MU-NLPC/Calc-aqua_rat huggingface dataset:
If a, b, c, and d are integers; w, x, y, and z are prime numbers; w < x < y < z; and (wa)(xb)(yc)(zd)=660(wa)(xb)(yc)(zd)=660, what is the value of (a + b) – (c + d)?
Choose the most appropriate option.
A) –1 B) 0 C) (a + b) – (c + d)=1 D) 2 E) 3

Solution: 660660= 2^2 x 3^1 x 5^1 x 11^1   w < x < y < z = 2 < 3 < 5 < 11   So, can can say -   w = 2   x = 3   y = 5   z = 11   Hence a = 2 , b = c = d = 1   (a + b) – (c + d) will be (2 + 1) – (1 + 1) = 1   Answer will be ((a + b) – (c + d)=1)
Answer: C
A goods train runs at the speed of 72 km/hr and crosses a 150 m long platform in 26 sec. What is the length of the goods train? Choose the correct choice from the following
A) 370	B) 782	C) 278	D) 270	E) 881

Solution: Speed = 72 * 5/18= 
72 * 5/18 = 20
20 m/sec.   Time= 26 sec.   Let the length of the train be x meters.   Then, (x + 150)/26 = 20   x = 370 m.   370nswer: 370
Answer: A
A man could buy a certain number of notebooks for Rs.300. If each notebook cost is Rs.5 more, he could have bought 10 notebooks less for the same amount. Find the price of each notebook?	Choose the most appropriate option.
A) 10 B) 8 C) 6 D) 4 E) 2

Solution: Let the price of each note book be Rs.x.   Let the number of note books which can be brought for Rs.300 each at a price of Rs.x be y.   Hence xy = 300   => y = 300/x   (x + 5)(y - 10) = 300 => xy + 5y - 10x - 50 = xy   =>5(300/x) - 10x - 50 = 0 => -150 + x2 + 5x = 0   multiplying both sides by -1/10x   => x2 + 15x - 10x - 150 = 0   => x(x + 15) - 10(x + 15) = 0   => x = 10 or -15   As x>0, x = 10.   10NSWER:10
Answer: A
If a code word is defined to be a sequence of different letters chosen from the 10 letters A, B, C, D, E, F, G, H, I, and J, what is the ratio of the number of 5-letter code words to the number of 6-letter code words?
Choose the correct option:
A) 1 B) 1/4 C) 1/5 D) 1/3 E) 1/2

Solution: Method #1: Using the permutation formula   # of 5 letter code words:   nPr = n! / (n – r)! = 10! / (10 – 5)! = 10*9*8*7*6   # of 6 letter code words:   nPr = 10! / (10 – 6)! = 10*9*8*7*6*5   # of 5 words / # of 4 words = (10*9*8*7*6)/(10*9*8*7*6*5) = 1/5   1/5
Answer: C
What is 120% of 13/24 of 960?
Pick one.
A) 420	B) 484	C) 526	D) 578	E) 624

Solution: 120% * 13/24 * 360 = 1.2 * 13 * 40= 
1.2 * 13 * 40 = 624
624   The answer is 624.
Answer: E
A man can row 40km upstream and 55km downstream in 13 hours also, he can row 30km upstream and 44km downstream in 10 hours. find the speed of the man in still water and the speed of the current.
Choose the correct choice from the following options:	A) 5 and 3	B) 8 and 3	C) 3 and 8	D) 3 and 5	E) None of them

Solution: let rate upstream=x km/hr and rate downstream=y km/hr.   Then,40/x +55/y =13…(i) and 30/x +44/y =10   Multiplying (ii) by 4 and (i) by 3 and subtracting ,we get:11/y=1 or y=11.   Substituting y=11 in (i),we get:x=5.   Rate in still water =1/2(11+5)kmph=8kmph.   Rate of current=1/2(11-5)kmph=3kmph   Answer is 8 and 3.
Answer: B
A single reservoir supplies the petrol to the whole city, while the reservoir is fed by a single pipeline filling the reservoir with the stream of uniform volume. When the reservoir is full and if 40,000 liters of petrol is used daily, the suply fails in 90 days.If 32,000 liters of petrol is used daily, it fails in 60 days. How much petrol can be used daily with out the supply ever failing? Select:
A) 64000 liters
B) 56000 liters of petrol
C) 78000 liters
D) 60000 liters
E) None of these

