MU-NLPC/Calc-aqua_rat huggingface dataset:
Find out the C.I on Rs.6000 at 4% p.a. compound half-yearly for 1 1/2 years Choose the correct choice.
A) 367.25 B) 306.07 C) 306.04 D) 306.03 E) 306.01

Solution: 367.25 = 6000(51/50)3   = 6367.248   6000   -----------   367.25   367.25nswer:367.25
Answer: A
The number of meters in BB is equal to the square root of the number of centimeters in BB. What is the length of BB (1 meter=100 centimeters)?	Choose the correct choice from the following answers.
A) 100 meters B) 10 meters C) 100 centimeters D) 10 centimeter E) 1 centimeter

Solution: I'd plug in the options for this question.   Check option A: if the number of meters in BB is 100, then the number of centimeters is 100*100. The square root of 100*100 is 100: 100 = 100.   100 metersnswer: 100 meters.
Answer: A
The Lulu mall in city charges 80 cents for the first hour of parking and $5 for each additional hour until the customer reaches 4 hours, after that the parking fee is $2 per hour. If David parked his bike in the mall for 7 hours and 30 minutes, how much is he going to pay?
Choose the correct option.
A) $36.6 B) $12. C) $13. D) $14.5. E) $15.

Solution: 0.80+5*5+2*5+0.80= 
0.80+5*5+2*5+0.80 = 36.6
$36.6   $36.6nswer: $36.6
Answer: A
Population of a city in 20004 was 1400000. If in 2005 there isan increment of 15% , in 2006 there is a decrements of 35 % and in 2007 there is an increment of 45%, then find the population of city at the end of the year 2007  Select
A) 354354 B) 545454 C) 465785 D) 456573 E) 2818075/2

Solution: Required population = P (1 + R1/100)(1 - R2/100)(1 + R3/100)   = P (1 + 15/100)(1 - 35/100)(1 + 45/100)   = 2818075/2   2818075/2
Answer: E
What number is obtained by adding the units digits of 734^99 and 347^82?	Choose the correct choice from the following.
A) 10 B) 11 C) 12 D) 13 E) 14

Solution: The units digit of 734^99 is 4 because 4 raised to the power of an odd integer ends in 4.   The units digit of 347^82 is 9 because powers of 7 end in 7, 9, 3, or 1 cyclically. Since 82 is in the form 4n+2, the units digit is 9.   Then   4+9= 
  4+9 = 13
13.   The answer is 13.
Answer: D
In an increasing sequence of 8 consecutive even integers, the sum of the first 4 integers is 292. What is the sum of all the integers in the sequence?
Options:
A) 552	B) 616	C) 774	D) 886	E) 990

Solution: let the first term of the sequence be x   since it is consecutive even integers the terms be we x, x+2,x+4...x+14 (up to 8 terms)   now,   sum of first 4 terms =292   or,   4x+12=292   x=280/4= 
280/4 = 70
70   Thus the answer can now be calculated by either summing up 70+72+74+... 8th term   or   s=n/2(2a+(n-1)d   =8/2(2*70+(7*2))   =4(140+14)=616   616
Answer: B
The average salary of all the workers in a workshop is Rs. 8000. The average salary of 7 technicians is Rs. 10000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is:	Choose the correct choice from the following answers
A) 23	B) 19	C) 22	D) 20	E) 14

Solution: Let the total number of workers be x. Then,   8000x = (10000 * 7) + 6000(x - 7)   = 2000x = 28000   = x = 14.   ANSW14R:14
Answer: E
A man rows his boat 90 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream?	Choices:
A) 9 kmph  B) 6 kmph  C) 5 kmph  D) 8 kmph  E) 7 kmph

