MU-NLPC/Calc-aqua_rat huggingface dataset:
A cow leaps 8 leaps for every 3 leaps of a bull, but 6 leaps of the bull are equal to 4 leaps of the cow. What is the ratio of the speed of the cow to that of the bull?  Choose the correct answer.
A) 4:1
B) 1:1
C) 3:2
D) 4:5
E) 7:8

Solution: Given;   6 bull = 4 cow;   Or, bull/cow = 4/6;   Let cow's 1 leap = 6 meter and bulls 1 leap = 4 meter.   Then, ratio of speed of cow and bull = 6*8/4*3 = 4:1.''4:1nswer: 4:1
Answer: A
A certain automobile company’s best-selling model is the Speedster. The Speedster, like all of their other models, comes in coupe and convertible styles. 2/3 of the current inventory is Speedsters, of which 4/5 are convertibles. If there are 40 vehicles that are not Speedsters, how many Speedster convertibles are there?	Choose the correct choice from the following answers
A) 30
B) 64
C) 60
D) 70
E) 90

Solution: Total Vehicle = 2/3 of speedster + 1/3 of others.   Speedster convertibles = 2/3 total vehicle * 4 /5   Given : 1/3 constitutes 40 Vehicles. hence 2/3 constitutes 80   Speedster convertibls = 80 * 4/5= 
80 * 4/5 = 64
64   64
Answer: B
A jar contains 8 marbles consisting of an equal number of red, green, and blue marbles. Four marbles are removed from the jar and discarded. What is the probability that only two colors will remain in the jar after the four marbles have been removed? Choices.
A) 1/495	B) 1/165	C) 3/70	D) 1/35	E) 11/20

Solution: Jar contains {4-red, 4-green, 4-blue} marbles. We are asked to find the probability that after removing 4 marbles only 2 colours remain in the jar, i.e., the probability of removing EITHER red, OR green, OR blue.   Sample space = 8C4 = 495.   Probability of choosing 4 red = 4C4/8C4 = 1/70.   Probability of choosing 4 green = 4C4/8C4 = 1/70.   Probability of choosing 4 blue = 4C4/8C4 = 1/70.   Required probability = 1+1+1/70 = 3/70 Ans (3/70).
Answer: C
Jill invests $10000 in an account that pays an annual rate of 3.96%, compounding semi-annually. Approximately how much E does she have in her account after two years?
Pick.
A) $10079.44 B) E=$10815.83 C) $12652.61 D) $14232.14 E) $20598.11

Solution: PS. I guess one can use simple interest to solve cause the answer choices are quite spread between you can easily arrive at something near 8%   Hence E=$10815.83 the answer
Answer: B
Two trains of length 100 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 72 kmph. In how much time will the trains cross each other?
Choose the correct choice from the following answers.
A) 89/7 sec B) 80/7 sec C) 80/8 sec D) 89/7 sec E) 80/7 sec

Solution: Relative speed = (54 + 72)* 5/18 = 7 * 5= 
7 * 5 = 35
35 mps.   The time required= d/s = (100 + 100 + 200)/35   = 400/35 = 80/7 sec.   Answer:80/7 sec
Answer: B
If |7x+4|=|3x+5|, which of the following could be a value of x?  Select
A) 1	B) 9/10	C) 1/4	D) -2	E) 10

Solution: 7x + 4 = 3x + 5 or 7x + 4 = -3x - 5   4x = 1 or 10x = -9   x = 1/4 or x = -9/10   Answer: 1/4
Answer: C
The calendar for 1992 is the same as for
Choose the correct choice from the following:	A) 1997	B) 1996	C) 1995	D) 1994	E) 1992

Solution: consider 1992 has 0 odd days   therefore sum of years which is equal to 0 odd days is   1992 + 1993 + 1994 + 1995 + 1996   ( 2 + 1 + 1 + 1 + 2 )= 
( 2 + 1 + 1 + 1 + 2 ) = 7
7 or 0 odd days   therefore 1997 is the answer and its calender is similar to 1992   1997NSWER:1997
Answer: A
Sandy is younger than Molly by 12 years. If their ages are in the respective ratio of 7:9, how old is Molly?  Choose the correct answer.
A) 36	B) 45	C) 54	D) 63	E) 72

