MU-NLPC/Calc-aqua_rat huggingface dataset:
Anand starts from a point P towards point Q, where PQ = 80 km. After 1 hour, Ram starts from P and catches up with Anand after 2 more hours. After meeting they continue to travel towards Q. On reaching Q, Ram reverses his direction and meets Anand 6 hours after the first meeting. Find Anand's speed. Choose the correct choice from the following answers: A) (45/7) kmph B) (160/21) kmph C) (40/7) kmph D) (30/7) kmph E) (65/7) kmph

Solution: Let the first meeting point be at a distance of x km from P, the remaining distance until Q would be (80-x) km   Anand traveled this x kms in 3 hours, making his speed x/3 kmph   Ram traveled the same x kms in 2 hours, making his speed x/2 kmph   So, in 6 hours:   Anand will cover=6x/3=2x km   Ram will cover6 /3= 
6 /3 = 2
2x km   Ram will cover=6x/2=3x km   And between their first meeting point and second, they both together covered a distance of 2(90-x) km.   2x+3x6 /2= 
6 /2 = 3
3x km   And between their first meeting point and second, they both together covered a distance of 2(90-x) km.   2x+3x=2(80-x)   5x=160-2x   7x=160   x=160/7 km   Anand's speed=x/3=160/(3*7)=160/21 kmph   Ans:(160/21) kmph
Answer: B
The sum of 5 different positive 2-digit integers is 130. What is the highest possible value of the largest of these integers? Choose the correct choice from the following
A) 88	B) 84	C) 78	D) 74	E) 68

Solution: sum of 5 different 2 digit integers=130   to find out the largest number, we need to make other 4 numbers to the smallest as possible.   smallest 2 digit number is 10   =>10+11+12+13+n=130   =>n=130-46= 
130-46 = 84
84   Answer is 84
Answer: B
For any triangle T in the xy–coordinate plan, the center of T is defined to be the point whose x–coordinate is the average (arithmetic mean) of the x–coordinates of the vertices of T and whose y–coordinate is the average of the y–coordinates of the vertices of T. If a certain triangle has vertices at the points (0,0) and (9,3) and center at the point (4,3), what are the coordinates of the remaining vertex?  Choose the correct answer:  A) (3,4)  B) (3,9)  C) (4,9)  D) (6,4)  E) (3,6)

Solution: Let (a,b) be the remaining vertex.   x: 0 + 9 + a = 3*4. Then a = 3.   y: 0 + 3 + b = 3*3. Then b = 6.   The answer is (3,6).
Answer: E
What could be the maximum value of Q in the following equation?
5P9 + 3R7 + 2Q8 = 1114	Options
A) 5
B) 6
C) 7
D) 8
E) 9

Solution: 5 P 9   3 R 7   2 Q 8 +   ———-   11 1 4   ———-   =>2+P+Q+R=11   so at max Q, P=R=0,   therefore Q=11-2= 
11-2 = 9
9.   ANSW9R:9
Answer: E
In a local school district, the high school and middle school each received r dollars toward funding for the student arts program. The high school enrolled 150 students and the middle school enrolled 75 students. Later, the middle school transferred s dollars to the high school so that they would have received the same funding per student. Which of the following is equivalent to s?	Choose one: A) r/8 B) r/5 C) r/2 D) r/3 E) r/9

Solution: Total per head = 2r/225   After s transfer both schools have total for head.   So at High School it will be:   r+s = (150)* (2r/225) = 12r/9=4r/3   i.e. s = 4r/3 - r/1 =4r-3r/3=r/3   Answer :r/3
Answer: D
A chemical supply company has 60 liters of a 25% HNO3 solution. How many liters of pure undiluted HNO3 must the chemists add so that the resultant solution is a 50% solution? Choose the correct answer
A) 12 B) 15 C) 20 D) 24 E) 30

