MU-NLPC/Calc-aqua_rat huggingface dataset:
If xy not equal 0 and x^2*y^2 -xy =30, which of the following could be y in terms of x?
I. 1/2x
II. -6/x
III. 5/x	Choose the correct choice from the following answers
A) I &II  B) II  C) II and III  D) IV  E) III

Solution: x2y2 - xy = 30   x2y2-xy-30 = 0   (xy-5)(xy+6)=0   xy = 5 or xy=-6   y = 5/x or y = -6/x   II and III only   II and III
Answer: C
An amount at compound interest sums to Rs.17640/- in 2 years and to Rs.22932/- in 3 years at the same rate of interest. Find the rate percentage? Select
A) 5%
B) 7%
C) 9%
D) 11%
E) 30%

Solution: Explanation:   The difference of two successive amounts must be the simple interest in 1 year on the lower amount of money.   S.I = 22932/- - 17640/- = Rs. 5292/-   Rate of interest = (5292/22932) × (100/1) => 30%   Answer: Option 30%
Answer: E
A goods train runs at a speed of 72 kmph and crosses a 290 m long platform in 26 seconds.What is the length of the goods train? Pick one
A) 230 m  B) 240 m  C) 260 m  D) 270 m  E) 250 m

Solution: s=290+x/t   72*5/18=290+x/26   x=230   230 mNSWER:230 m
Answer: A
How many numbers are there between 100 and 1000 such that at least one of their digits is 6?  Choose the most appropriate option
A) 648 B) 252 C) 900 D) 1000 E) None of these

Solution: Explanation :   numbers between 100 and 1000:=900numbers between 100 and 1000 which do not have digit 6 in any place:=8×9×9=648Unit digit could take any value of the 9 values (0 to 9, except 6)Tens Digit could take any value of the 9 values (0 to 9, except 6)Hundreds digit could take any value of the 8 values (1 to 9, except 6)numbers between 100 and 1000 which have at least one digit as 6:=900−648= 252   Answer : 252
Answer: B
Nancy obtained 66, 75, 52, 68 and 89 marks (out of 100) in American Literature, History, Home Economics, Physical Education and Art. Calculate her average marks ?	Choose the most appropriate option:
A) 50  B) 80  C) 70  D) 60  E) 71

Solution: Explanation:   Average = (66 + 75 + 52 + 68 + 89 )/ 5= 
(66 + 75 + 52 + 68 + 89 )/ 5 = 70
70.   Answer: 70) 70
Answer: C
The jogging track in a sports complex is 726 m in circumference. Suresh and his wife start from the same point and walk in opposite direction at 4.5 km/hr and 3.75 km/hr respectively. They will meet for the first time in:	Answers
A) 5.5 min. B) 6 min. C) 4.9 min. D) 5.28 min. E) 5 min.

Solution: Let both of them meet after T min   4500 m are covered by Suresh in 60 m.   In T min he will cover 4500T/60   Likewise, In T min Suresh's wife will cover 3750T/60   Given,   (4500T/60)+(3750T/60)=726   T = 5.28 minutes   Answer : 5.28 min.
Answer: D
Rs.100 amounts to Rs.320 in 4 years at simple interest. If the interest is increased by 3%, it would amount to how much?  Choose one:  A) 246  B) 650  C) 110  D) 240  E) 360

Solution: (100*4*3)/100= 
(100*4*3)/100 = 12
12   100+ 12= 
100+ 12 = 112
112   Answer: 110
Answer: C
A circular ground whose diameter is 40 metres, has a garden of area 1100m^2around it. What is the wide of the path of the garden ?
Choices:
A) 8.07
B) 7.07
C) 6.07
D) 7.0
E) 8.5

Solution: Req. area = Ï€[(20)2 â€“ (r)2]   = 22â„7 Ã— (400- r^2)[since a2 - b2 = (a + b)(a - b)]   ie)22/7(400-r^2)=1100 , ie) r^2=50, r=7.07m   Answer 7.07
Answer: B
what is rate of interest if principal.amount be 400,simple interest 140 and time 2year. Choose the correct option.
A) 10
B) 17.5
C) 25
D) 12
E) 14.5