Solution: S = M - 12   S / M = 7/9   9S = 7M   9(M-12) = 7M   M = 54   The answer is 54.
Answer: C
A rectangular grass field is 75 m * 55 m, it has a path of 2.5 m wide all round it on the outside. Find the area of the path and the cost of constructing it at Rs.2 per sq m?	Answers
A) 1350 B) 2999 C) 2772 D) 2672 E) 2871

Solution: 1350rea = (l + b +2d) 2d   = (75 + 55 +2.5 * 2) 2*2.5 => 675   675 * 2 = Rs.1350   1350nswer:1350
Answer: A
How many of the following numbers are divisible by 132?
264, 396, 462, 792, 968, 2178, 5184, 6336 Choose the correct choice from the following answers
A) 4
B) 5
C) 6
D) 7
E) 8

Solution: A number is divisible by 132, if it is divisible by each one of 11, 3 and 4.   Clearly, 968 is not divisible by 3. None of 462 and 2178 is divisible by 4.   Also, 5184 is not divisible by 11.   Each one of remaining 4 is divisible by each one of 11, 3 and 4 and therefore, by 132.   4NSWER:4
Answer: A
The average price of 10 oranges is Rs. 12 while the average price of 8 of these oranges is Rs. 11.75. Of the remaining two oranges, if the price of one orange is 75% more than the price of the other, what is the price of each of these two oranges?
Choose the correct choice from the following: A) Rs 5, Rs 7.50 B) Rs 8, Rs 12 C) Rs 9.5, Rs 16.5 D) Rs 12, Rs 14 E) None of these

Solution: Explanation :   Total price of the two oranges = Rs. [(12 x 10) (11.75 x 8)]   = Rs. (120 - 94) = Rs. 26.   Let the price of one orange be Rs. x.   Then, the price of other orange = Rs. (x + 75% of x) = Rs. x + 3/4x = Rs. 7x/4   So, x + 7x/4 = 26   11x = 104   x = 9.5   The prices of the two oranges are Rs. 9.5 and Rs. 16.5   Answer : Rs 9.5, Rs 16.5
Answer: C
In how many K ways can a four-letter password be chosen, using the letters A, B, C, D, E, and/or F, such that at least one letter is repeated within the password?  Choose the correct option
A) 720	B) 864	C) 900	D) 936	E) 1,296

Solution: Total number of four letter passwords = 6*6*6*6= 
6*6*6*6 = 1_296
1296 ------(1)   Total number of passwords in which no letter repeats= 6C4*4!= 15*24= 
15*24 = 360
360------(2)   therefore required value K= (1)-(2)= 1296-360=936.936
Answer: D
If x is real, find the maximum value of the expression -2x^2 + 7x + 9. Select the correct option
A) 6.125 B) 9.125 C) 12.125 D) 15.125 E) 18.125

Solution: This is an equation of a downward facing parabola.   The maximum value is the top point of the parabola.   -2x^2+7x+9 = (-2x+9)(x+1)   The roots are 9/2 and -1.   The maximum value must be when x is halfway between these two points.   x = 1.75   The maximum value is -2(1.75)^2+7(1.75)+9 = 15.125   The answer is 15.125.
Answer: D
John went to the Hospital at the speed of 60 km per hour while returning for his home he covered the half of the distance at the speed of 10 per hour, but suddenly he realized that he was getting late so he increased the speed and reached the home by covering rest 1/2 of the distance at the speed of 30km per hour. The average speed of the John in the whole length of journey is?
Choose the correct choice from the following answers
A) 19 km/hr	B) 21 km/hr	C) 24 km/hr	D) 28 km/hr	E) 34 km/hr

