MU-NLPC/Calc-aqua_rat huggingface dataset:
Which of the following CANNOT be a product of two distinct positive integers c and d?	Choose the correct answer
A) c	B) d	C) 3d + 2c	D) d - c	E) dc

Solution: In these questions it is best to take an example as if something is true for all positive integers than it as to be true for the smallest and the easiest integers to work with   take c = 1 and d = 2 and work with the options   cd = 2   A) c take c =2, d = 1   B) d take c = 1 d = 2   C) 3d + 2c Seems tricky, lets see other options and then come back to it.   D) d - c take d = 1 and c = 2 --> d - c = -1 .. How the hell can product of two positive integers be negative ?? or less than each of them?   E) dc Always true   You don't even have to worry what C is !   ans d - c
Answer: D
How much time will it take for an amount of 450 to yield 81 as interest at 4.5% per annum of simple interest?  Choose the correct answer.
A) 5 years  B) 8 years  C) 2 years  D) 4 years  E) 9 years

Solution: 4 years   4 years   Time = (100 x 81)/(450 x 4.5) years = 4 years.
Answer: D
A straight pipe 1 meter in length was marked off in fourths and also in thirds. If the pipe was then cut into separate pieces at each of these markings, which of the following gives all the different lengths of the pieces, in fractions of a meter?
Choose the correct choice from the following
A) 1/6 and 1/4 only  B) 1/4 and 1/3 only  C) 1/12, 1/6 and 1/4  D) 1/6, 1/4, and 1/3  E) 1/12, 1/6, and 1/3

Solution: Generally fast way to solve such problem is writing the different marks in ascending/descending order with same denominator:   Here 4th : 0/4, 1/4, 2/4, 3/4, 4/4   and 3rd : 0/3, 1/3, 2/3, 3/3   Now with understood common denominator 12 write the numbers : for 4th : 0,3,6,9,12 and for 3rd : 0,4,8,12   Now comine : 0,3,4,6,8,9,12   Now find the cut with denominator 12 (Substracrt adjacent terms : 3/12, 1/12, 2/12, 1/12,3/12 i.e. 1/4, 1/12 and 1/6 after removing duplicates.   Answer - 1/12, 1/6 and 1/4
Answer: C
A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is?
Select the correct option
A) 33
B) 50
C) 88
D) 26
E) 23

Solution: Speed of the train relative to man = (125/10) m/sec = (25/2) m/sec. [(25/2) * (18/5)] km/hr = 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 45 ==> x = 50 km/hr.   Answer: 50
Answer: B
A man buys Rs. 20 shares paying 9% dividend. The man wants to have an interest of 12% on his money. What is the market value of each share? Select the correct option:  A) Rs.12  B) Rs.18  C) Rs.15  D) Rs.21  E) Rs.25

Solution: Explanation :   Face value of each share = Rs.20   Dividend per share = 9% of 20 = 9×20/100=9/5   He needs to have an interest of 12% on his money   ie, Money Paid for a share 9×12/100=9/5   Money Paid for a share=9/5×100/12=15   ie, Market Value of the share = Rs.15   Answer : Option Rs.15
Answer: C
If x^2 - 4 = 0 and x > 0, which of the following must be equal to 0 ?	Choose the most appropriate option:
A) x^2 - 2x
B) x^2 - 9x + 20
C) x^2 - 2x + 3
D) x^2 + 2x - 3
E) x^2 + 5x + 6

Solution: x^2-4 = 0   x= +2 or x = -2   if we substitute x= 2 in the equation x^2 - 2x = 4-4= 
4-4 = 0
0   x^2 - 2x is also the answer
Answer: A
If the number is divided by 3, it reduced by 42. The number is  Choose the correct choice from the following:
A) A)51
B) B)63
C) C)45
D) D)40
E) E)36

Solution: Explanation:   Let the number be x. Then,   x - (x/3) = 42 => 2x/3 = 42   => x = 63   Answer: Option 63
Answer: B
30 is what percent of 100?  Choose the correct choice.
A) 35% B) 30% C) 45% D) 50% E) 55%