Solution: s.i=(p*r*t)/100   140=800r/100   r=140/8= 
140/8 = 35/2 = around 17.5
17.5%   answer 17.5
Answer: B
A prize of $400 is to be distributed among 20 winners, each of whom must be awarded at least $20. If 2/5 of the prize will be distributed to 3/5 of the winners, what is the greatest possible individual award?	Choose the correct choice from the following choices:
A) $100
B) $220
C) $280
D) $300
E) $360

Solution: Total value of the prize =$400   Number of people = 20   2/5 of 400 (=$160) should be distributed among 3/5 of 20 (=12 people ) with each getting $20 each. Remaining money = 400-160= 
400-160 = 240
$240. Now in order to 'maximize' 1 prize, we need to minimise the others and we have been given that each should get $20. Thus, minimising the remaining 7 people (=20-12-1. '-1' to exclude 1 that needs to be maximised) = 7*20= 
7*20 = 140
140.   Thus the maximum award can be= 240-140= 
240-140 = 100
$100, hence $100 is the correct answer.
Answer: A
For an integer n greater than 1, n* denotes the product of all the integers from 1 to n inclusive. How many prime numbers are there between 6*+3 and 6*+6, inclusive ?  Pick:
A) 0
B) 1
C) 2
D) 3
E) 4

Solution: Given that n* denotes the product of all the integers from 1 to n, inclusive so, 6* + 3 = 6! + 3 and 6* + 6 = 6! + 6.   Now, notice that we can factor out 3 our of 6! + 3 so it cannot be a prime number, we can factor out 4 our of 6! + 4 so it cannot be a prime number, ... The same way for all numbers between 6! + 3 and 6! +6, inclusive. Which means that there are no primes in this range.   0nswer: 0.
Answer: A
Two trains, each 120 m long, moving in opposite directions, cross other in 8 sec. If one is moving twice as fast the other, then the speed of the faster train is?
Choose the correct choice from the following
A) 72 km/hr B) 17 km/hr C) 60 km/hr D) 77 km/hr E) 46 km/hr

Solution: Let the speed of the slower train be x m/sec.   Then, speed of the train = 2x m/sec.   Relative speed = ( x + 2x) = 3x m/sec.   (120 + 120)/8 = 3x => x = 10.   So, speed of the faster train = 20 = 20 * 18/5= 
20 * 18/5 = 72
72 km/hr.   72 km/hrnswer:72 km/hr
Answer: A
Three unbiased coins are tossed, what is the probability of geƫng at least 2 tails ? Select:
A) 1/3  B) 1/6  C) 1/2  D) 1/8  E) None of these

Solution: Explanation:   Total cases are = 2*2*2= 
2*2*2 = 8
8, which are as follows   [TTT, HHH, TTH, THT, HTT, THH, HTH, HHT]   Favoured cases are= [TTH, THT, HTT, TTT] = 4   So required probability = 4/8 = 1/2   Answer: 1/2
Answer: C
In a neighborhood having 90 households, 11 did not have either a car or a bike. If 20 households had a both a car and a bike and 44 had a car, how many had bike only?	Choose the correct choice from the following choices: A) 30 B) 35 C) 20 D) 18 E) 10

Solution: {Total}={Car}+{Bike}-{Both}+{Neither} --> 90=44+{Bike}-20+11 --> {Bike}=55 --> # those who have bike only is {Bike}-{Both}=55-20= 
55-20 = 35
35.   Answer: 35.
Answer: B
Find the sum of the local value and absolute value of 4 in 564823 Answers:
A) 4004  B) 8000  C) 16000  D) 12000  E) 18000

Solution: Explanation:   Place value = Local value   Face value = Absolute value   The place value of 4 in 564823 is 4 x 1000 = 4000   The face value of 4 in 564823 is nothing but 4.   => 4000 + 4= 
4000 + 4 = 4_004
4004   4004nswer: Option 4004
Answer: A
A team scored a total of 140 points. If each player on the team scored at least 14 points, then what is the greatest possible number of players on the team? Choices
A) A)6  B) B)7  C) C)8  D) D)9  E) E)10