Solution: Explanation:   Let x liter be the per day filling and v litr be the capacity of the reservoir, then   90x + v = 40000 × 90 -----(1)   60x + v= 32000 × 60 ------(2)   solving eq.(1) and (2) , we get   x = 56000   Hence , 56000 liters per day can be used without the failure of supply.   Answer: 56000 liters of petrol
Answer: B
A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? Pick one:
A) 180 m B) 200 m C) 240 m D) 320 m E) None

Solution: Sol.   Speed = [54 * 5/18] m/sec = 15 m/sec.   Length of the train = (15 * 20)= 
(15 * 20) = 300
300 m.   Let the length of the platform be x metres.   Then, x + 300 / 36= 15 ⇔ x + 300 = 540 ⇔ x = 240 m.   Answer 240 m
Answer: C
If p#q denotes the least common multiple of p and q, then T=((12#16)#(18#24)) = ? Choose the correct answer
A) 216	B) 180	C) 144	D) 108	E) 72

Solution: There are several ways to find the Least Common Multiple of two numbers. In this case, the most efficient method is to use the Greatest Common Factor: (A * B) / (GCF AB) = LCM AB   The greatest common factor of 12 and 16 is 4. So, 12#16 = 12*16/4= 
12*16/4 = 48
48.   The greatest common factor of 18 and 24 is 6. So, 18#24= 18*24/6= 
18*24/6 = 72
72   Finally, the greatest common factor of 48 and 72 is 24. So,T= ((12#16)#(18#24)) = 48#72 = (48*72)/24 = 2*72= 
2*72 = 144
144   The correct answer is 144.
Answer: C
In a certain brick wall, each row of bricks above the bottom row contains one less brick than the row just below it. If there are 4 rows in all and a total of 134 bricks in the wall, how many bricks does the bottom row contain ?  Pick one.
A) 30
B) 31
C) 32
D) 33
E) 34

Solution: The bottom row has x bricks   x+x-1+x-2+x-3 = 134   4x-6=134   4x=128   x=32   Answer:32
Answer: C
A and B entered into a partnership investing Rs.25000 and Rs.30000 respectively. After 4 months C also joined the business with an investment of Rs.35000. What is the share of C in an annual profit of Rs.47000?
Select:
A) Rs.14000  B) Rs.1000  C) Rs.10500  D) Rs.2050  E) Rs.5500

Solution: Explanation:   25*12: 30*12: 35*8   15:18:14   14/47 * 47000 = Rs.14000   Rs.14000NSWER:Rs.14000
Answer: A
Machine A can finish a job in 6 hours, Machine В can finish the job in 12 hours, and Machine С can finish the job in 8 hours. How many hours will it take for A, B, and С together to finish the job?  Answers: A) 6/5 B) 7/4 C) 8/3 D) 9/2 E) 12/5

Solution: The combined rate is 1/6+1/12+1/8 = 9/24 of the job per hour.   The time to complete the job is 24/9 = 8/3 hours.   The answer is 8/3.
Answer: C
How many two-digit numbers satisfy this property.: The last digit (unit's digit) of the square of the two-digit number is 2 ?  Choose the correct answer
A) 2	B) 3	C) 4	D) 5	E) 0

Solution: A number ending with 2 can never be a perfect square.   Answer: 0
Answer: E
Diesel costs Rs.4 per lit and petrol costs 6.83 per litre. If the price of diesel rise by 10% a month and the price of petrol is unchanged.How many months will it take until a litre of Diesel costs more than a litre of petrol.  Choose the correct option:
A) 9 months
B) 5 months
C) 6 months
D) 3 months
E) 2 months