Solution: 60 liters of a 25% HNO3 solution means HNO3 = 15 liters in 60 liters of the solution.   Now, let x be the pure HNO3 added.   As per question,   15 + x = 50% of (60 + x)   or x =30. Hence, 30
Answer: E
The speed at which a man can row a boat in still water is 15 kmph. If he rows downstream, where the speed of current is 3 kmph, what time will he take to cover 60 metres?
Choose the correct choice from the following answers:  A) 65 seconds  B) 14 seconds  C) 14 seconds  D) 12 seconds  E) 12 seconds

Solution: Speed of the boat downstream   = 15 + 3= 
15 + 3 = 18
18 kmph= 18 * 5/18= 
18 * 5/18 = 5
5 m/s   Hence time taken to cover 60 m= 60/5= 
60/5 = 12
12 seconds.   Answer: 12 seconds
Answer: D
A 4-letter code word consists of letters X, Y, and Z. If the code includes all the three letters, how many such codes are possible?	Choose the correct choice from the following answers.
A) 36 B) 72 C) 48 D) 24 E) 18

Solution: Note that the correct answer to this question is 36, not 72.   X-XYZ can be arranged in 4!/2!=12 ways;   Y-XYZ can be arranged in 4!/2!=12 ways;   Z-XYZ can be arranged in 4!/2!=12 ways;   Total:  12+12+12= 
 12+12+12 = 36
36.   36nswer: 36.
Answer: A
If y exceeds x by 22%, then x is less than y by? Pick one
A) 18 2/8%  B) 18 8/3%  C) 18 2/61%  D) 76 2/3%  E) 17 2/3%

Solution: X=100	y=122   122------22   100-------? => 18 2/61%   Answer:18 2/61%
Answer: C
Two persons starting from the same place walk at a rate of 5kmph and 5.5kmph respectively. What time will they take to be 12.5km apart, if they walk in the same direction? Select:
A) 17 hrs  B) 22 hrs  C) 25 hrs  D) 12 hrs  E) 14 hrs

Solution: The relative speed of the boys = 5.5kmph â€“ 5kmph   = 0.5 kmph   Distance between them is 12.5 km   Time= 12.5km / 0.5 kmph = 25 hrs   Answer : 25 hrs.
Answer: C
If n is a positive integer, then n(n-1)(n-2) is +ve even	Choose the correct choice from the following options.
A) odd whenever n is odd	B) divisible by 3 only when n is odd	C) divisible by 4 whenever n is even	D) even only when n is odd	E) even only when n is even

Solution: n*(n-1)*(n-2)= +ve even integer divisible by 4 ( e.g 6,7&8)   divisible by 4 whenever n is even
Answer: C
In a friendship gang Andrew has 8 gang, in how many ways can he invite one or more of the gang to his house?  Choose the correct choice from the following
A) 245	B) 255	C) 260	D) 267	E) 459

Solution: Andrew can select one or more than one of his 8 gang.   => Required number of ways = 28 – 1= 255.   255
Answer: B
What sum of money put at C.I amounts in 2 years to Rs.8820 and in 3 years to Rs.9261?
Choose the correct choice from the following answers:	A) Rs.8000	B) Rs.8400	C) Rs.7500	D) Rs.7800	E) None

Solution: 8820 ---- 441   100 ---- ? => 5%   x *105/100 * 105/100 = 8820   x*1.1025=8820   x=8820/1.1025= 
8820/1.1025 = 8_000
> 8000   Rs.8000NSWER:Rs.8000
Answer: A
Find the sum of prime numbers lying between 60 and 72? Select the correct option
A) 198	B) 201	C) 199	D) 272	E) None

Solution: Solution   Required sum	= 61 + 67 + 71)   = 199.   Answer 199
Answer: C
Workers decided to raise Rs.3lacs by equal contribution from each. Had they contributed Rs.50 eachextra, the contribution would have been Rs.3.25lacs. How many workers were they?
Choose the correct choice from the following answers:
A) 400
B) 600
C) 500
D) 700
E) 800