Solution: 30/100×100=30% ANSWER : 30%
Answer: B
On a sum of money, the simple interest for 2 years is Rs.660, while the compound interest is Rs.696.30, the rate of interest being the same in both the cases. The rate of interest is Choices.
A) 10% B) 11% C) 12% D) 10.5% E) None

Solution: Solution   Difference in C.I and S.I for 2 years	= Rs(696.30-660)   =Rs. 36.30.   S.I for one years	= Rs330.   S.I on Rs.330 for 1 year	=Rs. 36.30   Rate	= (100x36.30/330x1)%   =11%.   Answer 11%
Answer: B
During the last four years, a large truck company purchased diesel at rates of $1.2, $1.3, $1.8 and $2.1 per gallon. What was the mean cost of diesel over the four-year period if the company spends the same amount of dollars on diesel each year?	Choose one:
A) $2.5 B) $2.55 C) $1.52 D) $3.25 E) $3.0

Solution: finding the Harmonic mean here.   HM = 4/(1/12 + 1/13 + 1/18 + 1/21) = 15.18   $1.52
Answer: C
If n is an integer and 101n^2 is less than or equal to 10000, what is the greatest possible value of n?  Choose the correct answer.
A) 7 B) 8 C) 9 D) 10 E) 11

Solution: 101 * n^2 <=10000   n^2 <=10000/101 which will be less than 100 since  10000/100= 
 10000/100 = 100
100 which is the square of 9   Next closest value of n where n^2<=100 is 9   Ans 9
Answer: C
Reema took a loan of Rs 1200 with simple interest for as many years as the rate of interest. If she paid Rs. 432 as interest at the end of the loan period, what was the rate of interest.
Options:
A) 5%  B) 6%  C) 7%  D) 8%  E) 9%

Solution: Explanation:   Let rate = R% then Time = R years.   =>1200∗R∗R /100=432   =>R2=36   =>R=6%   Option 6%
Answer: B
A and B complete a work in 6 days. A alone can do it in 10 days. If both together can do the work in how many days?  Choose the correct choice from the following answers
A) 3.75 days  B) 4 days  C) 5 days  D) 6 days  E) 7 days

Solution: Explanation:   1/6 + 1/10 = 8/30 = 4/15   15/4= 
15/4 = 15/4 = around 3.75
3.75 days   3.75 daysnswer: 3.75 days
Answer: A
John has 5 friends who want to ride in his new car that can accommodate only 4 people at a time (John plus 3 passengers). How many different combinations of 3 passengers can be formed from the 5 friends?	Select the correct option
A) 3.	B) 8.	C) 10.	D) 15.	E) 20.

Solution: 510.3 = 10   The answer is 10..
Answer: C
57, 55, 50, 48, 43, 41, ?	Answers.
A) 30  B) 23  C) 36  D) 25  E) 32

Solution: This is a simple alternating subtraction series, with a pattern -2, -5, -2, -5 ....   Answer : 36.
Answer: C
which one is odd?
4377
3954
9864
8454
9831	Choices.
A) 4377	B) 3954	C) 9864	D) 8454	E) None

Solution: 9864orrect Answer : 9864   sum of digit of all other number is 21, but sum of digit of 9864 is 27
Answer: C
x percent of y percent of z is decreased by y percent, What is the result? Pick one: A) (100xyz - xy^3z) / 1,000,000 *(-1/48) B) (xz - y) / 100 C) (xz - y) / 10,000 D) (xyz - 2y) / 100 E) (xyz - 2y) / 10,000