Solution: 140/14= 
140/14 = 10
10 plus remainder.   The answer is 10.
Answer: E
The length of the bridge, which a train 180 meters long and travelling at 48 km/hr can cross in 70 seconds, is:  Choose the correct choice from the following choices:
A) 245
B) 276
C) 987
D) 168
E) 1981

Solution: Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (130 + X)/30 = 25/2 ==> 2(130 + X) = 750 ==> X = 245 m.   245nswer: 245
Answer: A
When positive integer m is divided by positive integer x, the reminder is 7 and when positive integer n is divided by positive integer y, the reminder is 11. Which of the following Q is a possible value for x + y?
I. 18
II. 19
III. 20	Choose the correct choice:
A) I only	B) II only	C) Q=III only	D) II and III only	E) None

Solution: TIP FOR SUCH QUESTIONS:Make Algebraic Equation in the beginning to understand how to proceed further. Then Start thinking the possible values of variables asked about   i.e.When positive integer m is divided by positive integer x, the reminder is 7can be understood as   m = ax +7which means thevalue of x must be greater than 7as the remainder 7 is possible only when the Divisor is bigger than the Remainder 7   i.e. Min Value of x = 8   AND   i.e.When positive integer n is divided by positive integer y, the reminder is 11can be understood as   n = by +11which means thevalue of y must be greater than 11as the remainder 11 is possible only when the Divisor is bigger than the Remainder 11   i.e. Min Value of y = 12   i.e. Minimum Value of x+y = 8+12= 
8+12 = 20
20   Hence III only can be True   Answer: Option   Q=III only
Answer: C
Two heavily loaded sixteen-wheeler transport trucks are 1025 kilometers apart, sitting at two rest stops on opposite sides of the same highway. Driver A begins heading down the highway driving at an average speed of 90 kilometers per hour. Exactly one hour later, Driver B starts down the highway toward Driver A, maintaining an average speed of 80 kilometers per hour. How many kilometers farther than Driver B, will Driver A have driven when they meet and pass each other on the highway?  Choose the correct choice:
A) 90 B) 130 C) 150 D) 320 E) 145

Solution: I've been reading the website for a while and I'm always keen to see different approaches so I would like to share one that works for me:   Short version:   Truck A travels for an hour.   Distance remaining = 1025-90= 
1025-90 = 935
935k   Ratio of speeds 9:8 -> 935/17= 55   Truck A = 90 + 55*9= 
90 + 55*9 = 585
585   Truck B= 55*8= 
55*8 = 440
440   Delta= 145km   Answer 145
Answer: E
If x < 0 and 0 < y < 1, which of the following has the greatest value L?
Choices:
A) x^2 B) (xy)^2 C) (x/y)^2 D) x^2/y E) x^2*y

Solution: Given, x < 0 and 0 < y < 1   Let, x = -2 and y = 1/2   A. x^2 = (-2)^2 =4   B. (xy)^2 = (-2*1/2)^2 =1   C. (x/y)^2 = {-2/(1/2)}^2 = (-4)^2 =16   D. x^2/y = (-2)^2 / (1/2) = 4*2= 
4*2 = 8
8   E. x^2*y= (-2)^2*(1/2) =2   Answer: option (x/y)^2
Answer: C
The current birth rate per thousand is 52, where as corresponding death rate is 11 per thousand. The net growth rate in terms of population increase in percent is given by? Pick
A) 4.1%  B) 3.2%  C) 3.9%  D) 4%  E) 5.1%