Solution: N * 50 = (325000 - 300000)= 
(325000 - 300000) = 25_000
25000   N= 25000 / 50= 
25000 / 50 = 500
500   500
Answer: C
What is the greatest power that 7 can be raised to so that the resulting number is a factor of 21!? Choose the most appropriate option
A) 2	B) 3	C) 4	D) 5	E) 6

Solution: the number of 7s in 21!= 21/7=3..   ans 3
Answer: B
In one hour, a boat goes 11 km/hr along the stream and 5 km/hr against the stream. The speed of the boat in still water (in km/hr) is:	Choose the correct choice from the following options:
A) 2kmph
B) 3kmph
C) 8kmph
D) 9kmph
E) 7kmph

Solution: Speed in still water = (11+5)/2= 
(11+5)/2 = 8
8 kmph   Ans- 8kmph
Answer: C
A, B, C hired a car for Rs. 520 and used it for 7,8 and 11 hours respectively. Hire charges paid by B were :	Choose the correct choice from the following choices.
A) 160 B) 180 C) 220 D) 225 E) None

Solution: Sol.   A : B : C = 7 : 8 : 11.   Hire charges paid by B = Rs. [520 * 8/26] = Rs.160   160nswer 160
Answer: A
If [B] denotes the least integer greater than or equal to B and [B] = 0, which of the following statements must be true?  Select
A) B = 0  B) 0 <= B < 1  C) 0 < B <= 1  D) -1 < B <= 0  E) -1 <= B < 0

Solution: The answer for this is 0 < = B < = 1   However it is not available in the options. The match to the above is-1 < B <= 0   Answer = -1 < B <= 0
Answer: D
The average of non-zero number and its square is 5 times the number. The number is:  Choose the most appropriate option.
A) 9
B) 7
C) 8
D) 5
E) 3

Solution: Let the number be x. Then,   (x + x2)/2 = 5x => x2 - 9x = 0   => x(x - 9) = 0   => x = 0 or x = 9   So, the number is 9.   9nswer: 9
Answer: A
Pipe A can fill a tank in 6 hours. Due to a leak at the bottom, it takes 9 hours for the pipe A to fill the tank. In what time can the leak alone empty the full tank?
Choose the correct choice from the following options
A) 67  B) 88  C) 18  D) 26  E) 12

Solution: Let the leak can empty the full tank in x hours 1/6 - 1/x = 1/9   => 1/x = 1/6 - 1/9 = (3 - 2)/18 = 1/18   => x = 18. Answer:18
Answer: C
If 7 parallel lines in a plane is intersected by a family of another 8 parallel lines, how many parallelograms are there in the network thus formed?
Choose the correct choice from the following answers.
A) 588
B) 263
C) 120
D) 160
E) 1260

Solution: parallelogram can formed by 2 horizontal and 2 vertical lines   for horizontal 7c2   for vertical 8c2   total parallelogram is 7 c2*8c2=21*28= 
21*28 = 588
588   588NSWER:588
Answer: A
The least number which is a perfect square and is divisible by each of the numbers 16,20, and 24, is :
Choose the correct choice from the following choices.
A) 1600 B) 3600 C) 6400 D) 11400 E) None of these

Solution: Solution   The least number divisible by 16, 20, 24   = L.C.M. of 16, 20, 24 = 240 = 2 × 2 × 2 × 2 × 3 × 5.   To make it a perfect square it must be multiplied by 3 × 5.   ∴ Required number = 240 × 3 × 5 = 3600. Answer 3600
Answer: B
In 2triangle, the ratio of the areas is 4:3 and that of their heights is 3:4. Find the ratio of their bases? Options
A) 10:8
B) 11:8
C) 16:9
D) 17:19
E) 17:10

Solution: Given a1/a2 =4/3, h1/h2=3/4   also, we know that   a1/a2=(1/2×b1×h1)/(1/2×b2×h2)   on substituting in above equation, we get   b1/b2= 16/9   therefore b1:b2= 16:9   16:9
Answer: C
My age is two year more than twice than of Ram. If I am 34 years old, how old is Ram?	Answers:  A) 18  B) 14  C) 16  D) 20  E) 12