Solution: We're told that X percent of Y percent of Z is DECREASED by Y percent. We're asked for the result of all of this math.   IF....   X = 10   Y = 50   Z = 100   First, 50% of 100 = 50   Next, 10% of 50 = 5   Finally, 5 decreased by 50% of itself is 2.5   So we're looking for an answer that equals 2.5 when X=10, Y=50 and Z=100.   Answer A. (100xyz - xy^2z) / 1,000,000 = (5,000,000 - 2,500,000)/1,000,000 *(-1/48) = 2,500,000/1,000,000 = 2.5   This is a M(100xyz - xy^3z) / 1,000,000 *(-1/48)TCH   (100xyz - xy^3z) / 1,000,000 *(-1/48)
Answer: A
I forgot the last digit of a 7-digit telephone number. If 1 randomly dial the final 3 digits after correctly dialling the first four, then what is the chance of dialling the correct number?
Pick one:
A) 1/1001.	B) 1/1000	C) 1/999	D) 1/990	E) 1/968

Solution: Explanation :   Given, the last three digits are randomly dialled, then each of the digit can be selected out of 10 digits in 10 ways.   Hence, the required probability is:-   =>(1/10)3.   =>1/1000.   Answer : 1/1000
Answer: B
x an y are two truck parks 500 km apart, if a truck leaves park x at 9 a.m. and travels at a speed of 70 kmph at what time will the first truck meet the second truck which left station y at 10am and travels at a speed of 50 kmph Choose the correct choice from the following answers
A) 1.30 p.m
B) 2.30 p.m
C) 11.30 a.m
D) 12.30 p.m
E) 1.30 a.m

Solution: Suppose they meet x hours after 9 a.m.   Distance moved by first truck in x hours + distance moved by 2nd truck in x-1 hrs = 500   70x+50(x-1) = 500   70x+50x-50= 400   120x= 450   x = 4.5   So they meet 4.5 hr after 9 a.m. which is at 1.30 p.m.   1.30 p.mnswer is 1.30 p.m
Answer: A
If 40 percent of all students at college X have brown hair and 70 percent of all students at college X have blue eyes what is the difference between the minimum and maximum probability of picking a student from college X who has neither brown hair nor blue eyes?
Choose the correct choice from the following choices: A) 0.2 B) 0.3 C) 0.4 D) 0.6 E) 0.7

Solution: Max value for y = minimum of (40,70).   Because the number of students with brown hair is 40, the maximum number of students to have both brown hair and blue eyes can only be 40.   When y=40   x=30   Probability of selecting 30 students out of 100 students = 30/100= 
30/100 = 3/10 = around 0.3
0.3   x will be minimum when y is minimum.   The minimum possible value for y=10   x = y-10   x=0   Because if "y" gets less than 10; the number of students get more than 100 which is not possible.   In this case; 0 students fit the criterion of not having either. Because all students have brown hair, blue eyes or both.   Probability becomes   0/100= 
  0/100 = 0
0   Difference between two probabilities= 0.3-0= 
0.3-0 = 0.3
0.3   Ans: "0.3"   _______
Answer: B
If John runs in the speed of 9 km/hr from his house, in what time will he reach the park which is 300 m long from his house?	Choose the correct answer:  A) 2  B) 4  C) 5  D) 3  E) 6

Solution: Speed = 9 * 5/18= 
9 * 5/18 = 5/2 = around 2.5
2.5 m/sec   Time taken= 300/2.5= 
300/2.5 = 120
120 sec ie. 2 mins.   2nswer:2
Answer: A
A certain bus driver is paid a regular rate of $12 per hour for any number of hours that does not exceed 40 hours per week. For any overtime hours worked in excess of 40 hours per week, the bus driver is paid a rate that is 75% higher than his regular rate. If last week the bus driver earned $976 in total compensation, how many total hours did he work that week?
Choose the correct choice:
A) 54  B) 51  C) 59  D) 55  E) 64

Solution: For 40 hrs = 40*12= 
40*12 = 480
480   Excess= 976-480= 
976-480 = 496
496   For extra hours=.75(12)=9+12= 
9+12 = 21
21   Number of extra hrs=496/21=23.6=24 approx.   Total hrs =40+24= 
40+24 = 64
64   Answer 64
Answer: E
In how many ways can 5 letters be posted in 3 post boxes, if any number of letters can be posted in all of the three post boxes?	Options.
A) 235  B) 451  C) 623  D) 215  E) 3^5