Solution: Net growth on 1000 = 52-11= 
52-11 = 41
41   Net growth on 100= 41*100/1000= 
41*100/1000 = 41/10 = around 4.1
4.1%   4.1%nswer is 4.1%
Answer: A
Huey's Hip Pizza sells two sizes of square pizzas: a small pizza that measures 9 inches on a side and costs $10, and a large pizza that measures 14 inches on a side and costs $20. If two friends go to Huey's with $30 apiece, how many more square inches of pizza can they buy if they pool their money than if they each purchase pizza alone?  Choose the most appropriate option:	A) 5 square inches	B) 10 square inches	C) 15 square inches	D) 25 square inches	E) 34 square inches

Solution: In the first case each can buy one pizza of $10 and one pizza of $20.   In square inches that would be (9*9=81) for the small pizza and (14*14=196) for the large pizza. In total sq inches that would be  (81+196)*2= 
 (81+196)*2 = 554
554 sq inches.   In the second case if they pool their money together they can buy 3 large pizzas. In terms of square inches that would be   3*196= 
  3*196 = 588
588 sq inches.   Hence, the difference is 34 square inches more (588-554).   The correct answer is 34 square inches
Answer: E
There are 6 girls and 6 boys. If they are to be seated in a row, what is the probability that no two boys sit together? Select the correct option.
A) A)2*6!6!/12! B) B)6!5!/12! C) C)6!6!/12! D) D)6!/12! E) E)6!7!/12!

Solution: If girls are alternate, then only no 2 boys can be together.   So among 12 places, boys can be seated in 6 alternate places in 6! ways.   And girls can be seated in the remaining 6 places in 6! ways.   Therefore total number of ways = 6! * 6!   But there could be 2 such arrangements-->   1. When first place is filled by a girl   2. When first place is filled by a boy   Therefore total number of ways = 2*6! * 6!   2*6!6!/12!lso total number of ways to fill 12 places = 12!   Hence probability =2∗6!6!/12!   2*6!6!/12!nswer:2*6!6!/12!
Answer: A
A fill pipe can fill 1/4 of cistern in 16 minutes. In how many minutes, it can fill 3/4 of the cistern?  Choose one:
A) 24min
B) 30min
C) 48min
D) 26min
E) 16min

Solution: Required time = 16*4*3/4= 
16*4*3/4 = 48
48 minutes   Answer is 48min
Answer: C
Find the area of the quadrilateral of one of its diagonals is 20 cm and its off sets 9 cm and 6 cm?	Choose the correct choice from the following answers
A) 188 cm2	B) 150 cm2	C) 168 cm2	D) 198 cm2	E) 987 cm2

Solution: 1/2 * 20(9 + 6)   = 150 cm2   Answer: 150 cm2
Answer: B
Arun purchased 30 kg of wheat at the rate of Rs. 11.50 per kg and 20 kg of wheat at the rate of 14.25 per kg. He mixed the two and sold the mixture. Approximately what price per kg should be sell the mixture to make 30% profit?	Choose the correct option:
A) 66.3
B) 76.3
C) 86.3
D) 16.3
E) 36.3

Solution: Explanation:   C.P. of 50 kg wheat = (30 * 11.50 + 20 * 14.25) = Rs. 630.   S.P. of 50 kg wheat = 130% of Rs. 630 = 130/100 * 630 = Rs. 819.   S.P. per kg = 819/50 = Rs. 16.38 = 16.30.   Answer: 16.3
Answer: D
Calculate the HCF of 16, 108, 220	Choose the correct answer.
A) 3 B) 5 C) 4 D) 1 E) 2

Solution: Explanation:   Lets solve this question by factorization method.   The factors of 16 are: 1, 2, 4, 8, 16   The factors of 108 are: 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108   The factors of 220 are: 1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110, 220   Then the greatest common factor is 4.   Answer: Option 4
Answer: C
Each of the 39 points is placed either inside or on the surface of a perfect sphere. If 72% or fewer of the points touch the surface, what is the maximum number of segments which, if connected from those points to form chords, could be the diameter of the sphere? Choose the correct choice
A) 7
B) 11
C) 13
D) 14
E) 38