Solution: myage = 2 + 2*Ram   34 = 2 + 2*Ram   2(Ram) = 32   Ram = 16   ANSWER:16
Answer: C
The juice stall at the circus stocked just 2 brands of orange juice tetra packs. Brand A costs $1 per pack and brand B costs $1.5 per pack. Last week , brand A contributed to r% of stall’s revenue and accounted for s% of sales of juice tetra packs. Which of the following expresses r in terms of s?
Choose the correct choice from the following answers:
A) 100s/(150 – s)
B) 200s/(250-s)
C) 200s/(300-s)
D) 250s/(400-s)
E) 300s/(500-s)

Solution: 1. Let the number of units sold be 100. Then n units of A are sold and (100-n) units of B are sold.   Total revenue= Revenue due to A + Revenue due to B   = (No.of units of A sold * Cost/unit of A) + (No.of units of B sold * cost/unit of B)   = s *1 + (100-s) *1.5   = s + (150-1.5s) --- (1)   2. But we know, revenue due to A = r%. of the total revenue --- (2)   3. To express r in terms of s we need to relate (1) and (2)   4. r% = s / ( s + (150-1.5s))   or r= 100s / 150-0.5s = 200s/(300-s)   200s/(300-s)
Answer: C
In an animal behavior experiment, 50 tagged white pigeons and 300 tagged gray pigeons were released from a laboratory. Within one week, 88 percent of the white pigeons and 80.5 percent of the gray pigeons had returned to the laboratory. What percent of the total number of pigeons returned to the laboratory?	Choose one
A) 80.5	B) 82	C) 81.75	D) 85	E) 86.5

Solution: Weighted mix method is best here....   Ratio is 1:6 for 88:80.5...   So the answer required = 80.5+ (88-80.5)*1/6=80.5+7.5*1/6   80.5+1.75=81.75   81.75
Answer: C
The product of all the prime numbers less than 15 is closest to which of the following powers of 10?	Pick:
A) 10^2 B) 10^4 C) 10^7 D) 10^6 E) 10^5

Solution: Quickly approximate   2, 3, 5, 7, 11,13   3*10^4   10^2
Answer: A
What is the difference between the compound interests on Rs. 5000 for 1 years at 4% per annum compounded yearly and half-yearly?  Choose the most appropriate option:	A) Rs. 2.04	B) Rs. 3.06	C) Rs. 4.80	D) Rs. 6.30	E) Rs. 8.30

Solution: As per formula it should be,   C.I. when interest = 5304-5000= 
5304-5000 = 304
304   compounded yearly   C.I. when interest is= 5306.04-5000= 
5306.04-5000 = 306.04
306.04   compounded half-yearly   Difference= Rs. (306.04 - 304) = Rs. 2.04   answer :Rs. 2.04
Answer: A
What is the smallest number W which when increased by 5 is completely divisible by 8, 11 and 24?
Choose the correct answer.
A) 264
B) 259
C) 269
D) 270
E) 282

Solution: This question includes a number of great Number Property shortcuts that you can take advantage of:   1) The question asks for the SMALLEST number that, when increased by 5 is divisible by 8, 11 and 24. Since the answers are numbers, we can TEST THE ANSWERS.   2) Any number that is divisible by 24 is ALSO divisible by 8, so we really just need to consider the 11 and the 24.   3) To be divisible by 24, the end number MUST be EVEN. Since we're adding 5 to get to that end number, the starting number MUST be ODD.   The last shortcut allows us to eliminate Answers A, D and E. Between Answers B and C, TESTING B first will prove that, when increased by 5, the end sum is divisible by both 11 and 24.   Final Answer:   259
Answer: B
How long does a train 110 m long running at the speed of 72 km/hr takes to cross a bridge 142 m length?	Choose the correct choice from the following answers:
A) 82.1 sec. B) 12.6 sec C) 19.1 sec. D) 17.1 sec. E) 42.1 sec.