Solution: Let distance between his home and hospital =   d   d km   Total distance travelled   =   d   +   d   =   2   d   =d+d=2d km   Total time taken   =   d   60   +   (   d   2   )   10   +   (   d   2   )   30   =d60+(d2)10+(d2)30   =   d   60   +   d   20   +   d   60   =   5   d   60   =   d   12   =d60+d20+d60=5d60=d12 hr   Average speed in the whole journey   =   2   d   (   d   12   )   =   2   d   ×   12   d   =   24   =2d(d12)=2d×12d=24 km/hr   24 km/hr
Answer: C
Sakshi can do a piece of work in 20 days.Tanya is 25% more efficient than Sakshi. The number of days taken by Tanya to do the same piece of work :	Choose the correct choice from the following choices:	A) 15	B) 16	C) 18	D) 25	E) 29

Solution: Solution   Ratio of times taken by Sakshi and Tanya = 125 : 100 = 5 : 4 .   Suppose Tanya taken x days to do the work.   5 : 4 : : 20 : x ⇒ x = (20x4/5)=x 16 days.   Hence,Tanya takes 16 days is complete the work   Answer 16
Answer: B
David works at a resort from the beginning of March to the end of September. During the month of August this past year, he made 2 times the average (arithmetic mean) of his monthly totals in tips for the other months. His total tips for August were what fraction of his total tips for all of the months he worked? Choose the correct choice from the following answers
A) 1/6  B) 1/7  C) 1/8  D) 1/4  E) 1/3

Solution: First notice the number of months for which he worked - March to Sept i.e. 7 months   Avg of monthly totals in tips for months other than August = x   Tips in August = 2x   Total tips for all months = 6*x + 2x = 8x   Tips for August/Total tips for all months = 2x/8x = 1/4   Answer : 1/4
Answer: D
P, Q, R enter into a partnership. P initially invests 25 lakh and adds another 10 lakh after one year. Q initially invests 35 lakh and withdraws 10 lakh after 2 years. R's investment is Rs 30 lakh. In what ratio should the profit be divided at the end of 3 years? Choose the correct option:  A) 18:19:19  B) 18:18:19  C) 19:19:18  D) 18:19:18  E) none

Solution: Explanation:   P : Q : R   25×1+35×2):(35×2+25×1) :(30×3)   =95:95:90   =19:19:18   Answer: Option 19:19:18
Answer: C
A Man can row upstream at 98kmph and downward stream at 10 kmph. Find Man's rate still in water
Choose the correct option:
A) 6.8km/hr  B) 54km/hr  C) 90km/hr  D) 3.8km/hr  E) 7.9km/hr

Solution: still in water=1/2(98+10)km/hr   =54km/hr   correct option is :54km/hr
Answer: B
7 does not occur in 1000. So we have to count the number of times it appears between 1 and 999. Any number between 1 and 999 can be expressed in the form of xyz where 0 < x, y, z < 9.	Choose the correct choice from the following answers.
A) 150	B) 300	C) 275	D) 135	E) 451

Solution: 1. The numbers in which 7 occurs only once. e.g 7, 17, 78, 217, 743 etc   This means that 7 is one of the digits and the remaining two digits will be any of the other 9 digits (i.e 0 to 9 with the exception of 7)   You have 1*9*9= 
1*9*9 = 81
81 such numbers. However, 7 could appear as the first or the second or the third digit. Therefore, there will be 3*81= 
3*81 = 243
243 numbers (1-digit, 2-digits and 3- digits) in which 7 will appear only once.   In each of these numbers, 7 is written once. Therefore, 243 times.   2. The numbers in which 7 will appear twice. e.g 772 or 377 or 747 or 77   In these numbers, one of the digits is not 7 and it can be any of the 9 digits ( 0 to 9 with the exception of 7).   There will be 9 such numbers. However, this digit which is not 7 can appear in the first or second or the third place. So there are   3 * 9= 
  3 * 9 = 27
27 such numbers.   In each of these 27 numbers, the digit 7 is written twice. Therefore, 7 is written 54 times.   3. The number in which 7 appears thrice - 777 - 1 number. 7 is written thrice in it.   Therefore, the total number of times the digit 7 is written between 1 and 999 is  243 + 54 + 3= 
 243 + 54 + 3 = 300
300   Ans: 300
Answer: B
Two trains 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time (in seconds) which they take to cross each other, is:
Choose the correct choice from the following answers:
A) 9	B) 9.6	C) 10	D) 10.2	E) 10.8