Solution: Maximum number of points on the surface is 72%*39 = 28.08 ... or 28 since it has to be an integer   Now note that if two points form a diameter, they cannot be part of any other diameter.   So in the best case we can pair up the points   We have 28 points, so at best we can form 14 pairs (28).   So, answer is (14)
Answer: D
Sum of the digits number is 8 and their product is 12. Find the difference between the digits? Choose the most appropriate option
A) 4 B) 5 C) 3 D) 7 E) 2

Solution: Explanation:   x + y = 8   xy = 12   (x â€“ y)2 = (x + y)2 â€“ 4xy   (x â€“ y)2 = 64 â€“ 48 => (x â€“ y) = 4   4nswer:4
Answer: A
If sequence T is defined for all positive integers n such that t(n +1) = t(n) + n, and t 3 = 14, what is t 25?  Choose the correct option:
A) 101  B) 187  C) 191  D) 201  E) 311

Solution: ok, not sure if this is the best explanation, but here is my way of solving this :   tn +1 = tn + n,   t 3 = 14   so:   t 4 = t 3 + 3   t 5 = t 4 + 4, so we replace t 4 with the previous result : t 5 = (t 3 + 3 ) + 4   ....   so we get   t 25 = t 3 + 3 + 4 + 5 + 6....+ 24   the 3 + 4 + 5 + ... + 24 sequence is equal the sequence 1 + 2 + ... + 24, minus 1 + 2 at the beginning (so, minus 3)   and the 1 + 2 ... + 24 sequence is equal to n*(n+1)/2 with n being 24, so equal to  24 * 25 / 2= 
 24 * 25 / 2 = 300
300   so :   t 20= t 3 + 300 - 3   t 20 = 14 + 300 - 3 = 300 + 11= 
300 + 11 = 311
311, hence answer 311
Answer: E
The length of the bridge, which a train 120 meters long and travelling at 45 km/hr can cross in 30 seconds, is? Choose one
A) 328
B) 279
C) 255
D) 288
E) 211

Solution: Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (120 + X)/30 = 25/2 ==> 2(120 + X) = 750 ==> X = 255 m.Answer: 255
Answer: C
If Aaron is now twice as old as Bailey was 5 years ago, and B is Bailey's current age in years, which of the following represents the sum of Aaron and Bailey's ages 4 years from now? Choose the correct option:
A) 3B
B) 3B-1
C) 3B-21
D) 3B-11
E) 3B-2

Solution: B is Bailey's current age.   Let Aaron's current age be A.   given A = 2(B-5).   four years from now Aaron's age will be = 2(B-5) + 4 = 2B-6   four years from now Bailey's age will be = B+4   Sum of ages of Mason and Gunther's after 4 years = 2B-6+B+4 = 3B-2   Ans : 3B-2
Answer: E
Find the least number which when divided by 20,25,35 and 40 leaves remainders 14,19,29 and 34 respectively.	Answers:
A) 1394
B) 1294
C) 1194
D) 1094
E) None of them

Solution: Here,(20-14) = 6,(25 – 19)=6,(35-29)=6 and   (40-34)= 
  (40-34) = 6
6.   Therefore, Required number= (L.C.M. of 20,25,35,40) – 6 =1394.   1394nswer is 1394.
Answer: A
present ages of sameer and anand are in the ratio of 5:4 respectively. three years hence, the ratio of their ages will become 11:9 respectively . what anand's present age in years	Choose the correct choice from the following answers:
A) 27
B) 24
C) 40
D) 32
E) 35

Solution: sameer and anand be 5x years and 4x years respectively   (5x+3)/(4x+3)=11/9   9(5x+3)= 11(4x+3), 45x+27=44x+33   45x-44x=33-27= 
33-27 = 6
6, therefore anand's present age : 4x=24 years   correct answer(24)
Answer: B
Jo's collection contains US, Indian and British stamps. If the ratio of US to Indian stamps is 5 to 2 and the ratio of Indian to British stamps is 4 to 1, what is the ratio of US to British stamps? Choose the correct choice from the following
A) 5 : 1  B) 10 : 5  C) 15 : 2  D) 20 : 2  E) 25 : 2