Solution: Speed downstream = d/t = 90/(2 1/2) = 36 kmph   Speed upstream = d/t = 45/(2 1/2) = 18 kmph   The speed of the stream = (36 - 18)/2= 
(36 - 18)/2 = 9
9 kmph   9 kmphnswer:9 kmph
Answer: A
Robert is travelling on his cycle and has calculated to reach point A at 2 P.M. if he travels at 10 kmph, he will reach there at 12 noon if he travels at 15 kmph. At what speed must he travel to reach A at 1 P.M.?
Answers:
A) 8 kmph
B) 11 kmph
C) 12 kmph
D) 14 kmph
E) 16 kmph

Solution: Explanation:   Let the distance travelled by x km.   Then,	x/10-x/15=2   3x - 2x = 60   x = 60 km.   Time taken to travel 60 km at 10 km/hr =60/10= 
60/10 = 6
6 hrs.   So, Robert started 6 hours before 2 P.M. i.e., at 8 A.M.   Required speed=	60/5= 
60/5 = 12
12 kmph   ANSWER IS 12 kmph
Answer: C
The total of 324 of 20 paise and 25 paise make a sum of Rs. 71. The no of 20 paise coins is  Choose the correct answer:
A) 238  B) 277  C) 278  D) 200  E) 288

Solution: Explanation:   Let the number of 20 paise coins be x. Then the no of 25 paise coins = (324 - x).   0.20 * (x) + 0.25 (324 - x) = 71 => x = 200..   Answer: 200) 200
Answer: D
A boy has nine trousers and 12 shirts. In how many different ways can he select a trouser and a shirt?
Select the correct option
A) 928	B) 278	C) 192	D) 108	E) 289

Solution: The boy can select one trouser in nine ways.   The boy can select one shirt in 12 ways.   The number of ways in which he can select one trouser and one shirt is   9 * 12= 
  9 * 12 = 108
108 ways.   Answer:108
Answer: D
10 is subtracted from 50% of a number, the result is 25. Find the number?	Choose the correct choice from the following options
A) 75 B) 70 C) 35 D) 170 E) 50

Solution: (50/100) * X â€“ 10 = 25   5X = 350   X = 70   Answer:70
Answer: B
If 4 men can colour 48 m long cloth in 2 days, then 6 women can colour 36 m long cloth in?	Select the correct option: A) day B) day C) days D) days E) days

Solution: The length of cloth painted by one man in one day = 48 / 4 × 2 = 6 m   No. of days required to paint 36 m cloth by 6 men = 36/ 6 × 6 = 1 day.   day)
Answer: B
How many positive numbers not greater than 4300 can be formed using the digits 0,1,2,3,4 where repeatation is allowed?
Choose the most appropriate option
A) 576
B) 575
C) 620
D) 640
E) 660

Solution: 1 digit = 5   2 digits = 4* 5= 
4* 5 = 20
20   3 digits= 4*5*5= 
4*5*5 = 100
100   Now,4 digit number till 4000 can have digits 1,2,3 in thousands place ( total choices= 3 )   0,1,2,3,4 in hundreds ,tens and ones place   I.e 3*5*5*5 = 375   Now From 4000 to 4299 = 1*3*5*5= 
1*3*5*5 = 75
75   Total= 5+20+100+375+75+1= 
5+20+100+375+75+1 = 576
576 (1 for 4300)   576NSWER:576
Answer: A
T=(429)^2 * 237 * (1243)^3 is thrice of ?  Choose the most appropriate option:
A) 33605 * 31960 * (1243)^2  B) 33654 * 538219 * (1243)^2  C) 33891 * 533247 * (1243)^2  D) 34122 * 532004 * (1243)^2  E) 34606 * 534572 * (1243)^2

Solution: T=(429)^2*237*(1243)^3 is an odd number.   Among answer choices only C is an odd number, (so thrice C also will be an odd number).   Answer: 33891 * 533247 * (1243)^2.
Answer: C
-20 , -16 , -12 , -8 ....
In the sequence above, each term after the first is 8 greater than the preceding term. Which of the following could not be a term in the sequence?  Select
A) 0  B) 200  C) 440  D) 664  E) 762