Solution: Speed = 72 * 5/18= 
72 * 5/18 = 20
20 m/sec   Total distance covered= 110 + 142= 
110 + 142 = 252
252 m.   Required time= 252/20= 
252/20 = 63/5 = around 12.6
12.6 sec.   Answer: 12.6 sec
Answer: B
The sum of three consecutive odd natural numbers, each divisible by 3 is 66. What is the largest among them? Choices:	A) 21	B) 24	C) 25	D) 36	E) 57

Solution: Let the 3 consecutive odd numbers each divisible by 3 be X, X+3, X+6   Given, X + X+3 + X+6 = 66   3X = 57   X = 19   The numbers are 19, 22, 25   Therefore the largest number is 25   Answer 25.
Answer: C
Find the number of ways of arranging the letters of the word "MATERIAL" such that all the vowels in the word are to come together?  Choose the correct choice from the following answers:  A) 2207 ways  B) 1440 ways  C) 1220 ways  D) 2810 ways  E) 2760 ways

Solution: Explanation:   In the word, "MATERIAL" there are three vowels A, I, E.   If all the vowels are together, the arrangement is MTRL'AAEI'.   Consider AAEI as one unit. The arrangement is as follows.   M T R L A A E I   The above 5 items can be arranged in 5! ways and AAEI can be arranged among themselves in 4!/2! ways.   Number of required ways of arranging the above letters = 5! * 4!/2!   = (120 * 24)/2= 
(120 * 24)/2 = 1_440
1440 ways.   Answer: 1440 ways
Answer: B
A bike covers a certain distance at the speed of 16km/h in 2 hrs. If the bike was to cover the same distance in approximately 4 hrs, at what approximate speed should the bike travel? Choose the most appropriate option: A) 8 km/h B) 9 km/h C) 7 km/h D) 6 km/h E) 10 km/h

Solution: Ans.(A)   Sol. Total distance = 16 × 2 = 32 km   Now speed = 32/4= 
32/4 = 8
8 km/h
Answer: A
A snooker tournament charges $40.00 for VIP seats and $15.00 for general admission (“regular” seats). On a certain night, a total of 320 tickets were sold, for a total cost of $7,500. How many fewer tickets were sold that night for VIP seats than for general admission seats?	Choose the correct choice.
A) 212
B) 200
C) 220
D) 230
E) 240

Solution: let no of sits in vip enclosure is x then x*40 +15( 320-x) =7500 or 25x = 7500 -4800 , x = 2700/25= 
2700/25 = 108
108   vip=108 general 212   212
Answer: A
Mariah has decided to hire three workers. To determine whom she will hire, she has selected a group of 15 candidates. She plans to have one working interview with 3 of the 15 candidates every day to see how well they work together. How many days will it take her to have working interviews with all the different combinations of job candidates?	Pick one:
A) 720	B) 120	C) 300	D) 360	E) 333

Solution: 360.   Answer 360
Answer: D
When divided by 5, x has a remainder of 4 and y has a remainder of 3. Which of the following could be the remainder when x + y is divided by 10? Answers:
A) 6
B) 7
C) 8
D) 9
E) 0

Solution: x = 5k+4 and y = 5j+3   x+y = 5(j+k) + 7   When divided by 10, the remainder is either 7 or 2.   The answer is 7.
Answer: B
Brandon has cans of both diet soda as well as regular soda. The ratio of diet soda to regular soda is 3 to 7. He has 12 more cans of soda than diet. How many cans of diet soda does he have left?  Choose the most appropriate option:
A) 6  B) 7  C) 8  D) 9  E) 10

Solution: Let x equal the cans of diet soda, and y equal the cans of regular soda.   Since we want to solve for x (cans of diet soda), we convert the ratio from 3/7 to 7/3.   So, we know that y = 7/3x.   We also know that y = x + 12.   We can simplify:   x + 12 = 7/3x   To isolate x, we get:   4/3x = 12   And to solve for x, we get:   x = 9   Answer: 9
Answer: D
Two trains, each 100 m long, moving in opposite directions, cross each other in 8 seconds. If one is moving twice as fast the other, then the speed of the faster train is:
Select the correct option.
A) 30 km/hr  B) 45 km/hr  C) 60 km/hr  D) 75 km/hr  E) 65 km/hr

