 and 7.6?	Select.
A) 12.95	B) 13.95	C) 15.23	D) 15.95	E) 16

Solution: Formula = Fourth propotional = (b Ã— c)/a   12.95 = 2.7 , B = 4.6 and C = 7.6   (4.6 Ã— 7.6)/2.7 = 12.95   12.95
Answer: A
If x and y are integers such that |y + 3| ≤ 3 and 2y – 3x + 6 = 0, what is the least possible value Q of the product xy?  Answers.
A) -12
B) -3
C) 0
D) 2
E) None of the above

Solution: How to deal with inequalities involving absolute values? First example shows us the so callednumber case   In this case we have |y + 3| ≤ 3 which is generalized |something| ≤ some number. First we solve as if there were no absolute value brackets:   y + 3 ≤ 3   y ≤ 0   So y is 0 or negative   Second scenario - remove the absolute value brackets. Put a negative sign around the other side of the inequality,ANDflip the sign:   y + 3 >= -3   y >= -6   Therefore we have a possible range for y: -6=<y<=0   Ok, so far so good, we're half way through. What about x?   Here's the formula: 2y – 3x + 6 = 0, rewrite it as 2y + 6 = 3x.   You can say that 2y + 6 is a multiple of 3 (=3x). So all values which must be integer must also satisfy this constraint. I'm just saying that, so it's easier to evaluate all the possible numbers (-6, -3, 0). If you plug in y = 0, x will be 2 and xy = 0 as the lowest possible value Q.   Hence, Answer 0hoice 0 is the one to go.
Answer: C
The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 400 resolutions?  Choose the most appropriate option:	A) 563.2 m	B) 704 m	C) 287 m	D) 278 m	E) 927 m

Solution: In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 400 resolutions.   = 400 * 2 * 22/7 * 22.4= 
400 * 2 * 22/7 * 22.4 = 56_320
56320 cm= 563.2 m   563.2 mnswer:563.2 m
Answer: A
The sector of a circle has radius of 21 cm and central angle 135o. Find its perimeter? Choose one:
A) 91.5 cm	B) 23.9 cm	C) 62.9 cm	D) 27.8 cm	E) 21.2 cm

Solution: Perimeter of the sector = length of the arc + 2(radius)   = (135/360 * 2 * 22/7 * 21) + 2(21)   = 49.5 + 42= 
49.5 + 42 = 91.5
91.5 cm   91.5 cmnswer:91.5 cm
Answer: A