Solution: Ans : 762 762   Since 762 is not divisible by 8 , all the other options are divisible by 8
Answer: E
A confectioner decides to sell all of his pastry due to the coming holiday. His pastry goods are equally divided among a group of 28 regular customers. If only 49 customers come to the bakery, each one will receive 6 less pastry goods. How much pastry does the confectioner needs to sell?	Pick one
A) 392	B) 412.	C) 432.	D) 502	E) 522

Solution: Solution 1 : Given that number of pastries are equally divided in to 28 groups, so the answer should be a multiple of 28. And in the given choices, only 392 is divisible by 28 with remainder 0(Make sure others are no multiples of 28). So this is good enough to stop here, but to verify, 392/28 = 14 and   392/49= 
  392/49 = 8
8, which confirms the second part of question, 14-8 , 6 pastry short of each customer.   Solution 2 : Going mathematical, expressing in the equation form, Let x be the number of pastries and , n be the number of customers in 28 groups.   So, x= 28 * n,   as per second statement, x = 49 * (n - 6 )   Solve the above 2 for n and then we get x as 392.   392nswer is 392 : 392.
Answer: A
A 6 by 8 rectangle is inscribed in circle. What is the circumference of the circle?  Options:
A) 5π
B) 10π
C) 15π
D) 20π
E) 25π

Solution: The diagonal of the rectangle will be the diameter of the circle.   and perimeter= 2*pi*r   Ans: 10π
Answer: B
In a series of six football matches between Germany and Argentina , the probability of Germany winning a match is 1/3 and the probability that the match ends in a draw is 1/4. If a win gets the team 2 points, a draw 1 point and a loss 0 Points, What is the probability that Germany will end up in 6 draws in the series? Pick:
A) 24/576
B) 125/864
C) 1/25
D) 1/4096
E) 1/5

Solution: Since the probability of a draw is 1/4, then the probability of 6 draws in 6 matches is (1/4)^6=1/4096.   Answer: 1/4096.
Answer: D
A train is 327 meter long is running at a speed of 40 km/hour. In what time will it pass a bridge of 122 meter length?
Choose the correct choice from the following:
A) 32.7	B) 41	C) 50.29	D) 40.41	E) 20.28

Solution: Speed = 40 Km/hr = 40*(5/18) m/sec = 100/9 m/sec   Total distance = 327+122= 
327+122 = 449
449 meter   Time= Distance/speed   = 449 * (9/100)= 
449 * (9/100) = 4_041/100 = around 40.41
40.41 seconds.   Answer: 40.41
Answer: D
The value of a stock is X dollars. On Sunday the stock's value grew by half of its value, but on Monday its value dropped to a half of its new value. What is the stock's value at the end of Monday? Choose the correct choice from the following choices.
A) X.  B) X/2.  C) 2X/3.  D) 3X/4.  E) X/4.

Solution: Stock value= X   AT sunday end= x+.5X= 1.5 X   On monday the value drop to 1/2rd of its value on sunday   1.5x/2= .75x 1.5 /2= 
 1.5 /2 = 0.75
.75x= 3X/4   3X/4. is the answer
Answer: D
P alone can complete a piece of work in 10 days. Work done by Q alone in one day is equal to one-third of the work done by P alone in one day. In how many days can the work be completed if P and Q work together?
Choose the correct choice.
A) 6 (1/4) days
B) 30/4 days
C) 7 (3/4) days
D) 9/4 days
E) 9 (3/4) days

Solution: Work done by P alone in one day = 1/10th of the total work done by Q alone in one day = 1/3(of that done by P in one day) = 1/3(1/10 of the total) = 1/30 of the total.   Work done by P and Q, working together in one day = 1/10 + 1/30 = 4/30 of the total   They would take 30/4 days to complete the work working together.   ANSWER:30/4 days
Answer: B
A thief is noticed by a policeman from a distance of 200 m. The thief starts running and the policeman chases him. The thief and the policeman run at the rate of 10 km and 11 km per hour respectively. What is the distance between them after 6 minutes ? Choose the correct choice from the following answers
A) 50 meter	B) 100 meter	C) 110 meter	D) 120 meter	E) 130 meter