Solution: The first letter can be posted in any of the 3 post boxes. Therefore, we have 3 possibilities.   Similarly, the second, the third, the fourth and the fifth letter can each be posted in any of the 3 post boxes.   Each of the 5 letters has 3 possibilities because we can post any number of letters in all of the boxes.   Therefore, the total number of ways the 5 letters can be posted in 3 boxes is   3 * 3 * 3 * 3 * 3 = 3^5   Ans: 3^5
Answer: E
If 195,001, football shoes need to be placed in boxes and each box can contain at most 3 pair of football shoes. How many pair of football shoes will be in the last unfilled box?
Options:	Choose the correct choice from the following answers:
A) 1football shoes B) 3 football shoes C) 4 football shoes D) 7 football shoes E) 9 football shoes

Solution: The number of football shoes that can be placed in boxes of 3 football shoes is the first number that is divisible by 3 that occurs before 195,001.   In order to divide the sum in 3 parts, the amount must be divisible by 3   Divisibility rule of 3: The sum of the digits must be divisible by 3   Sum of digits of 195,001 =1+9+5+0+0+1= 
1+9+5+0+0+1 = 16
16 and   1+6= 
  1+6 = 7
7 is not divisible by 3   Hence, we need to remove 1 to this number for it to be divisible by 3   Correct Option: 1football shoes
Answer: A
A train 240 m in length crosses a telegraph post in 16 seconds. The speed of the train is?  Choose the correct option:  A) 50 kmph  B) 52 kmph  C) 54 kmph  D) 56 kmph  E) 58 kmph

Solution: Explanation:   S = 240/16 * 18/5= 
240/16 * 18/5 = 54
54 kmph   ANSWER IS 54 kmph
Answer: C
If the area of the equilateral triangle above is 0.75, what is the area of the adjacent square?
Options.
A) (√3)/2 B) √3 C) √6 D) 3 E) 2√3

Solution: Area of equilateral triangle: a^2*(square root of 3)/4 = 0.75   Hence, area of square = a^2 = 0.75 *4/ (square root of 3) = 3/ (square root of 3) = square root of 3   Answer: √3
Answer: B
When Robert discontinued his retainer-ship contract with a Pvt Company, management held his fees Rs. 15000/- for one month. Earlier Robert had completed a work worth fees of 7280/- from company, which was still not paid. But Robert forgot that. After one month Robert asked his fees and accountant gives Rs.18500/- to him. What is the incentive amount given to Robert?  Select the correct option:
A) A)9500	B) B)12500	C) C)10780	D) D)10500	E) E)8600

Solution: Total fees = Rs.15000/-   Earlier fees not paid = 7280/-   Balance Salary = 15000-7280= 
15000-7280 = 7_720
7720   Paid amount= 18500/-   Incentive amount = 18500-7720= 
18500-7720 = 10_780
10780/-   Answer is 10780
Answer: C
The difference between the local value and the face value of 9 in the numeral 62975148 is Choose one
A) 899999
B) 899991
C) 899891
D) 899981
E) 899000

Solution: Explanation:   (Local value of 9) - (Face value of 9) = (900000 - 9)= 
(900000 - 9) = 899_991
899991   899991)
Answer: B
A salesman’s terms were changed from a flat commission of 5% on all his sales to a fixed salary of Rs.1300 plus 2.5% commission on all sales exceeding Rs. 4,000. If his remuneration as per new scheme was Rs. 600 more than that by the previous schema, his sales were worth? Choose the correct choice
A) 12028
B) 12000
C) 12019
D) 12197
E) 18000

Solution: [1300 + (X-4000) * (2.5/100)] - X * (5/100)   = 600   X = 18000   Answer: 12019
Answer: C
How many five-digit numbers exist such that the product of their digits is 400?	Answers:
A) 60  B) 120  C) 180  D) 30  E) 75