Solution: Let the speed of the slower train be x   and the faster train = 2x   Relative speed = x+2x = 3x   therefore (100+100)/8 = 3x   => x = 25/3   So, Speed of the faster train = 2(25/3) = 50/3 m/s = (50/3*18/5)km/hr = 60km/hr   ANSWER:60 km/hr
Answer: C
The total marks obtained by a student in Mathematics and Physics is 50 and his score in Chemistry is 20 marks more than that in Physics. Find the average marks scored in Mathamatics and Chemistry together.	Answers: A) 15 B) 25 C) 35 D) 45 E) 55

Solution: Let the marks obtained by the student in Mathematics, Physics and Chemistry be M, P and C respectively.   Given , M + C = 50 and C - P = 20 M + C / 2 = [(M + P) + (C - P)] / 2 = (50 + 20) / 2= 
(50 + 20) / 2 = 35
35.   ANSWER:35
Answer: C
What least number must be added to 1056, so that the sum is completely divisible by 23 ? Choose one.
A) 2  B) 4  C) 6  D) 8  E) 10

Solution: 23) 1056 (45   92   ---   136   115   ---   21   ---   Required number = (23 - 21)= 
(23 - 21) = 2
2.   2)
Answer: A
A number is increased by 40% and then decreased by 40%, the final value of the number is ?	Choose the correct choice:
A) decrease by 13%	B) decrease by 12%	C) decrease by 16%	D) decrease by 14%	E) decrease by 15%

Solution: Here, x = 40 and y = - 40   Therefore, the net % change in value   = ( x + y + xy/100)%   = [40 - 40 + (40 * -40)/100]% or - 16%   Since the sign is negative, there is a decrease in value by 16%.   ANSWER: decrease by 16%
Answer: C
Of the people who responded to a market survey, 150 preferred Brand X and the rest preferred Brand Y. If the respondents indicated a preference for Brand X over Brand Y by ratio of 5 to 1, how many people responded to the survey? Choose the most appropriate option:
A) 80	B) 180	C) 240	D) 360	E) 480

Solution: Ratio = 5:1 => 5x respondents preferred Brand X and x preferred Brand Y   Since, no. of respondents who preferred Brand X = 150 => 5x=150 => x=30   Hence Total no. of respondents = 150 + 30= 
150 + 30 = 180
180   Hence 180 is the answer.
Answer: B
A bag consists of 20 marbles, of which 5 are blue, 7 are red, and the remainder are white. If Lisa is to select a marble from the bag at random, what is the probability that the marble will be red or white?	Choices:  A) 3/4  B) 2/4  C) 1/4  D) 1/8  E) 1/16

Solution: bag consists of 20 marbles, of which 5 are blue, 7 are red   remainder are white. So, white = 20 - 5 - 7= 
20 - 5 - 7 = 8
8.   probability that the marble will be red or white= probability that the marble will be red + probability that the marble will be white   probability that the marble will be red or white = 7/20+8/20 = 15/20 = 3/4   Hence, answer will be 3/4.
Answer: A
Exactly 36% of the numbers in set A are even multiples of 3. If 40% of the even integers in set A are not multiples of 3, what percent of the numbers in set A are not even integers?  Select the correct option
A) 76%  B) 60%  C) 50%  D) 40%  E) 24%

Solution: Everything is correct except the red part with a typo: it should be N=0.6A --> even numbers are 60% of A --> 40% of A are not even integers.   Answer: 40%.
Answer: D
A pump can fill a tank with water in 2 hours. Because of a leak, it took 2 hours to fill the tank. The leak can drain all the water of the tank in:	Choose the correct choice from the following
A) 4 hours	B) 7 hours	C) 8 hours	D) 14 hours	E) 15 hours