Solution: Explanation:   Relative speed of the thief and policeman = (11 – 10) km/hr = 1 km/hr   Distance covered in 6 minutes =   1/60∗6=1/10=100meters   So distance between them after 6 minutes = 200 - 100= 
200 - 100 = 100
100 meters   Option 100 meter
Answer: B
1+3=2 2+3=10 3+3=30 4+3=68 5+3=??  Choose the correct option:
A) 110
B) 120
C) 130
D) 140
E) 150

Solution: 1^3+3-2=2,   2^3+3-1=10,   3^3+3-0=30,   4^3+3+1=68,   5^3+3+2=130   ANSWER:130
Answer: C
Find the average of all the numbers between 6 and 29 which are divisible by 5?  Choices:
A) 17
B) 20
C) 25
D) 30
E) 15

Solution: 17verage = (10+15+20+25) 4 = 70/4 = 17   17nswer is 17
Answer: A
If two numbers are in the ratio 2:3. If 10 is added to both of the numbers then the ratio becomes 3:4 then find the largest number?
Choices.
A) 20  B) 22  C) 30  D) 32  E) 27

Solution: Ratio is 2:3   2x + 10 : 3x + 10 = 3 : 4   4[2x + 10] = 3[3x + 10]   8x + 40 = 9x + 30   9x - 8x = 40 - 30= 
40 - 30 = 10
10   Then largest number is= 3x   3x = 30   Ans = 30
Answer: C
What is the area of square field whose side of length 18 m?	Choose the most appropriate option.
A) 225 sq m B) 186 sq m C) 586 sq m D) 324 sq m E) 296 sq m

Solution: 18 * 18= 
18 * 18 = 324
324 sq m   Answer: 324 sq m
Answer: D
How many ways are there to split a group of 12 students into two groups of 6 students each? (The order of the groups does not matter)	Pick one: A) 180 B) 262 C) 384 D) 462 E) 512

Solution: 12C6 = 924   If we consider these groups, each group will be counted twice.   The number of ways to choose 2 groups of 6 is  924/2= 
 924/2 = 462
462   The answer is 462.
Answer: D
From the given equation find the value of x: x² − 3x + 2
Choices
A) 0
B) 1
C) 2
D) 3
E) 6

Solution: (x − 1)(x − 2)   x = 1 or 2.   2
Answer: C
A woman has 7 daughters and they each have a brother, how many children does she have?
Choose the most appropriate option
A) 7  B) 8  C) 9  D) 5  E) 3

Solution: 8   8   8 children, the sisters have just one brother!
Answer: B
In a kilometer race, A beats B by 50 meters or 10 seconds. What time does A take to complete the race?	Select the correct option.
A) 187 sec B) 190 sec C) 168 sec D) 197 sec E) 191 sec

Solution: Time taken by B run 1000 meters   = (1000 * 10)/50= 
(1000 * 10)/50 = 200
200 sec.   Time taken by A= 200 - 10= 
200 - 10 = 190
190 sec.   Answer: 190 sec
Answer: B
A die is rolled twice. What is the probability of getting a sum equal to 9? Select:
A) 2/8  B) 1/9  C) 3/9  D) 7/4  E) 2/7

Solution: Explanation :   Total number of outcomes possible when a die is rolled =6   Hence, total number of outcomes possible when a die is rolled twice, n(S)=6*6= 
6*6 = 36
36   E= Getting a sum of 9 when the two dice fall = {(3, 6), {4, 5}, {5, 4}, (6, 3)}   Hence, n(E) = 4   P(E) =n(E)/n(S)=4/36=1/9   1/9
Answer: B
A and Bâ€™s salaries together amount to Rs. 2,000. A spends 95% of his salary and B spends 85% of his. If now their savings are the same, what is Aâ€™s salary?
Choose the correct choice from the following
A) Rs.500	B) Rs.750	C) Rs.1250	D) Rs.1500	E) Rs.2000

