MU-NLPC/Calc-aqua_rat huggingface dataset:
In an electric circuit, two resistors with resistances x and y are connected in parallel. If R is the combined resistance of these two resistors, then the reciprocal of R is equal to the sum of the reciprocals of x and y. What is R if x is 4 Ohms and y is 5 Ohms?	Answers: A) 7/9 B) 20/9 C) 7/20 D) 9/20 E) 11/20

Solution: 1/R = 1/x + 1/y   1/R = 1/4+1/5 = 9/20   R = 20/9   The answer is 20/9.
Answer: B
Which of the following number is divisible by 24 ?
Choose the correct option:  A) 3125736  B) 35718  C) 63810  D) 537804  E) None of these

Solution: 24 = 3 x8, where 3 and 8 co-prime.   Clearly, 35718 is not divisible by 8, as 718 is not divisible by 8.   Similarly, 63810 is not divisible by 8 and 537804 is not divisible by 8.   Consider option (D),   Sum of digits = (3 + 1 + 2 + 5 + 7 + 3 + 6)= 
(3 + 1 + 2 + 5 + 7 + 3 + 6) = 27
27, which is divisible by 3.   Also, 736 is divisible by 8.   3125736 is divisible by (3 x 8), i.e., 24.   3125736)
Answer: A
In the arithmetic sequence t1, t2, t3, ..., tn, t1=23 and tn= tn-1 - 3 for each n > 1. What is the value of n when tn = 8?	Choose the correct choice from the following choices.
A) -1  B) 6  C) 10  D) 14  E) 20

Solution: We know that t1 = 23   So, using the given formula we have:   t1=(t1-1) -3 =23   t0 - 3 = 23   t0= 26   The same way we find that t2= 20   It seems that the sequence goes like this:   t0 = 26   t1 = 23   t2 = 20   t3 = 17   t4 = 14   t5 = 11   t6 = 8   So, ourANS is 6.
Answer: B
If equal numbers of people are born on each day, find the approximate percentage of the people whose birthday will fall on 29thFebruary.(if we are to consider people born in 20thcentury and assuming no deaths).
Choices.
A) 0.374  B) 0.5732  C) 0.0684  D) None of these  E) Cannot be determined

Solution: Explanation :   Let the number of people born on each day = n.   Total years in the 20th century = 100.   Total number of leap years (years in which 29th February appear) = 25.   Sample Space (days) = 365*75 + 366*25= 
365*75 + 366*25 = 36_525
36525 days.   So, Sample Space (population)= 36525*n   Favourable Set (population) = 25*n   Hence, the required probability = 25 * n /36525*n = 0.000684.   = 0.0684%.   Answer : 0.0684
Answer: C
I know a number which when multiplied by multiple of 9 i.e 9 18 27 36 45 ... the output consist of number containing only one digit.
Can you identify the number ?
Options.
A) 12345678  B) 12345674  C) 12745679  D) 12345679  E) 12645679

Solution: 12345679   12345679   12345679 × 9 = 111111111 (only 1s)   12345679 × 18 = 222222222 (only 2s)   12345679 × 27 = 333333333 (only 3s)   12345679 × 36 = 444444444 (only 4s)   12345679 × 45 = 555555555 (only 5s)
Answer: D
What is the maximum value of vx - yz. If the value of v,x,y,z have to be chosen from the set A where A(-3,-2,-1,0,1,2,3) Choose the most appropriate option
A) 15 B) 66 C) 25 D) 88 E) 17

Solution: Explanation:   To maximize the value of vx - yz, we make yz negative and vx as maximum as possible using given value.   vx−yz=(−3)2−(−3×2)vx−yz=(−3)2−(−3×2) = 15   15nswer:15
Answer: A
In terms of percentage profit, which among following the best transaction	Choose the correct choice from the following answers
A) C.P. 36, Profit 17  B) C.P. 50, Profit 24  C) C.P. 40, Profit 19  D) C.P. 60, Profit 29  E) None of these

Solution: Explanation:   Hint: Calculate profit percent as   Profit% = (profit/cost) * 100   Option C.P. 60, Profit 29
Answer: D
Excluding stoppages, the speed of a train is 35 kmph and including stoppages it is 22 kmph. Of how many minutes does the train stop per hour?
Choose the most appropriate option:
A) 82
B) 17
C) 22
D) 82
E) 18

Solution: Explanation:   T = 13/35 * 60 = 22   Answer: Option 22
Answer: C
The cash difference between the selling prices of an article at a profit of 4% and 6% is Rs. 3. The ratio of the two selling prices is:  Pick one:
A) 31:32	B) 39:42	C) 48:46	D) 52:63	E) 52:53