Solution: Explanation :   =>In the First Month the price of the diesel would be 4*110/100= 
4*110/100 = 22/5 = around 4.4
4.4=>In the Second Month the price of the diesel would be 4.4*110/100= 
4.4*110/100 = 4.84
4.84=>In the Third Month the price of the diesel would be 4.84*110/100= 
4.84*110/100 = 5.324
5.324=>In the fourth Month the price of the diesel would be 5.324*110/100 = 5.85   =>In the fifth Month the price of the diesel would be 5.85*110/100 = 6.44   =>In the sixth Month the price of the diesel would be 6.44*110/100 = 7.08 which is higher than the price of petrol   Answer : 6 months
Answer: C
y = 248 - 343x
Which of the following values of x gives the greatest value of y in the equation above?
Choices
A) 200	B) 100	C) -7	D) 0	E) 10

Solution: Clearly, the negative value of x will result in maximum value of y.   Don't even look at the rest of the answer choices as only one negative value is being present.   Answer is -7
Answer: C
Reena took a loan of 1000 with simple interest for as many years as the rate of interest. If she paid 40 as interest at the end of the loan period, what was the rate of interest?
Select:
A) 3.8
B) 2
C) 6
D) Cannot be determined
E) None

Solution: Explanation: Let rate = R% and time = R years.   Then, (1000 x R x R)/100 = 40   10RÂ² = 40   RÂ² = 4   R = 2.   Answer: Option 2
Answer: B
Evaluate 28% of 450 + 45% of 280 Choices.
A) 232 B) 242 C) 252 D) 262 E) 250

Solution: Explanation:   = (28/100) * 450 + (45/100) * 280   = 126 + 126= 
126 + 126 = 252
252   Answer IS 252
Answer: C
If a:b = 4:1, then find (a - 3b)/(2a - b)?  Choose the correct answer:
A) 6/7
B) 1/7
C) 5/7
D) 3/2
E) 4/7

Solution: Answer: Option 1/7   a/b = 4/1 => a = 4b   (a - 3b)/(2a - b) = (4b - 3b)/(8b - b)   = b/7b => 1/7
Answer: B
In a car wheel, two spokes cover 10 degree. Then for the entire car,how many spokes are there?	Choose the correct choice from the following choices:	A) 128	B) 168	C) 248	D) 268	E) 288

Solution: given, 2 spokes cover 10degrees,   so for 360 degrees.---->360*2/10=72..   so, for entire car, 4*72=288   ANSW288R:288
Answer: E
If one-third of one-fourth of a number is 15, then three-tenth of that number is  Choose the correct choice from the following answers
A) 35 B) 15 C) 60 D) 54 E) 57

Solution: Let the number be x. then 1/3 of ¼ of x=15   X=15x12=180   The required number=(3/10)*180= 
(3/10)*180 = 54
54   ANSWER 54 54
Answer: D
If x and y are both integers such that 41y = 36x and y is not negative, which of the following must be true?
(i) x is prime
(ii) y is even
(iii) xy is positive Answers
A) ii only
B) iii only
C) i and iii only
D) ii and iii only
E) i, ii and iii

Solution: Effectively y = 36x/41   (i) x is prime: now if y = 36x/41 and both x and y are integers; then if x= 41, 36(41)/41 .....so the 41s cancel each other out and you get x=36. Hunky dory. But if x = 82; you get y =72 which also works. Hence x is not necessarily prime.   (ii) y is even: y = 36(41)/41 = 36 (even). Or try 36(82)/41 = 72 (even). When you multiply even with odd, answer is even. So Y HAS TO BE EVEN.   (iii) xy is positive. Hmm. So if y is positive, then x is positive. Because if you have a -ve value of x, it leads to -ve value of y. Hence I would say iii is the answer. ANSWER:iii only
Answer: B
A certain company has budgeted $1560 for entertainment expenses for the year, divided into 12 equal monthly allocations. If by the end of the third month, the total amount spent on entertainment was $420, how much was the company under budget or over budget?  Options.
A) $60 under budget
B) $30 under budget
C) $30 over budget
D) $60 over budget
E) $180 over budget