Solution: U/I = 5/2   I/B = 4/1   Since I is multiple of both 2 (as per first ratio) and 5 (as per second ratio) so let's assume that I = 10   i.e. Multiplying teh first ratio by 5 and second ration by 2 in each numerator and denominator   then, U : I : B = 20 : 8: 2   i.e. U : B = 20 : 2   Answer: Option 20 : 2
Answer: D
A wooden cube whose edge length is 6 inches is composed of smaller cubes with edge lengths of one inch. The outside surface of the large cube is painted red and then it is split up into its smaller cubes. If one cube is randomly selected from the small cubes, what is the probability that the cube will have at least one red face?	Choose the correct option:
A) 54.9%  B) 58.7%  C) 62.5%  D) 66.3%  E) 70.4%

Solution: There are a total of 6*6*6= 
6*6*6 = 216
216 cubes.   All the exterior cubes will have at least one face painted red.   The interior is formed by   4*4*4= 
  4*4*4 = 64
64 cubes.   The number of cubes with at least one side painted red is  216 - 64= 
 216 - 64 = 152
152 cubes   The probability that a cube has at least one side painted red is 152/216 which is about 70.4%   The answer is 70.4%.
Answer: E
Two twins sisters Sita and Geeta were standing back to back and suddenly they started running in opposite directions for 2 km each. Then they turned left and ran for another 1.5 km.
What is the distance (in kilometers) between the the two twins when they stop?  Choose the most appropriate option:
A) 5	B) 7	C) 9	D) 11	E) 13

Solution: The distance between them is the hypotenuse of a right angle triangle with sides 3 km and 4 km.   hypotenuse = sqrt(3^2 + 4^2) = 5   The answer is 5.
Answer: A
A wheel rotates 10 times every minute and moves 10 cm during each rotation. How many metres does
the wheel move in one hour?  Select the correct option:
A) 6 metre
B) 60 metre
C) 1500 metre
D) 1200 metre
E) 2200 metre

Solution: Expl : Number of times wheel moves in 1 hour = 10 * 60= 
10 * 60 = 600
600   :. Distance moves= (600 *10)= 
(600 *10) = 6_000
6000 cms   In metres= 60 metre   Answer: 60 metre
Answer: B
A person travels equal distances with speeds of 4km/hr, 8km/hr, 12km/hr. and takes a total time of 11 minutes. Find the total distance ?  Choose the correct choice:
A) 1km  B) 500mts  C) 600mts  D) 2km  E) 1200mts

Solution: Let the each distance be x km   total distance = 3x   then total time,   (x/4)+(x/8)+(x/12) = 11/60   x=0.4   total distance = 3*0.4= 
3*0.4 = 1.2
1.2km= 1200meters   correct option is 1200mts
Answer: E
If x > y^3 > z^4, which of the following statements could be true?
I. x>y>z
II. x>z
III.y=z	Choose the correct choice from the following options:  A) III only  B) I,II only  C) II only  D) I only  E) II,III only

Solution: Answer : I,II only
Answer: B
A local restaurant recently renovated its dining space, purchasing new tables and chairs to use in addition to the original tables and chairs. The new tables each seat six customers, while the original tables each seat four customers. Altogether, the restaurant now has 40 tables and is capable of seating 206 customers. How many more new tables than original tables does the restaurant have?
Choices:	A) 6	B) 9	C) 12	D) 15	E) 18

Solution: If all the tables seated 4, the number of customers could be  4*40= 
 4*40 = 160
160.   206-160= 
206-160 = 46
46, so  46/2= 
 46/2 = 23
23 tables must be new tables seating 6 people.   The number of tables seating 4 people is   40-23= 
  40-23 = 17
17.   The number of new tables is  23-17= 
 23-17 = 6
6 more than the number of old tables.   The answer is 6.
Answer: A
what is the angle between the hands of a clock when time is 8:30? Answers
A) 65deg
B) 75deg
C) 45deg
D) 15deg
E) 30deg