Solution: Relative speed of the trains=60+40= 
60+40 = 100
100km/hr=100*5/18 m/s=250/9   Time taken to cross each other=total distance/speed   300/250/9=54/5= 
54/5 = 54/5 = around 10.8
10.8sec   ANSW10.8R:10.8
Answer: E
A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 390 m long?  Select the correct option:  A) 40 sec  B) 60 sec  C) 45 sec  D) 48 sec  E) 50 sec

Solution: Speed = 45 * 5/18 = 25/2 m/sec   Total distance covered = 360 + 140 = 750 m   Required time = 750 * 2/25 = 40 sec   ANSWER:60 sec
Answer: B
The average of 1st 3 of 4 numbers is 6 and of the last 3 are 5. If the sum of the first and the last number is 13. What is the last numbers?	Choose the correct choice from the following answers:
A) 4	B) 5	C) 6	D) 7	E) 8

Solution: A + 5 + C = 18   5 + C + D = 15   A + D = 13   A – D = 3   A + D = 13   2D = 10   D = 5   ANSWER:5
Answer: B
A banker paid Rs.5767.20 for a bill of Rs.5840, drawn of Apr 4 at 6 months. If the rate of interest was 7%, what was the day on which the bill was discounted?	Options:
A) 3rd March
B) 3rd September
C) 3rd October
D) 3rd August
E) None of these

Solution: Explanation :   F = Rs.5840   R = 7%   B3rd August = 5840 - 5767.20 = Rs.72.8   B3rd August = FTR/100   ⇒ 72.8 = (5840 × T × 7)/100   ⇒ T = (72.8×100)/(7×5840) = (10.4×100)/5840 = 1040/5840 = 104/584 = 13/73 years   = (13 × 365)/73 3rd Augustays = 65 3rd Augustays   => Unexpired Time = 65 3rd Augustays   Given that 3rd Augustate of 3rd Augustraw of the bill = 4th April at 6 months   => Nominally 3rd Augustue 3rd Augustate = 4th October   => Legally 3rd Augustue 3rd Augustate = (4th October + 3 days) = 7th October   Hence, The date on which the bill was discounted   = (7th October - 65 days)   = (7th October - 7 days in October - 30 days in September - 28 days in August)   = 3rd August Answer : Option 3rd August
Answer: D
Tea worth Rs.126 per kg are mixed with a third variety in the ratio 1: 1 : 2. If the mixture is worth Rs.163 per kg, the price of the third variety per kg will be  Choose one: A) Rs.169.50 B) Rs.1700 C) Rs. 185.50 D) Rs. 180 E) None

Solution: Solution   Since first second varieties are mixed in equal proportions, so their average price = Rs.(126+135/2) = Rs.130.50   So, the mixture is formed by mixing two varieties, one at Rs. 130.50 per kg and the other at say, Rs. x per kg in the ratio 2 : 2, i.e., 1 : 1. We have to find x.   x-163/22.50 = 1 =â€º x - 163 = 22.50 =â€º x=185.50.   Hence, price of the third variety = Rs.175.50 per kg.   Answer Rs. 185.50
Answer: C
FIND THE VALUE OF X ?
(2/7)^-8*(7/2)^-2=(2/7)^X  Select the correct option
A) -5
B) -6
C) 4
D) 0
E) -4

Solution: (2/7)^-8*(7/2)^-2=(2/7)^x   Now, (7/2)^8*(2/7)^2=(2/7)^x   on solving,   (7/2)^6=(2/7)^x   (2/7)^-6=(2/7)^x   Thus, x=-6.   ANSWER:-6
Answer: B
Which of the following numbers does NOT have a divisor greater than 1 that is the square of an integer?	Choose the correct choice
A) 82	B) 27	C) 64	D) 48	E) 50