Solution: We're asked to name all of the 5-digit numbers whose product-of-digits is 400. We can use prime-factorization to figure out the digits, BUT this comes with a "twist".....NOT ALL of the digits have to be primes....   400 = (25)(16)   The 25 = (5)(5) and there's no way around that. Every option MUST have two 5s as two of the digits.   The 16 can be broken down in a few different ways though:   16 = (1)(2)(8)   16 = (1)(4)(4)   16 = (2)(2)(4)   Each of those options has to be accounted for.   So, we have 3 sets of 5 digits:   1) 1, 2, 8, 5, 5 --> This gives us 5!/2! arrangements = 120/2= 
120/2 = 60
60 different 5-digit numbers.   2) 1, 4, 4, 5, 5 --> This gives us 5!/(2!2!) arrangements= 120/4= 
120/4 = 30
30 different 5-digit numbers.   3) 2, 2, 4, 5, 5 --> This gives us 5!/(2!2!) arrangements= 120/4= 
120/4 = 30
30 different 5-digit numbers.   60 + 30 + 30= 
60 + 30 + 30 = 120
120 different 5-digit numbers   Final Answer:120
Answer: B
A starts business with a capital of Rs.1200 B and C join with some investments after 3 and 6 months respectively. If the end of a year, the profit is divided in the ratio 2:3:5 respectively. What is B's investment in the business?	Choose the correct choice.
A) 2400  B) 2782  C) 2097  D) 7922  E) 2877

Solution: 1200 * 12: x * 9 = 2:3   x = 2400   2400nswer: 2400
Answer: A
Look at this series: 32, 35, 33, 36, 34, 37, ... What number should come next? Choose the correct option:
A) 39
B) 31
C) 35
D) 32
E) 33

Solution: This is a simple alternating addition and subtraction series. In the first pattern, 3 is added; in the second, 2 is subtracted.   The answer is option 35 (35)
Answer: C
Raman buys an old scooter for Rs. 5000 and spends Rs. 1000 on its repairs. If he sells the scooter for Rs. 7200, his gain percent is :	Select:  A) 20%  B) 12%  C) 10%  D) 5%  E) None of these

Solution: Explanation :   Solution: C.P. =Rs. (5000+1000) =Rs. 6000; S.P. = Rs. 7200.   Gain% = (1200*100/6000)= 
(1200*100/6000) = 20
20%.   20%nswer : 20%
Answer: A
8 machines, each working at the same constant rate, together can complete a certain job in 24 days. How many additional machines, each working at the same constant rate, will be needed to complete the Job in 16 days? Choose the correct answer
A) 2 B) 3 C) 4 D) 6 E) 8

Solution: Another solution which is faster is Since each machine works at a constant rate. The time needs to bought down from 24 to 16. So the new time is 2/3 of the original time. Thus to achieve this we need the rate to be 3/2 of original.   So 3/2* 8= 
3/2* 8 = 12
12   So we need   12-8= 
  12-8 = 4
4 more machines.   Answer : 4
Answer: C
A wheel that has 3 cogs is meshed with a larger wheel of 7 cogs. When the smaller wheel has made 21 revolutions, then the number of revolutions made by the larger wheel is:  Select
A) 9 B) 10 C) 6 D) 8 E) 7

Solution: Explanation :   Let the required number of revolutions made by larger wheel be x.   Then, More cogs, Less revolutions (Indirect Proportion)   7:3::21:x => 7 * x = 21 * 3   => x = (21 * 3)/7   => x = 9   9nswer : 9
Answer: A
A tour group of 25 people paid a total of $650 for entrance to a museum. If this price included a 5% sales tax, and all the tickets cost the same amount, what was the face value of each ticket price without the sales tax?
Choices  Choose the correct choice from the following answers:
A) $24.7
B) $23.94
C) $24
D) $25.20
E) $30