Solution: Explanation:   Let C.P. of the article be Rs. x.   Then, required ratio = 104% of x / 106% of x   = 104/106 = 52/53 = 52:53   Answer: Option 52:53
Answer: E
What will be the difference between simple interest and compound interest @10% per annum on a sum of Rs. 1000 after 4 years? Choose the most appropriate option:
A) Rs. 31
B) Rs. 32.10
C) Rs. 40.40
D) Rs. 64.10
E) None

Solution: Solution   S.I.	=Rs(1000x10x4 / 100)   = Rs.400.   C.I.	=Rs.[1000x(1x10/100)4-1000]   = Rs. 464.10   ∴ Difference = Rs.(464.10 - 400)   = Rs. 64.10   Answer Rs. 64.10
Answer: D
A man can row his boat with the stream at 19 km/h and against the stream in 11 km/h. The man's rate is?	Choices:
A) 4 kmph
B) 2 kmph
C) 7 kmph
D) 8 kmph
E) 3 kmph

Solution: DS = 19   US = 11   S = ?   S = (19 - 11)/2= 
(19 - 11)/2 = 4
4 kmph   4 kmphnswer:4 kmph
Answer: A
Set A consists of 19 elements. The average of set A is L. If a new element is added to the set and the average grows by K, what is the value of the new element?	Choose the correct choice from the following:
A) a) L(1 + K / 5) B) b) L * (K/100) - 20L C) c) 20L(1+K/100) D) d) 20(1+K/100)-19L E) e) L*(K/5)-19

Solution: Let's assume the value of new element to bea. So converting the word problem into equation,   (19*L + a) / (19 + 1) = L + k ==> after solving the equation we will get a (value of newly added element) = L + 20K   But according to the answer options, problem writer wanted to conveyk% percent rise in average value.   If we consider this case than resulting equation will be,   (19*L + a) / ( 19+1 ) = L + (K/100)*L ==> 19L + a = 20 [ L + KL/100]   ==> a= 20L + KL/5 -19L   ==> a= L + KL/5 , which is equivalent to option [a) L(1 + K / 5)]
Answer: A
Money invested at x%, compounded annually, triples in value in approximately every 112/x years. If $1800 is invested at a rate of 8%, compounded annually, what will be its approximate worth in 28 years?	Choose the correct answer:
A) $16,200
B) $5,600
C) $8,100
D) $15,000
E) $22,500

Solution: x=8%   112/x years=112/8= 
112/8 = 14
14 years   Now, money triples every 14 years   Therefore, in 14 yrs , if $1800 triples to $5400, in 28 years, it will again triple to $5400*3=$16,200   $16,200nswer $16,200
Answer: A
If 3 pounds of dried apricots that cost x dollars per pound are mixed with 3 pounds of prunes that cost y dollars per pound, what is the cost, in dollars, per pound of the mixture?
Options.
A) (3x + 3y)/5  B) (3x + 3y)/(x + y)  C) (3x + 3y)/(xy)  D) 5(3x + 3y)  E) 3x + 3y

Solution: Total Cost = Weight(in pounds) * Price/pound;   To find Total cost/pound, Divide by total pounds.   Cost of Dried apricots = 3x;   Cost of prunes = 3y;   Cost per pound = (3x + 3y)/5;   (3x + 3y)/5ns is ((3x + 3y)/5).
Answer: A
The weight of every type A widget is the same, the weight of every type B widget is the same, and the weight of every type C widget is the same. If the weight of 7 type A widgets is equal to the weight of 2 type B widgets, and the weight of 4 type B widgets is equal to the weight of 7 type C widgets. What is the ratio of the total weight of 1 type A widget and 1 type B widget, to the total weight of 1 type B widget and 1 type C widget? Choose the correct choice from the following options:
A) 3:5
B) 5:7
C) 7:9
D) 9:11
E) 11:13

Solution: 4B = 7C and so B = 7C/4   7A = 2B and so A = 2B/7 = C/2   A+B = C/2 + 7C/4 = 9C/4   B+C = 7C/4 + C = 11C/4   The ratio of A+B:B+C = 9:11   The answer is 9:11.
Answer: D
The product of two positive integers is 675 and their difference is 2. What is the bigger number?  Choose the most appropriate option.
A) 21  B) 23  C) 25  D) 27  E) 29