Solution: Prime Factorization   82=41*2 We got our candidate. No perfect squares here.   27= 3*3*3= 3^2*3. Includes a perfect square of 9.   64=8^2. Is a perfect square.   48=2*2*2*2*3=4^2*3. Includes a perfect square of 16.   50= 5*5*2=5^2*2. Includes a perfect square of 25.   All but 82 have perfect squares in them as a factor.   82=41*2 No perfect squares here.   27= 3*3*3= 3^2*3. Perfect square of 9.   64=8^2. Perfect square.   48=2*2*2*2*3=4^2*3. Perfect square of 16.   50= 5*5*2=5^2*2. Perfect square of 25.
Answer: A
A committee that includes 9 members is about to be divided into 3 subcommittees with 3 members each. On what percent of the possible subcommittees that Michael is a member of is Annie also a member? Choose the correct choice from the following.
A) 10%	B) 20%	C) 25%	D) 40%	E) 50%

Solution: Michael is a member of one of the subcommittees.   P(Annie is on the same subcommittee) = 2/8 = 25%.   The answer is 25%.
Answer: C
The radius of a circular wheel is 1.75 m, how many revolutions will it make in traveling 1 km? Select: A) 1000 B) 1988 C) 1998 D) 2789 E) 2677

Solution: 2 * 22/7 * 1.75 * x   = 11000   x = 1000   1000nswer: 1000
Answer: A
Fresh grapes contain 90% by weight while dried grapes contain 20% water by weight. What is the weight of dry grapes available from 10 kg of fresh grapes?  Choose the correct choice from the following choices
A) 2 kg  B) 2.4 kg  C) 2.5 kg  D) 1.250 kg  E) none of these

Solution: The weight of non-water in 10 kg of fresh grapes (which is 100-90= 
100-90 = 10
10% of whole weight) will be the same as the weight of non-water in x kg of dried grapes (which is 100-20= 
100-20 = 80
80% of whole weight), so 10âˆ—0.1=xâˆ—0.8--> x=1.25   Answer: 1.250 kg
Answer: D
he population of a city is 140,000. If it increases at the rate of 6% per annum, then what will be its population 2 years hence?	Choose one:
A) 1797787	B) 1597723	C) 159776	D) 159728	E) 157304

Solution: Population after n years = P [1 + (R/100)]2   Population after 2 years = 140000 * [1 + 6/100]2 = (160000 x 53/50 x 53/50) = 157304   ANSW157304R: 157304
Answer: E
The sum of four consecutive odd numbers is equal to the sum of 3 consecutive even numbers. Given that the middle term of the even numbers is greater than 101 and lesser than 212, how many such sequences can be formed?  Choose the correct choice from the following options:	A) 27	B) 17	C) 25	D) 33	E) 50

Solution: Four consecutive odd numbers: k-2, k, k+2, k+4   Three consecutive even numbers: n-2, n, n+2   k-2+k+k+2+k+4=n-2+n+n+2   4k+4=3n   4(k+1)=3n   k+1=(3/4)n   k=(3/4)n-1   All n's that's divisible by 4 will have an integral k. So, we need to find out how many such n's are available within given range:   We know,   101<n<212   104<=n<=208   Count=(208-104)/4+1=104/4+1=26+1= 
26+1 = 27
27   27ns: 27.
Answer: A
The average monthly salary of laborers and supervisors in a factory is Rs.1250 per month; where as the average monthly salary of 6 supervisors is Rs.2450. If the average monthly salary of the laborers is Rs.950 find the number of laborers?	Choose the correct choice
A) 11 B) 42 C) 77 D) 88 E) 12