Solution: The budget for 3 months is (3/12)*$1560 = $390   The company is $30 over budget.   The answer is $30 over budget.  (3/12)* 1560= 
  (3/12)* 1560 = 390
$390   The company is $30 over budget.   The answer is $30 over budget.
Answer: C
In a consignment of eggs 552 were cracked, which was 12 percent of the total consignment. How many eggs were in the consignment? Choose the correct choice
A) 4400 B) 4800 C) 4300 D) 4600 E) 4900

Solution: 4600   4600   (552 ÷ 12) × 100 = 4600.
Answer: D
P,Q and R together earn Rs.1800 in 9 days. P and R can earn Rs.600 in 5 days. Q and R in 7 days can earn Rs.910. How much amount does R can earn per day? Choose the correct choice from the following options:
A) s.50  B) s.70  C) s.90  D) s.100  E) s.120

Solution: Explanation :   s.50mount Earned by P,Q and R in 1 day = 1800/9= 
1800/9 = 200
200 ---(1)   s.50mount Earned by P and R in 1 day= 600/5= 
600/5 = 120
120	---(2)   s.50mount Earned by Q and R in 1 day= 910/7= 
910/7 = 130
130	---(3)   (2)+(3)-(1)=> s.50mount Earned by P , Q and 2R in 1 day   - s.50mount Earned by P,Q and R in 1 day = 120+130-200= 
120+130-200 = 50
50=>s.50mount Earned by R in 1 day = 50   s.50nswer : Option s.50
Answer: A
A certain meter records voltage between 0 and 10 volts inclusive. If the average value of 3 recordings on the meter was 6 volts, what was the smallest possible recording in volts?  Select:
A) 2
B) 3
C) 4
D) 5
E) 6

Solution: if average of 3 is 6 so sum of 3 should be 18   3 recording can be from 0-10 inclusive   to find one smallest other two should be highest   so, lets assume three var are a,b,c   say a is smallest and give b and c greatest readings say 8 and 8   so a has to be 2   2
Answer: A
A sum of money becomes triple itself in 5 years at simple interest. How many years will it become nine times at the same rate?
Choose the correct option: A) 12 Â½ years B) 62 Â½ years C) 18 Â½ years D) 72 Â½ years E) 12 Â½ years

Solution: 100 ---- 200 ---- 5   200 ---- 5   100 ---- 2 1/2   ------------------   900 ---- 18 Â½ years   Answer:18 Â½ years
Answer: C
A and B start from house at 10am. They travel on the MG road at 20kmph and 40 kmph. there is a Junction T on their path. A turns left at T junction at 12:00 noon, B reaches T earlier, and turns right. Both of them continue to travel till 2pm. What is the distance between A and B at 2 pm
Choose the correct answer
A) 160kilometre	B) 170km	C) 180km	D) 190km	E) 150km

Solution: at 12 A will travel=20*2= 
20*2 = 40
40km   B will travel this 40 km in  40/40= 
 40/40 = 1
1 hr i.e. by 11am.   after T junction for 160kilometre- distance travelled=2*20= 
2*20 = 40
40 km   for b distance travelled=40*3= 
40*3 = 120
120   so distance between 160kilometre & B is=120+40= 
120+40 = 160
160km   160kilometreNSWER:160kilometre
Answer: A
A car salesman earns a base salary of $800 per month plus a commission of $200 for each car he sells. If the car salesman earned $2600 in September, how many cars does he need to sell in October in order to double his September earnings?	Choose the correct answer
A) 18 B) 19 C) 20 D) 21 E) 22

Solution: 800+200x=5200   x=22 cars.   The answer is 22.
Answer: E
What is the place value of 2 in the numeral 12734?  Pick one
A) 1500  B) 4500  C) 2000  D) 6000  E) 4000