Solution: Let's use trial and error to find the two numbers.   25*23= 
25*23 = 575
575 (too low)   27*25= 
27*25 = 675
675   The answer is 27.
Answer: D
What is the area of square field whose side of length 15 m?
Choose one:
A) 225 sq m
B) 220 sq m
C) 100 sq m
D) 30 sq m
E) 35 sq m

Solution: Explanation:   15 * 15= 
15 * 15 = 225
225 sq m   225 sq mNSWER IS 225 sq m
Answer: A
A and B are two partially filled buckets of water. If 5 liters are transferred from A to B, then A would contain one-third of the amount of water in B. Alternatively, if 4 liters are transferred from B to A, B would contain one-half of the amount of water in A. Bucket A contains how many liters of water?
Choose the correct choice from the following choices.
A) 11	B) 52/5	C) 17	D) 21	E) 23

Solution: Let A contains A, 52/5 contains 52/5 liters   so, (A-5)/(52/5+5)= 1/3.......(1)   again, (52/5-4)/(A+4)= 1/2..........(2)   from (1)(2) we find A= 52/5   ans: (52/5)
Answer: B
Average of 10 matches is 32, How many runs one should should score to increase his average by 5 runs.
Pick: A) A)70 B) B)76 C) C)78 D) D)80 E) E)87

Solution: 87xplanation:   Average after 11 innings should be 37   So, Required score = (11 * 37) - (10 * 32)   = 407 - 320= 
407 - 320 = 87
87   Answer: Option 87
Answer: E
Three boys, two girls, and two women are to be seated on a bench. If one specific boy must be seated on one of the end seats, and one specific girl must me seated exactly in the middle, find the number of possible arrangements. Answers
A) 48	B) 144	C) 240	D) 288	E) 120

Solution: "One specific boy is seated to either of end seat", lets call him b1   "One specific girl is seated in the middle", lets call her g1   Note the question says *specific girl* and *specific boy*, so we do not consider for example the other girl , g2, being seated on seat #4. Same goes with the specific boy, b1.   b1 can be seated 2 different seats : 2!   g1 is seated on the seat #4, fixed (no other alternative) : 1   the remaining 5 seats can be filled with the remaining people b2,b3,g2,w1,w2: 5!   2! x 1 x 5! = 240   Answer 240
Answer: C
In a race of 200 m, A can beat B by 21 m and C by 15 m. In a race of 425 m, C will beat B by ?
Choose the correct choice from the following answers
A) 30 m	B) 75 m	C) 85 m	D) 25 m	E) 15 m

Solution: Explanation:   A:B = 100 : 79   A:C = 100 : 85   => B:C = 79:85   When C covers 85 m , B Covers 79 m   When C covers 425 m , B Covers   => 395 m   So C beats B by (425 - 395)= 
(425 - 395) = 30
30 m.   30 mnswer: 30 m
Answer: A
Positive Integer A gives the remainder of 12 when divided by another positive Integer B. If A/B = 47.24, what is the value of B?
Choose the correct choice.
A) 96
B) 75
C) 48
D) 25
E) 50

Solution: .24 of B = Remainder   .24 of B = 12   B = (12 *100) / 24= 
(12 *100) / 24 = 50
50.   50
Answer: E
How many positive integers less than 1000 are multiples of 5 but NOT of 4 or 7?	Choose one:
A) 114  B) 121  C) 122  D) 129  E) 136

Solution: There are 1000/5= 
1000/5 = 200
200 multiples of 5 . now we have to find the number of multiples of 5 and 4 that is 20 between 0 to 1000 and 5 and 7 that is 35 between 0 to 1000.   multiples of 20=1000/20= 
1000/20 = 50
50 multiples. and multiples of 35= 1000/35 =28.5 so 28 multiples of 35.   So multiples of 5 between o to 1000 not including multiples of 20 and 35 are equal to   200-78= 
  200-78 = 122
122 multiples.   So the answer is 122.
Answer: C
If k^3 is divisible by 168, what is the least possible value of integer k? Pick:
A) 36
B) 42
C) 48
D) 54
E) 60

Solution: k^3 = 168*x = 2^3*3*7*x   The factors of k must at minimum include 2*3*7= 
2*3*7 = 42
42.   The answer is 42.
Answer: B
At a certain supplier, a machine of type A costs $22,000 and a machine of type B costs $50,000. Each machine can be purchased by making a 20 percent down payment and repaying the remainder of the cost and the finance charges over a period of time. If the finance charges are equal to 40 percent of the remainder of the cost, how much less would 2 machines of type A cost than 1 machine of type B under this arrangement?	Choose the correct choice from the following choices:
A) $7,920 B) $11,200 C) $12,000 D) $12,800 E) $13,200