Solution: Explanation:   (5/100) A = (15/100) B   A = 3B   A + B = 2000   4B = 2000 => B = 500   A = 1500   ANSWER IS Rs.1500
Answer: D
Ramu bought an old car for Rs. 35000. He spent Rs. 13000 on repairs and sold it for Rs. 64900. What is his profit percent? Pick one:
A) A)14%
B) B)16%
C) C)18%
D) D)30.7%
E) of these

Solution: Total CP = Rs. 35000 + Rs. 13000 = Rs. 48000 and SP = Rs. 64900   Profit(%) = (64900 - 48000)/55000 * 100 = 30.7%   ANSWER:30.7%
Answer: D
Bob bikes to school every day at a steady rate of b miles per hour. On a particular day, Bob had a flat tire exactly halfway to school. He immediately started walking to school at a steady pace of y miles per hour. He arrived at school exactly t hours after leaving his home. How many miles is it from the school to Bob's home?	Choices
A) (b + y) / t B) 2(b + t) / by C) 2byt / (b + y) D) 2(b + y + t) / by E) x(y + t) + y(x + t)

Solution: If we choose for d (distance): 10 miles, for b 10 and for y 5.   t would be 90 minutes or 1,5 hours.   If I try this for answer choice 2byt / (b + y) it fits.
Answer: C
There are between 100 and 110 marbles in a collection of cards. If they are counted out 3 at a time, there are 1 left over, but if they are counted out 4 at a time, there is 4 left over. How many marbles are in the collection? Choose the correct choice from the following choices
A) 100
B) 103
C) 106
D) 108
E) 109

Solution: Let number of cards = x   If the cards are counted 3 at a time , there are 2 left over-   x = 3p+1   x can take values 100 , 104 , 109   If the cards are counted 4 at a time , there is 1 left over   x= 4q+4   x can take values 100 , 108   Therefore , x = 100   100nswer 100
Answer: A
Adding two non multiples of C always results in a multiple of C; which of the following must be the value of C ?	Choose the correct choice:
A) [A] two B) [B] three C) [C] five D) [D] ten E) [E] hundred

Solution: NON- multiples of 2 would always be ODD and sum of two odd would be EVEN.   so irrespective of value of non-multiples, sum of two them would always be even and thus multiple of 2..   [A] two
Answer: A
A bag contains 5 red, 4 blue and 3 green balls. If 2 ballsare picked at random, what is the probability that both are red?	Choose the correct answer:
A) 1/13  B) 2/23  C) 5/33  D) 4/27  E) 3/23

Solution: P(Both are red),   =55/332125/332=55/332125/332   =10/66=5/33   5/33
Answer: C
Johnny borrows $40,000 from Tony at 4% daily interest compounded daily. How much does Johnny owe Tony after 8 weeks?  Answers:
A) 40000*0.02^56
B) 30000*1.12
C) 40000*2.12
D) 40000*1.04^56
E) (40000*1.02)^56

Solution: A=A= P(1+r100)^n   So, A=40000(1+4/100)^7âˆ—8   So, A= 40000(1.04)^56   Hence answer will be (40000*1.04^56)
Answer: D
What least no. must be subtracted from 427398 so that remaining no.is divisible by 15?
Choose the most appropriate option
A) 344545629	B) 723437481	C) 354595321	D) 964564944	E) 458449909

Solution: Explanation:   On dividing 427398 by 15 we get the remainder 3, so 3 should be subtracted   Option 723437481
Answer: B
Of the teams competing in the world archery championships, Fifty percent are from Europe. Half as many are from the United States and one twentieth are from Africa. What fraction of teams are from neither Europe, the US or Africa. Select:	A) 13/20	B) 15/20	C) 13/15	D) 3/20	E) 4/20

Solution: Half as manymeans half of 4/20U, then   4/20U 50%   US 25%   AF 5%   the rest is 20%, answer 4/20
Answer: E
Light glows for every 17 seconds . How many times did it between 1:57:58 and 3:20:47 am  Choose the most appropriate option:
A) 291 B) 292 C) 293 D) 384 E) 285