Solution: Option '2000'    2 * 1000= 
 2 * 1000 = 2_000
2000
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:
Options:
A) 40	B) 50	C) 60	D) 70	E) 80

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: Option 50
Answer: B
In how many different number of ways a Committee of 3 person of can be selected from 5 boys and 3 girls such that at least 1 girl is included in the committee  Choose the correct choice from the following options
A) 41
B) 42
C) 46
D) 48
E) 50

Solution: 1G 2B 2G 1B 3G   = 3461 × 5462 + 3462 × 5461 + 3463s   = 3 × (5 × 4)/2 + 3 × 5 + 1   = 30 + 15 + 1= 
30 + 15 + 1 = 46
46   Total 5M 3W   8463= 56   5463 = 10   At least one girl = total - with out girl   At least one girl = 56 - 10= 
56 - 10 = 46
46   46)
Answer: C
A car gets 32 miles to the gallon. If it is modified to use a solar panel, it will use only 80 percent as much fuel as it does now. If the fuel tank holds 12 gallons, how many more miles will the car be able to travel, per full tank of fuel, after it has been modified? Choose the correct answer.
A) 84	B) 88	C) 92	D) 96	E) 100

Solution: Originally, the distance the car could go on a full tank was   12*32= 
  12*32 = 384
384 miles.   After it has been modified, the car can go  32/0.8= 
 32/0.8 = 40
40 miles per gallon.   On a full tank, the car can go  12*40= 
 12*40 = 480
480 miles, thus 96 miles more.   The answer is 96.
Answer: D
When Tom works alone he chops 2 lb. salad in 3 minutes, and when Tammy works alone she chops 3 lb. salad in 2 minutes. They start working together, and after some time finish chopping 65 lb. of salad. Of those 80 lb., the salad quantity chopped by Tammy is what percent greater than the quantifying chopped by Tom?.
Options
A) 44% B) 125% C) 105% D) 225% E) 400%

Solution: Tom chops 4 lbs in 6 minutes   Tammy chops 9 lbs in 6 minutes   So in the same amount of time, Tammy chops 125% more than Tom, since 9 is 125% greater than 4. So 125% is the answer.   Note that the actual time doesn't matter. If you multiply the time each work by x, you'll multiply the work each does by x, and 9x is still 125% greater than 4x.   Ans : 125%
Answer: B
Twelve animals of a circus has to be placed inside in twelve cages one in each cage. If 4 of the cage are too small for 6 of the animal then find the number of ways of caging the animal.
Pick one:  A) A.604800  B) B.808250  C) C.502450  D) D.784200  E) E.4838400

Solution: ways for cages that are too small = 5*4*3*2= 
5*4*3*2 = 120
120   since we have 8 cages and 8 animal left therefore ways for 8 cages=8!   total ways =120*8!=4838400   Answer E.4838400
Answer: E
There are 45 people in a certain community who belong to the local golf club, tennis club or both clubs. If twice as many people belong to the tennis club as belong to the golf club, what could be the number of people who belong to both clubs?  Pick one:	A) 4	B) 7	C) 17	D) 21	E) 27

Solution: let's find the range of Both and hence the range of x. Minimum value of Both: Say there is no overlap in the two sets.45 = x + 2xx =15In this case Both = 0 Maximum value of Both: Say there is maximum overlap between the two sets. One set has x so it could be a subset of the set 2x.45 = 2xBut x cannot be a decimal so (x-1) could be the overlap (= Both) and there could be 1 in only the Golf club.45 = 2 x + x - (x - 1)x = 22In this case Both = 22 - 1= 
22 - 1 = 21
21 So Both lies between 0 and 21 Only option (C) satisfies this condition. ANSWER:17
Answer: C
A certain number when divided by 110 leaves a remainder 25, what is the remainder if the same no.be divided by 15?	Choose the correct choice from the following choices.
A) 4 B) 5 C) 6 D) 8 E) 9

Solution: 9xplanation:     110 + 25= 
  110 + 25 = 135
135/15= 
135/15 = 9
9 (Remainder)   9
Answer: E
Alpha, Beta and Gamma are inner angles in a triangle. If Alpha = Beta + Gamma, what can't be the size of Beta?  Choose the correct choice from the following choices:
A) 44 degrees	B) 45 degrees.	C) 89 degrees	D) 90 degrees.	E) There isn't enough data to determine.