Solution: Total Cost of 2 Machines of Type $7,920   = 20% of (Cost of 2 machine $7,920) + remainder + 40 % remainder   = 20% of 44000 + (44000 - 20% of 44000) + 40% of (44000 - 20% of 44000)   = 58080   Total Cost of 1 Machine of Type B   = 20% of (Cost of 1 machine B) + remainder + 40 % remainder   = 20% of 50000 + (50000 - 20% of 50000) + 40% of (50000 - 20% of 50000)   = 66000   Diff = 66000 - 58080 = 7900   Hence, $7,920.
Answer: A
The average age of father and his two sons is 24 Years. Five years ago, the average age of the two sons was 15 Years. If the difference between the ages of the two sons is four years, what is the present age of the father?  Choose the correct choice from the following options:  A) 45  B) 32  C) 47  D) 48  E) 49

Solution: The total present age of father and two sons is 3x24 = 72 yrs   The total present age of sons is (15+5) X 2 = 40Years   so, present age of father is 72 â€“ 40 = 32 yrs   Answer 32
Answer: B
What is the cost of leveling the field in the form of parallelogram at the rate of Rs.30/10 sq.metre, whose base & perpendicular distance from the other side being 64m & 74m respectively?	Select.
A) s. 6000
B) s. 6300
C) s.4736
D) s. 6480
E) s. 7000

Solution: Area of the parallelogram = Length of the base * Perpendicular height   = 64 * 74= 
64 * 74 = 4_736
4736 m.   Total cost of levelling= Rs. 4736   s.4736
Answer: C
Due to construction, the speed limit along an 9-mile section of highway is reduced from 55 miles per hour to 20 miles per hour. Approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?
Choose the correct choice from the following:	A) A) 5.61	B) B) 8	C) C) 10	D) D) 17.19	E) E) 24

Solution: Old time in minutes to cross 9 miles stretch = 9*60/55 = 9*12/11 = 9.81   New time in minutes to cross 9 miles stretch = 9*60/20 = 9*3/1= 
9*3/1 = 27
27   Time difference= 17.19   Ans:17.19
Answer: D
Find the odd man out
2, 5, 11, 23, 48, 95	Choose the correct choice from the following options:
A) 5  B) 11  C) 23  D) 48  E) 28

Solution: 2*2+1= 
2*2+1 = 5
5   5*2+1= 
5*2+1 = 11
11   11*2+1= 
11*2+1 = 23
23   23*2+1= 
23*2+1 = 47
47   47*2+1= 
47*2+1 = 95
95   ANSWER:48
Answer: D
If 0 < a < 1, what is the median of the values a, x^-1, a^2, a^1/2 and a^3?	Pick one: A) a B) a^-1 C) a^2 D) a^1/2 E) a^3

Solution: A. To make the problem less confusing, I picked a number between 0 and 1 such as a = 1/4 and calculate:   a = 1/4   a^-1 = 4   a^2 = 1/16   a^(1/2) = 1/2   a^3 = 1/8.   From this, rearrange the number and the median is 1/4, which is a. answer a
Answer: A
Rahim and his uncle differ in their ages by 30 years. After 7 years, if the sum of their ages is 66, what will be the age of the uncle ?	Choose the correct choice from the following:  A) 41 years  B) 36  C) 48  D) 33  E) 44

Solution: 41 years   41   Let uncle’s present age = x   Rahim's present age = y   y– x= 30 ...(i)   41 yearsfter 7 year   (x + 7) + (y+ 7) = 66   x + y + 14 = 66   x + y = 52 ...(ii)   combining (i) and (ii) we get   (x + y = 52) + (x – y = 30)   2x= 82   x= 41   Uncle's age is 41
Answer: A
4 dice are thrown simultaneously on the board. Find the probability show the same face.
Choose one.
A) 1/115 B) 3/113 C) 1/216 D) 3/119 E) 1/119

Solution: The total number of elementary events associated to the random experiments of throwing four dice simultaneously is:   =6×6×6×6=64=6×6×6×6=64   n(S)=64n(S)=64   Let XX be the event that all dice show the same face.   X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}   n(X)=6n(X)=6   Hence required probability,   =n(X)n(S)=664=n(X)n(S)=664   =1/216   1/216
Answer: C
Find the value of x if the mean of the series 245,564,458,125,36,x is 250  Choose the correct choice from the following answers:
A) 50  B) 72  C) 36  D) 45  E) 112