Solution: the diff in sec between 1:57:58 and 3:20:47 is 4969 sec, 4969/17 = 292.   so total 293 times light ll glow   ANSWER:293
Answer: C
A rectangular field has a length 10 feet more than it is width. If the area of the field is 264, what are the dimensions of the rectangular field?
Choose the correct choice from the following answers.
A) 22 B) 23 C) 24 D) 25 E) 26

Solution: Let x and y be the length and width of the field. The statement "a length 10 feet more than it is width" may be formulated by   x = 10 + y   The formula for the area is given by   A = x y   Substitute A and x in the above equation by 264 and 10 + y respectively to obtain   264 = (10 + y) y   Write the above equation in standard form as follows   y 2 + 10 y - 264 = 0   Solve the above equation for to obtain   y = 12 and y = - 22   Since y is the value of a width it must be positive. The dimensions of the field are given by   y = 12 and x = 10 + y = 22   As an exercise, check that the rectangular field has length 10 feet more than it is width and an area of 264.   22nswer 22
Answer: A
The average of first three prime numbers greater than 5 is? Options.
A) 12.6 B) 12.9 C) 22.3 D) 10.3 E) 12.7

Solution: 7 + 11+ 13= 
7 + 11+ 13 = 31
31/3= 10.3   Answer: 10.3
Answer: D
What is the tens digit of 6^20? Answers.
A) 1
B) 3
C) 5
D) 7
E) 9

Solution: The tens digit of 6 in integer power starting from 2 (6^1 has no tens digit) repeats in a pattern of 5: {3, 1, 9, 7, 5}:   The tens digit of 6^2=36 is 3.   The tens digit of 6^3=216 is 1.   The tens digit of 6^4=...96 is 9.   The tens digit of 6^5=...76 is 7.   The tens digit of 6^6=...56 is 5.   The tens digit of 6^7=...36 is 3 again.   etc...   20 has the form 5n, so the tens digit of 6^20 is 7.   The answer is 7.
Answer: D
96% of the population of a city is 23040. Find the total population of the city? Choose the correct answer.
A) 30000 B) 28000 C) 24000 D) 25000 E) 25500

Solution: Population consider as x   x*(96/100) = 23040   x=240*100   ==>24000   ANSWER 24000
Answer: C
A man complete a journey in 10 hours. He travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km.	Choices.
A) 220 km B) 224 km C) 230 km D) 232 km E) 234 km

Solution: 0.5x/21 + 0.5x/24 = 10   --> x/21 + x/24 = 20   --> 15x = 168 x 20   --> x = (168 x 20)/15 = 224 km.   Answer : 224 km.
Answer: B
If k is the greatest positive integer such that 3^k is a divisor of 21! then k = Select the correct option:  A) 3  B) 4  C) 5  D) 6  E) 9

Solution: 21/3= 
21/3 = 7
7   21/9=2.33=2   7+2= 
7+2 = 9
9   k=9   Answer: 9
Answer: E
Different breeds of dogs get older at different rates in “dog years.” Livonian wolfhounds age 7 times as fast as humans, whereas Khazarian terriers age 3 times as fast and Akkadian retrievers age 4 times as fast. If Dan bought a newborn Akkadian on January 1, 2010, a newborn Khazarian 1 year later, and a newborn Livonian 1 year after that, in what year will the sum of the dog-year ages of the Akkadian and the Khazarian first be exceeded by twice the age of the Livonian in dog years, rounding all ages down to the nearest integer?  Select the correct option.
A) 2013  B) 2014  C) 2015  D) 2016  E) 2017

Solution: chart starting at 2011: A=4 ;2012= A=8 ,K=3   A+K=11   L=0.   Then I added 7 to a+k for each year and 14 to L for each year.   2013:AK=18 L=14   2014:AK= 25 L=28   thus, 2014 is the correct answer.   2014
Answer: B
My 5 sons are enrolled in an army's platoon of 80 men. The General is choosing randomly 2 men to a suicide mission. What is the probability of both of the selected men will be two of my sons?
Choose the correct option:
A) 1/80
B) 2/80
C) 5/80
D) 1/316
E) 2/316