Solution: Given Alpha = Beta + Gamma, and Alpha, Beta and Gamma are inner angles in a triangle. Thus Alpha + Beta + Gamma = 180   Beta + Gamma + Beta + Gamma = 180 => 2(Beta + Gamma) = 180 => Beta + Gamma = 90. Thus beta will be less than 90.   Hence the answer is 90 degrees..
Answer: D
The sum of the squares of three consecutive odd numbers is 2531.Find the
numbers. Choose the correct choice from the following options:  A) 27,28 and 31  B) 25,29 and 31  C) 27,29 and 32  D) 26,33 and 31  E) 27,29 and 31

Solution: Let the numbers be x, x + 2 and x + 4.   Then, X2 + (x + 2)2 + (x + 4)2 = 2531 => 3x2 + 12x - 2511 = 0   => X2 + 4x - 837 = 0	=> (x - 27) (x + 31) = 0	=>	x = 27.   Hence, the required numbers are 27, 29 and 31.   Answer is 27,29 and 31.
Answer: E
Mrs. Napier has 45 stickers to give to 7 students for a reward. How many
stickers will each student get? Will there be any stickers left over?	Options:
A) 2-5	B) 6-4	C) 2-6	D) 2-3	E) 2-8

Solution: 45/7 = 6 R 4 Mrs. Napier will give each student 6 stickers and there   will be 4 left over.   correct answer 6-4
Answer: B
What is the probability that an integer selected randomly from 101 to 550, inclusive, begins with 1, 2, or 3, and ends with 4, 5, or 6? Pick one:	A) 1/5	B) 2/5	C) 3/5	D) 1/4	E) 1/3

Solution: Total = 550-101+1= 
550-101+1 = 450
450   Desired values= 3*10*3= 
3*10*3 = 90
90   P(1/5)= 90/450 = 1/5   1/5NSWER:1/5
Answer: A
A, B, C subscribe Rs. 50,000 for a business. A subscribes Rs. 4000 more than B and B Rs. 5000 more than C. Out of a total profit of Rs. 35,000, A receives:	Select the correct option.
A) Rs. 14,000
B) Rs. 14,200
C) Rs. 14,400
D) Rs. 14,700
E) Rs. 14,800

Solution: Let C = x.   Then, B = x + 5000 and A = x + 5000 + 4000 = x + 9000.   So, x + x + 5000 + x + 9000 = 50000   3x = 36000   x = 12000   A : B : C = 21000 : 17000 : 12000 = 21 : 17 : 12.   A's share = Rs. (35000 x 21/50) = Rs. 14,700.   Rs. 14,700
Answer: D
Robert left from a Pvt Company. Management hold his salary Rs. 15000/- for one month. Earlier Robert borrowed Rs. 7280/- from company. But Robert forget that. After one month Robert asked his salary and accountant gives Rs.18500/- to him. What is the incentive amount given to Robert? Choose the correct choice from the following:  A) 9500  B) 12500  C) 10780  D) 10500  E) 8600

Solution: Total Salary = Rs.15000/-   Borrowed Money = 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
How many seconds will a train 110 meters long take to cross a railway platform 165 meters long if the speed of the train is 132 kmph?	Choose the correct choice from the following choices:
A) 6 sec  B) 7.5 sec  C) 8 sec  D) 3 sec  E) 10 sec

Solution: D = 110+165= 
110+165 = 275
275   S= 132 * 5/18 = 110/3 mps   T = 275*3/110= 
275*3/110 = 15/2 = around 7.5
7.5 sec   7.5 sec)7.5 sec
Answer: B
How many liters of a 40% iodine solution need to be mixed with 35 liters of a 20% iodine solution to create a 35% iodine solution?
Choose the correct choice from the following choices
A) 35 B) 49 C) 100 D) 105 E) 140