Solution: mean = 245+564+458+125+36+x / 6 = 250   1428+x = 1500   x = 72   Answer is 72
Answer: B
If 6 is one solution of the equation x^2 + 3x + k = 10, where k is a constant, what is the other solution?
Choose the correct choice from the following:
A) -7
B) -4
C) -3
D) -9
E) 6

Solution: The phrase “6 is one solution of the equation” means that one value of x is 6. Thus, we first must plug 6 for x into the given equation to determine the value of k. So we have   6^2 + (3)(6) + k = 10   36 + 18 + k = 10   54 + k = 10   k = -44   Next we plug -44 into the given equation for k and then solve for x.   x^2 + 3x – 44 = 10   x^2 + 3x – 54 = 0   (x+9)(x-6) = 0   x = -9 or x = 6   Thus, -9 is the other solution. Answer -9.
Answer: D
The volume of a cube is 3375 cc. Find its surface. Choose the correct choice from the following options
A) 864  B) 556  C) 255  D) 287  E) 1350

Solution: a3 = 3375 => a = 15   6a2 = 6 * 15 * 15= 
6 * 15 * 15 = 1_350
1350   Answer:1350
Answer: E
How many liters of water must be evaporated from 50 liters of a 3-percent sugar solution to get a 2-percent solution?  Answers
A) 35  B) 33 1/3  C) 27  D) 16 2/3  E) 18

Solution: How many liters of water must be evaporated from 50 liters of a 3-percent sugar solution to get a 2-percent solution?   3% of a 50 liter solution is 1.5L. So you are trying to determine how many liters must a solution be for the 1.5L to represent 2% of the solution. Set up an inequality and solve for x:   1.5/x = 1/2   x = 3   Since you need a 15L solution, you must evaporate 18 of the original 50L solution to get a 2% solution.   Answer is 18.
Answer: E
A certain company retirement plan has arule of 70provision that allows an employee to retire when the employee's age plus years of employment with the company total at least 70. In what year could a female employee hired in 1990 on her 32nd birthday first be eligible to retire under this provision?	Answers.
A) 2003	B) 2009	C) 2005	D) 2006	E) 2007

Solution: She must gain at least 70 points, now she has 31 and every year gives her two more points: one for age and one for additional year of employment, so 32 + 2*(# of years) = 70 --> (# of years) = 19 --> 1990+19=2009.   Answer: 2009.
Answer: B
The concentration of spirit in three different vessels A, B and C are 45%, 30% and 12% respectively. If 4 litres from vessel A, 5 litres from vessel B and 6 litres from vessel C are mixed, find the concentration of spirit in the resultant solution. Choose the correct choice from the following choices:  A) 32.80%  B) 26.80%  C) 34%  D) 24.62%  E) 36%

Solution: Quantity of spirit in new solution=(4*45/100)+(5*30/100)+(6*12/100)=1.8+1.5+0.72= 
1.8+1.5+0.72 = 4.02
4.02 liters   So % concentration of spirit=100*4.02/(4+5+6)= 
100*4.02/(4+5+6) = 26.8
26.80%   ANSWER:26.80%
Answer: B
Two trains start from P and Q respectively and travel towards each other at a speed of 50 km/hr and 40 km/hr respectively. By the time they meet, the first train has traveled 100 km more than the second. The distance between P and Q is?	Answers.
A) 237 B) 278 C) 277 D) 900 E) 261

Solution: At the time of meeting, let the distance traveled by the second train be x km. Then, distance covered by the first train is (x + 100) km.   x/40 = (x + 100)/50   50x = 40x + 4000 => x = 400   So, distance between P and Q = (x + x + 100)km = 900 km.   Answer: 900
Answer: D
In a Pvt Company 15 staffs are working. Salary for 10 Staffs @ 15000/- and 5 staffs @ 9000/- per month. Owner deducted amount of 15 leaves from every one. Then how much amount will be given in total for One month?
Choose the correct choice from the following options:
A) 195000	B) 202000	C) 192000	D) 188000	E) 188500

Solution: Salary for 10 Staffs @ 15000/- : 1,50,000/-   Salary for 5 Staffs @ 9000/- : 45,000/-   Total Salary : 195000/-   Salary cutting 1 day for 10 Staffs: 5000/-   Salary cutting 1 days for 5 staffs : 1500/-   Total salary for one month : 195000/- - 6500/ =   Answer is 188500
Answer: E
What is the length of the longest pole which can be kept in a room 10 m long, 4 m broad and 3 m high?
Choices
A) 7	B) 9	C) 11.18	D) 13	E) None