Solution: My sons are 5 in a group of 80 men. Thus the probability of choosing 2 of my sons is: (5/80)(4/79) = 1/316. The correct answer is 1/316.
Answer: D
Ganet has to pay back her bank loan over 6 months following the below sequence.
$50, $55, $65, $80, $85, ?
How much will she pay back on the sixthmonth?
Choose the correct answer:
A) $155 B) $145 C) $95 D) $125 E) $130

Solution: The sequence progresses +5, +10, +15 repeated; The amount to pay back on the 6th Month is $95   Ans $95
Answer: C
a man owns 1/3 of market reserch beauro buzness,and sells 3/5 of his shares for 2000rs,what is the value of buzness?	Choose the correct choice
A) 40000	B) 60000	C) 10000	D) 25000	E) 50000

Solution: If value of business=x   Total sell (1x/3)(3/5)=2000   ->x=10000   ANSWER:10000
Answer: C
Two trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 25 hours and 81 hours respectively. The ratio of their speeds is: Choose the correct option.
A) 2 : 3	B) 4 : 3	C) 9 : 5	D) 9 : 16	E) None of these

Solution: Let us name the trains as A and B. Then,   (A's speed) : (B's speed) = âˆšb : âˆša = âˆš81 : âˆš25 = 9 : 5.   Answer 9 : 5
Answer: C
There are two examinations rooms A and B. If 10 students are sent from A to B, then the number of students in each room is the same. If 20 candidates are sent from B to A, then the number of students in A is double the number of students in B. The number of students in room A is:
Choose the correct choice from the following answers:  A) 100  B) 150  C) 200  D) 220  E) 240

Solution: Let the number of students in rooms A and B be x and y respectively.   Then, x - 10 = y + 10 x - y = 20 .... (i)   and x + 20 = 2(y - 20) x - 2y = -60 .... (ii)   Solving (i) and (ii) we get: x = 100 , y = 80.   The required answer 100 = 100.
Answer: A
A garrison of 2000 men has provisions for 62 days. At the end of 15 days, a reinforcement arrives, and it is now found that the provisions will last only for 20 days more. What is the reinforcement?	Choose the most appropriate option.
A) 1977
B) 1893
C) 2700
D) 1900
E) 1278

Solution: 2000 ---- 62   2000 ---- 47   x ----- 20   x*20 = 2000*47   x = 4700   2000   -------   2700   Answer: 2700
Answer: C
When x and y are rounded to the nearest tenth, x is 0.3 and y is 0.6. The exact value of (x/y) must be between  Choose the correct choice from the following options
A) 5/12 and 7/12  B) 6/11 and 6/13  C) 5/13 and 7/11  D) 3/7 and 7/12  E) 5/11 and 7/13

Solution: x rounded to nearest tenth is 0.3   i.e. x may vary from 0.25 to 0.34   0.25 < x < 0.34   y rounded to nearest tenth is 0.6   i.e. x may vary from 0.55 to 0.64   0.55 < y < 0.64   Min (x/y) = 0.25/0.64 = 25/64 = 25/65 (Approx) = 5/13 (Approx)   Max (x/y) = 0.34/0.55 = 34/55 = 35/55 (Approx) = 7/11 (Approx)   Answer: option 5/13 and 7/11
Answer: C
A motorist knows nine different routes from Bristol to Birmingham. From Birmingham to Sheffield he knows three different routes and from Sheffield to Carlisle he knows two different routes. How many routes does he know from Bristol to Carlisle ?
Choices:
A) 4
B) 8
C) 12
D) 24
E) 54

Solution: Explanation:   Total number of routes from Bristol to Carlisle = (9 x 3 x 2) = 54.   Answer: 54
Answer: E