Solution: Solution 1:   Assume the iodine solution to be mixed = x lts.   Iodine = 0.4x lts, Water = 0.6x lts.   Solution 2: 35 liters of a 20% iodine solution   Iodine = 7 lts, Water = 28 lts.   Total iodine = 0.4x + 7   Total water = 0.6x + 28   The resultant is a 35% iodine solution.   Hence (0.4x + 7) / (x + 35) = 35/100   40x + 700 = 35x + 1225   5x = 525   x = 105 lts   Correct Option: 105
Answer: D
How many 4-digit B numbers (ABCD) can be formed such that |A – D| = 2?  Choose the most appropriate option
A) 2,000	B) 1,900	C) 1,800	D) 1,600	E) 1,500

Solution: 1) A=0 and D-8   2) A and D as 1 and 9..so 3*100= 
3*100 = 300
300 extra ways ans  1800-300= 
 1800-300 = 1_500
1500.   we are looking for |A-D|=2 so any of the two can be bigger..   these two can have values (1,3) ; (2,4) so on till (7,9) so total 7*2 = 14..   another arrangement could be A as 2 and D as 0... D as 2 and A as 0 is not possible as number will become 3 digits..   so the ways A and D can be placed = 14+1= 
14+1 = 15
15 ways..   B and C can be placed in 10*10 ways..   Total B= 15*10*10=1500.1,500
Answer: E
A committee has 5 men and 6 women. What are the number of ways of selecting a group of eight persons? Answers.
A) 165 ways B) 176 ways C) 617 ways D) 136 ways E) 156 ways

Solution: Total number of persons in the committee = 5 + 6= 
5 + 6 = 11
11   Number of ways of selecting group of eight persons= ¹¹C₈ = ¹¹C₃ = (11 * 10 * 9)/(3 * 2)= 
(11 * 10 * 9)/(3 * 2) = 165
165 ways.   165 waysnswer: 165 ways
Answer: A
The ratio between the speeds of two trains is 3 : 5. If the second train runs 500 kms in 4 hours, then the speed of the first train is  Choose the correct choice from the following answers
A) 80 km/h
B) 75 km/h
C) 50 km/h
D) 125 km/h
E) 60 km/h

Solution: 75 km/h   75 km/h
Answer: B
Two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 11 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 most appropriate option:
A) 477 B) 384 C) 279 D) 276 E) 291

Solution: 1h ----- 5   ? ------ 60   12 h   RS = 11 + 21= 
11 + 21 = 32
32   T= 12   D = 32 * 12= 
32 * 12 = 384
384.Answer: 384
Answer: B
The present ages of three persons in proportions 4 : 7 : 9. Eight years ago, the sum of their ages was 16. Find their present ages (in years).	Choices
A) 8, 14, 18  B) 8, 28, 36  C) 20, 35, 45  D) 33,42,43  E) 23,42,43

Solution: Let their present ages be 4x, 7x and 9x years respectively.   Then, (4x - 8) + (7x - 8) + (9x - 8) = 16   20x = 40   x = 2.   Their present ages are 4x = 8 years, 7x = 14 years and 9x = 18 years respectively.   8, 14, 18NSWER:8, 14, 18
Answer: A
The parameter of a square is equal to the perimeter of a rectangle of length 16 cm and breadth 14 cm. Find the circumference of a semicircle whose diameter is equal to the side of the square. (Round off your answer to two decimal places  Choose the correct choice from the following options
A) 45
B) 43
C) 42
D) 47
E) 23.57

Solution: Let the side of the square be a cm.   Parameter of the rectangle = 2(16 + 14) = 60 cm Parameter of the square = 60 cm   i.e. 4a = 60   A = 15   Diameter of the semicircle = 15 cm   Circimference of the semicircle   = 1/2(∏)(15)   = 1/2(22/7)(15) = 330/14 = 23.57 cm to two decimal places   Answer: Option 23.57
Answer: E