Solution: Work done by the leak in 1 hour = (1/2 - 3/7) = 1/14   Leak will empty the tank in 14 hrs.   Answer = 14 hours
Answer: D
The side of a rhombus is 26 m and length of one of its diagonals is 20 m. The area of the rhombus is?	Choose the correct choice from the following:  A) 127  B) 297  C) 266  D) 480  E) 435

Solution: 262 – 102 = 242   d1 = 20 d2 = 48   1/2 * 20 * 48= 
1/2 * 20 * 48 = 480
480   Answer: 480
Answer: D
Given that p is a positive even integer with a positive units digit, if the units digit of p^3 minus the units digit of p^2 is equal to 0, what is the units digit of p + 5?	Choose the correct choice from the following options
A) 7 B) 8 C) 9 D) 10 E) 11

Solution: p is a positive even integer with a positive units digit--> the units digit of p can be 2, 4, 6, or 8 -->   In order the units digit of p^3 - p^2 to be 0, the units digit of p^3 and p^2 must be the same. Thus the units digit of p can be 0, 1, 5 or 6.   Intersection of values is 6, thus the units digit of p + 5 is  6 + 5= 
 6 + 5 = 11
11.   Answer: 11.
Answer: E
Walking with 4/5 of my usual speed, I arrive at the bus stop 6 minutes later than normal. How many minutes does it take to walk to the bus stop at my usual speed?	Choose one
A) 20 min  B) 22 min  C) 15 min  D) 18 min  E) 24 min

Solution: Let t = usual time = distance / usual speed   t + 6 = distance / (4* usual speed/5) = (5 * distance) / (4 * usual speed) = 5t/4   t = 24   The answer is 24 min.
Answer: E
A reduction of 20% in the price of salt enables a lady to obtain 10kgs more for Rs.100, find the original price per kg? Choices.
A) Rs.2.5  B) Rs.2.7  C) Rs.2.6  D) Rs.7.5  E) Rs.3.5

Solution: 100*(20/100)= 
100*(20/100) = 20
20 --- 10   ? --- 1=> Rs.2   100 --- 80   ? --- 2 => Rs.2.5   Rs.2.5nswer:Rs.2.5
Answer: A
If Teena is driving at 55 miles per hour and is currently 7.5 miles behind Joe, who is driving at 40 miles per hour in the same direction then in how many minutes will Teena be 30 miles ahead of Joe? Choose the correct choice from the following answers:	A) 150	B) 60	C) 75	D) 90	E) 105

Solution: This type of questions should be solved without any complex calculations as these questions become imperative in gaining that extra 30-40 seconds for a difficult one.   Teena covers 55 miles in 60 mins.   Joe covers 40 miles in 60 mins   So teena gains 15 miles every 60 mins   Teena need to cover 7.5 +30 miles.   Teena can cover 7.5 miles in 30 mins   Teena will cover 30 miles in 120 mins   So answer 30+120= 
30+120 = 150
150 mins. (150NSWER 150)
Answer: A
What is the square root of 81?
Choose the most appropriate option:	A) 2	B) 8	C) 12	D) 9	E) 16

Solution: 9X9 = 81   ANSWER 9
Answer: D
Bruce and Anne can clean their house in 4 hours working together at their respective constant rates. If Anne’s speed were doubled, they could clean their house in 3 hours working at their respective rates. How many D hours does it currently take Anne to clean the house on her own?
Answers:
A) 6
B) 7
C) 8
D) 12
E) 14

Solution: Lets suppose Anne and Bruce take A and B hrs working separately   So in 1 hour they can together finish 1/A + 1/B portion of the work which equals 1/4 (As the work is completed in 4 hours)   After anne doubles her rate of work the portion completed by the both is 1/A +2/B which is equal to 1/3 (As the work is completed in 12=3 hours)   Solving these 2 equations we can find B as 12   So, 12
Answer: D