Solution: 5x 6x 2x   50 25 100   250x + 150x + 200x = 4200   600x = 4200   x = 7 => 6x = 42   Answer:42
Answer: B
The Smiley Pie Eating team won 30% of the first contests they entered. An amazingly winning streak increased their average to 50%. How many consecutive contests must they have won to have achieved this average?	Choose the correct answer.
A) 30
B) 20
C) 10
D) 25
E) 35

Solution: Explanation: Let's set up an equation to find the solution. Total number of contest won to start was 30% of 75 = 22.5. Then, an amazing winning streak increases the percentage to 50%. Let x represent the unknown number of consecutive winning contests. Therefore, the total number of contests entered is (75+x). The total contests won is (22.5+x). With a 50% increase in the total contests won, we end up with a solution equation of 50% * (75+x)+22.5+x. Next, let's get rid of the percent sign and rewrite, then solve the equation. 50/100 * (75+x)=22.5+x   1/2 * (75+x)=22.5+x   2[ 1/2 * (75+x)]=2(22.5+x)   1 * (75+x)=45+2x   75+x=45+2x   (75-45)+x=(45-45)+2x   30+x=2x   (30+x =2x)/x   30=x   30nswer: 30
Answer: A
A teacher grades students’ tests by subtracting twice the number of incorrect responses from the number of correct responses. If Student A answers each of the 100 questions on her test and receives a score of 73, how many questions did Student A answer correctly?  Answers:
A) 55
B) 60
C) 73
D) 82
E) 91

Solution: let the number of correct responses be x   then the number of incorrect responses =100-x   according to question   x-2(100-x)=73 (subtracting twice of incorrect from correct)   3x=273   x=91   ANSW91R:91
Answer: E
There are 4 people of different heights standing in order of increasing height. The difference is 2 inches between the first person and the second person, and also between the second person and the third person. The difference between the third person and the fourth person is 6 inches and the average height is 75. How tall is the fourth person?
Answers
A) 73 B) 75 C) 77 D) 79 E) 81

Solution: Let x be the height of the first person.   Then the heights are x, x+2, x+4, and x+10.   4x+16 = 4(75) = 300   x = 71 and the fourth person has a height of 71+10= 
71+10 = 81
81 inches   The answer is 81.
Answer: E
If a boat goes 7 km upstream in 42 minutes and the speed of the stream is 3 kmph, then the speed of the boat in still water is
Choose the correct choice from the following options.
A) 4.2 Km /hr B) 9 Km /hr C) 13 Km /hr D) 21 Km /hr E) None

Solution: Solution   Rate upstream	= (7/42x60)kmph   = 10 kmph.   Speed upstream	= 3 kmph.   Let speed in still water be x km/hr. Then,   speed upstream = (x - 3) Km/hr.   ∴ x - 3 = 10 or   ‹=›x = 13 Km/hr   Answer 13 Km /hr
Answer: C
What is the diffference between the place value of 2 in the numeral 7229?
Choose the correct answer.
A) 150  B) 160  C) 180  D) 190  E) 200

Solution: Option '180'    200 - 20= 
 200 - 20 = 180
180
Answer: C
A boy wants to go abroad by boat and return by flight. He has a choice of 4 different boat to go and 5 flight to return. In how many ways, can the boy perform his journey?  Choose the correct answer.
A) 20
B) 40
C) 45
D) 60
E) 70

Solution: Ans.(A)   Sol. Number of choices to go by ship = 4 Number of choices to return by airline = 5 From, fundamental principle, total number of ways of performing the journey = 4 x 5 = 20 ways
Answer: A
If each digit in the set of A = {1,2,3,4,5,6,7} is exactly used once, in how many ways can the digits be arranged such that the 2 and 5 are not adjacent?	Choose the correct choice:
A) 7!	B) 5*6!	C) 7! - 6!	D) 7! - 2!	E) 7! / 2!