Solution: $24.7.
Answer: A
Find out the number of ways in which 6 rings of different types can be worn in 3 fingers?	Choose the correct answer:
A) 321	B) 729	C) 451	D) 152	E) 451

Solution: The first ring can be worn in any of the 3 fingers (3 ways).   Similarly each of the remaining 5 rings also can be worn in 3 ways.   Hence total number of ways   =3×3×3×3×3×3=36=729   Ans: 729
Answer: B
A cube marked 1, 2, 3, 4, 5, and 6 on its six faces. Three colors, red, blue, and green are used to paint the six faces of the cube. If the adjacent faces are painted with the different colors, in how many ways can the cube be painted? Choose the correct choice from the following options:  A) 3  B) 6  C) 8  D) 12  E) 27

Solution: There are 4 adjacent sides for every face of the cube.   Let's say side 1 is painted red, then the 4 adjacent sides can be either green or blue alternating. This can be done in 2 ways.   GBGB   BGBG   Sixth side should be the same color as side 1.   For each color chosen for side 1(and side6) there are 2 ways of painting side 2,3,4 and 5.   No. of colors that can be chosen for side 1(and side6) is 3.   So 3*2 = 6..   ANSWER:6
Answer: B
Find two consecutive integers whose sum is equal 129.	Choose the correct answer:  A) 63  B) 64  C) 65  D) 66  E) 67

Solution: Let x and x + 1 (consecutive integers differ by 1) be the two numbers. Use the fact that their sum is equal to   129 to write the equation   x + (x + 1) = 129   Solve for x to obtain   x = 64   The two numbers are   x = 64 and x + 1 = 65   We can see that the sum of the two numbers is 129.   Answer 65
Answer: C
Which is the smallest number divides 2800 and gives a perfect square. Pick one:  A) 5  B) 6  C) 7  D) 8  E) 9

Solution: 7 is the smallest number which divides 2800 and gives a perfect square.   As 2800=2*2*2*2*5*5*7 and 7 is not in a pair which gives 400(a perfect square of 20) on dividing 2800.   ANSWER:7
Answer: C
Sum of ages of two friends is 34 while difference is 2 then their ages are  Choose the correct choice from the following answers.
A) 18 years, 16 years	B) 17 years, 15 years	C) 16 years, 18 years	D) 18 years, 16 years	E) None

Solution: 18,16   18 years, 16 yearsNSWER:18 years, 16 years
Answer: A
If 4 men working 10 hours a day earn Rs. 1600 per week, then 9 men working 6 hours a day will earn how much per week?  Select:
A) Rs 840
B) Rs 1320
C) Rs 1620
D) Rs 2160
E) None of these

Solution: Explanation :   (Men 4:9) : (Hrs/Rs 2160ay 10:6) :: 1600 : x   hence 4 * 10 *x = 9 * 6 * 1600   or x = 9*6*1600/ 4*10 = 2160   Answer : Rs 2160
Answer: D
Two pipes P and Q can fill a cistern in 12 and 19 minutes respectively. Both are opened together, but at the end of 3 minutes the first is turned off. How much longer will the cistern take to fill?
Choose the correct choice from the following answers
A) 11 1/2 min
B) 14 1/4 min
C) 11 2/4 min
D) 11 1/5 min
E) 11 7/4 min

Solution: 3/12 + x/19 = 1   x= 14 1/4   Answer: 14 1/4 min
Answer: B
20 beavers, working together in a constant pace, can build a dam in 3 hours. How many hours X will it take 12 beavers that work at the same pace, to build the same dam?	Pick:
A) 2.  B) 4.  C) X=5.  D) X=6.  E) 8.