Solution: Angle between two hands =   30h - 11/2 m = 30*8 - 30*11/2 = 240 - 165= 
240 - 165 = 75
75deg   ANSWER:75deg
Answer: B
If the price of an article went up by 20%, then by what percent should it be brought down to bring it back to its original price?	Choose the correct option:
A) 16 2/3% B) 20% C) 22 1/3% D) 15% E) None of these

Solution: Let the price of the article be Rs. 100.   20% of 100 = 20.   New price = 100 + 20 = Rs. 120   Required percentage = (120 - 100)/120 * 100   = 20/120 * 100 = 50/3 = 16 2/3%.   16 2/3%NSWER:16 2/3%
Answer: A
In a camp,there is a meal for 120 men or 200 children.If 160 children have taken the meal,how many men will be catered to with the remaining meal ? Choose the correct choice from the following:	A) 20	B) 24	C) 40	D) 50	E) 60

Solution: Solution   There is a metal for 200 children. 160 children have taken the meal.   Remaining meal is to be catered to 40 children.   Now, 200 children = 120 men   40 children =( 120/200x40)men= 24 men. Answer 24
Answer: B
Find the amount on Rs.8000 in 9 months at 20% per annum, if the interest being compounded quarterly?	Answers.
A) Rs.1261	B) Rs.9261	C) Rs.9621	D) Rs.9162	E) Rs.9164

Solution: A = 8000(21/20)3 = 9261   ANSWER:Rs.9261
Answer: B
If the perimeter and diagonal of a rectangle are 14 and 5 cms respectively, find its area. Choose the correct choice from the following answers.
A) 12 cm2 B) 16 cm2 C) 20 cm2 D) 24 cm E) None of these

Solution: In a rectangle,   (Perimeter)2/4=(diagonal)2+2×area   ⇒ (14)2/4=5(2)+2×area   49 = 25 + 2 × area   ∴ 12 cm2rea = 49−25/2=24/2= 
24/2 = 12
12cm2   12 cm2nswer 12 cm2
Answer: A
The length of a rectangular plot is thrice its breadth. If the area of the rectangular plot is 867 sq m, then what is the breadth of the rectangular plot?	Answers:	A) 19 m	B) 17 m	C) 10 m	D) 12 m	E) 18 m

Solution: Answer: Option B   Explanation:   Let the breadth of the plot be b m.   Length of the plot = 3 b m   (3b)(b) = 867   3b2 = 867   b2 = 289 = 172 (b > 0)   b = 17 m.   Answer: Option 17 m
Answer: B
An empty fuel tank is filled with brand Z gasoline. When the tank is half empty, it is filled with brand Y gasoline. When the tank is half empty again, it is filled with brand Z gasoline. When the tank is half empty again, it is filled with brand Y gasoline. At this time, what percent Q of the gasoline in the tank is brand Z?	Choose one:
A) 50%  B) 40%  C) 37.5%  D) 331⁄3%  E) 25%

Solution: Work with fraction of brand Z in the tank.   1st step: brand Z is 1   2nd step: brand Z is 1/2   3rd step: brand Z is (1/2)*(1/2) + 1/2 = 3/4   4th step: brand Z is (1/2)*(3/4) Q= 3/8 = 37.5%   Answer (37.5%)
Answer: C
If a, b are integers and |a-b|=14, which of the following is the smallest possible value of ab? Choose the correct choice from the following:
A) -16
B) 0
C) 16
D) 7
E) -49

Solution: a=7, b=-7. Hence, the answer is -49.
Answer: E
The age of father 4 years ago was four times the age of his son. Five years hence, father's age will be twice that of his son. The ratio of their present ages is:	Options
A) 41 : 17 B) 42 : 17 C) 44 : 19 D) 44 : 17 E) 44 : 21

Solution: Let the ages of father and son 4 years ago be 4x and x years respectively.   Then, (4x + 4) + 5 = 2[(x + 4) + 5]   4x + 9 = 2x + 18   x = 4.5.   Required ratio = (4x + 4) : (x + 4) = 22 : 8.5 = 44 : 17.   Answer: Option 44 : 17
Answer: D