Solution: The answer should be the (total arrangements) - (arrangements when 2 and 5 are adjacent).   The number of ways to arrange 7 units is 7!   If we think of 2 and 5 as one single unit, the number of arrangements is 6!   Note that 2 and 5 can have two arrangements, so we multiply by 2 to get 2*6!   The total number of valid arrangements is 7! - 2*6! = 7*6! - 2*6! = 5*6!   The answer is 5*6!.
Answer: B
In a division sum, the quotient is 36, the divisor 85 and the remainder 26, find the dividend? Choose the correct option
A) 3066  B) 3586  C) 3086  D) 3968  E) 3286

Solution: Explanation:   36 * 85 + 26= 
36 * 85 + 26 = 3_086
3086   Answer : 3086
Answer: C
An airplane flies against the wind from A to B in 8 hours. The same airplane returns from B to A, in the same direction as the wind, in 7 hours. Find the ratio of the speed of the airplane (in still air) to the speed of the wind. Choose the correct choice from the following
A) 15  B) 25  C) 35  D) 45  E) 55

Solution: Let x = speed of airplane in still air, y = speed of wind and D the distance between A and B. Find the ratio x / y   15gainst the wind: D = 8(x - y), with the wind: D = 7(x + y)   8x - 8y = 7x + 7y, hence x / y = 15   correct answer is 15) 15
Answer: A
The area of a square land is A square feet and the perimeter is p feet. If 5A=10p+45, what is the perimeter of the land, in feet?	Choose the correct choice from the following.
A) 18	B) 56	C) 40	D) 36	E) 64

Solution: You can also solve this via using the given numbers in the answer choices!   Of course you need to be aware of the basic properties as outlined by the other posts above (a = x^2 and p = 4x)   Starting with B you will notice that x=14 is way too big for your area (14^2) and will not satisfy: 5A=10p+45 or A=2p+9   --> Eliminate B and E   Now pick 36 (its either too big, then its A, or too small then you know its C or it is B itsself)   And picking 36 indeed solves the problem! (36/4 --> 9; a= 9^2 = 81 and 81=2x36+9)
Answer: D
If 2 tic equals 3 tacs and 2 tacs equal 7 tocs, what is the ratio of one tic to one toc?
Choose the most appropriate option:
A) 15/2  B) 6/5  C) 21/4  D) 3/10  E) 1/15

Solution: 2Tic=3*Tac and 2*Tac=7*Toc;   4*Tic=6*Tac and 6*Tac=21*Toc --> 4*Tic=21*Toc --> Tic/Toc=21/4.   Answer: 21/4.
Answer: C
A train moves at average speed of 60kmph reaches its destination on time.what its average speed becomes 50kmph , then it reaches its destination 15 late. find the length of the journey?
Choose the correct option:
A) 4.86km	B) 2.5km	C) 6.86km	D) 5.867km	E) 3.25km

Solution: Difference between timings=15 min=1/4hr   let the length of the journey be x km.   then x/50-x/60=1/4   x/10=1/4   x=2.5km   Answer (2.5km)
Answer: B
Find the numbers which are in the ratio 3 : 2 : 4 such that the sum of the first and the second added to the difference of the third and the second is 21 ?  Choose the correct choice from the following answers:
A) 3,3,3  B) 4,4,3  C) 4,5,3  D) 9, 6, 12  E) 2,4,4

Solution: Let the numbers be a, b and c.   Given that a, b and c are in the ratio 3 : 2 : 4.   let, a = 3x, b = 2x and c = 4x   Given, (a+b) + (c - b) = 21   = > a + b + c - b = 21 = > a + c = 21   = > 3x + 4x = 21 = >7x = 21 = > x = 3   a , b , c are 3x, 2x, 4x.   a, b, c are 9 , 6 , 12.   Answer:9, 6, 12
Answer: D
In each series, look for the degree and direction of change between the numbers. In other words, do the numbers increase or decrease, and by how much
Look at this series: 80, 10, 70, 15, 60, ... What number should come next?
Pick:
A) 30
B) 40
C) 20
D) 50
E) 60

Solution: C   20   This is an alternating addition and subtraction series. In the first pattern, 10 is subtracted from each number to arrive at the next. In the second, 5 is added to each number to arrive at the next.
Answer: C