Solution: C. 5 hrs   If there were 10 beavers it qould have taken double X = 6hrs.. so closest to that option is 5.
Answer: C
Triangle XYZ is an isosceles right triangle. If side XY is longer than side YZ, and the area of the triangle is 64, what is the measure of side XY? Choose the correct option
A) 4  B) 16  C) 8  D) 8√2  E) Cannot be determined from the information provided

Solution: ans B ..16.   xy being larger means it is the hyp..   area =(1/2)*(yz)^2=64 or yz=8*\sqrt{2}..   therefore hyp=xy=16
Answer: B
A tank is 25m long 12m wide and 6m deep. The cost of plastering its walls and bottom at 70 paise per sq m is Choose one
A) Rs. 258.80 B) Rs. 358.80 C) Rs. 458.80 D) Rs. 520.80 E) None of these

Solution: Explanation:   Area to be plastered = [2(l + b) Ã— h] + (l Ã— b)   = [2(25 + 12) Ã— 6] + (25 Ã— 12) = 744 sq m   Cost of plastering = 744 Ã— (70/100) = Rs.520.80 Answer: Rs. 520.80
Answer: D
The product of two consecutive odd no is -1, then what is the value of the sum of them. Choose the correct choice:
A) -2  B) -1  C) 0  D) 1  E) 2

Solution: Two odd numbers are -1 and +1.   -1+1= 
-1+1 = 0
0   ANSWER:0
Answer: C
A shopkeeper expects a gain of 22.5% on his cost price. If in a week, his sale was of Rs. 441, what was his profit?  Pick one
A) s. 64	B) s. 69	C) s.72	D) s.75	E) s.81

Solution: C.P. = Rs. (100/122.5)x441   = Rs. (1000/1225)x441   = Rs. 360   Profit = Rs. (441 - 360) = Rs. 81.   Answer:s.81
Answer: E
In a certain animal shelter, the ratio of the number of dogs to the number of cats is 15 to 7. If 20 additional cats were to be taken in by the shelter, the ratio of the number of dogs to the number of cats would be 15 to 11. How many dogs are in the shelter? Choose the correct choice from the following options
A) 75  B) 25  C) 30  D) 45  E) 60

Solution: This ratio question can be solved in a couple of different ways. Here's an Algebraic approach...   We're told that the ratio of the number of dogs to the number of cats is 15:7. We're then told that 20 more cats are added to this group and the ratio becomes 15:11. We're asked for the number of dogs.   Algebraically, since the number of dogs is a multiple of 15 and the number of cats is a multiple of 7, we can write this initial relationship as...   15X/7X   When we add the 20 cats and factor in the 'ending ratio', we have an equation....   15X/(7X+20) = 15/11   Here we have 1 variable and 1 equation, so we can solve for X....   (15X)(11) = (7X+20)(15)   (X)(11) = (7X+20)(1)   11X = 7X + 20   4X = 20   X = 5   With this X, we can figure out the initial number of dogs and cats...   Initial dogs = 15X = 15(5) = 75   Final 75nswer: 75
Answer: A
An article is bought for Rs.675 and sold for Rs.900, find the gain percent?  Select:  A) 33 1/7%  B) 33 2/3%  C) 33 1/3%  D) 33 1/1%  E) 32 1/3%

Solution: 675 ---- 225   100 ---- ? => 33 1/3%   Answer: 33 1/3%
Answer: C
How many three letter words are formed using the letters of the word KEYBOARD?
Choose the correct option.
A) 220	B) 289	C) 27	D) 336	E) 346

Solution: Explanation:   The number of letters in the given word is EIGHT.   The number of three letter words that can be formed using these four letters is Ã¢Â´PÃ¢â€šÆ’ = 8*7*6= 
8*7*6 = 336
336.   Answer: 336
Answer: D
The difference between the length and breadth of a rectangle is 25 m. If its perimeter is 210 m, then its area is: Select:	A) 1520 m2	B) 2600 m2	C) 2480 m2	D) 2520 m2	E) None

Solution: EXPLANATION   We have: (l â€“ b) = 25 and 2(l + b) = 210 or (l + b) = 105.   Solving the two equations, we get: l = 65 and b = 40.   Area = (l x b) = (65 x 40) m2 = 2600 m2.   Answer 2600 m2
Answer: B