Solution: Explanation:   d2 = 102 + 42 + 32 = 11.18   11.18)
Answer: C
The area of a triangle will be when a = 1m, b = 2m, c = 3m, a, b, c being lengths of respective sides.
Choose the correct answer.
A) 0 sq m	B) 3 sq m	C) 2 sq m	D) 6 sq m	E) 8 sq m

Solution: Explanation:   S = (1 + 2 + 3)/2= 
(1 + 2 + 3)/2 = 3
3=> No triangle exists   0 sq mNSWER IS 0 sq m
Answer: A
The set S consists of 5 numbers: {1,2,3,4,5}. If all possible subsets including the null set are created and one subset is chosen at random, what is the probability that the subset has 2 as its largest number?	Choose the correct choice from the following options:
A) 1/2
B) 1/4
C) 1/8
D) 1/16
E) 1/32

Solution: The set S has 2^5 = 32 subsets.   The number 2 is the largest number in the subset {1,2} and the subset {2}.   Thus 2 is the largest number in 2 subsets of S.   The probability that 2 is the largest number is 2/32 = 1/16.   The answer is 1/16.
Answer: D
Andy solves problems 80 to 125 inclusive in a Math exercise. How many problems does he solve? Pick.
A) 53	B) 52	C) 51	D) 46	E) 49

Solution: 125-80+1= 52   '46' is the answer
Answer: D
Kamal was 4 times as old as his son 8 years ago. After 8 years, Kamal will be twice as old as his son. Find out the present age of Kamal.	Pick.
A) 30
B) 35
C) 40
D) 45
E) 50

Solution: Let age of the son before 8 years =x   Then, age of Kamal before 8 years ago =4x   After 8 years, Kamal will be twice as old as his son   ⇒4x+16=2(x+16)⇒x=8   Present age of Kamal   =4x+8=4×8+8=40   Answer is 40.
Answer: C
How long does a train 110 m long running at the speed of 72 km/hr takes to cross a bridge 175 m length?
Choose one
A) 12.9 sec B) 12.1 sec C) 17.9 sec D) 16.8 sec E) 14.25 sec

Solution: Speed = 72 * 5/18= 
72 * 5/18 = 20
20 m/sec   Total distance covered= 110 + 175= 
110 + 175 = 285
285 m.   Required time= 285/20= 
285/20 = 57/4 = around 14.25
14.25 sec.   Answer: 14.25 sec
Answer: E
Pipe A can fill a tank in 4 hours. Due to a leak at the bottom, it takes 8 hours for the pipe A to fill the tank. In what time can the leak alone empty the full tank?
Choose the correct option
A) 13  B) 17  C) 18  D) 8  E) 12

Solution: Let the leak can empty the full tank in x hours 1/4 - 1/x = 1/8   => 1/x = 1/4 - 1/8 = (2 - 1)/8 = 1/8   => x = 8.   Answer: 8
Answer: D
Train A travelling at 63 kmph takes 27 to sec to cross Train B when travelling in opposite direction whereas it takes 162 seconds to overtake it when travelling in the same direction. If the length of train B is 500 meters, find the length of Train A.  Choose the correct choice from the following:
A) 400 m	B) 810 m	C) 500 m	D) 310 m	E) 210 m

Solution: DETAILED SOLUTION   Let the length of Train A be x meters   Let speed of Train B be y kmph   Relative distance = Relative speed * time taken to cross/overtake   Crossing scenario:   Relative speed of 2 trains = 63 + y   Time taken to cross = 27 sec or 27/3600 hrs   Relative distance between 2 trains = Length of Train A + length of train B = (x + 0.5) km   Therefore, x + 0.5 = (63 + y) * 27 / 3600 ----- (1)   Overtaking scenario:   Relative speed of 2 trains = 63 – y   Time taken to overtake = 162 sec or 162/3600 hrs   Relative distance between 2 trains = x + 0.5   Therefore, x + 0.5 = (63 – y) * 162/3600 --- (2)   From (1) and (2), solve for y.   (63 + y) * 27 = (63 – y) * 162   27y + 162 y = 63*162 – 63 *27   189y = 63 * 135 or y = 45 kmph   Substitute in (2) to get x.   x + 0.5 = (63 – 45) * 162/3600   Or x = 0.31 km or 310 meters   CORRECT ANSWER 310 m
Answer: D
What is the total number of integers between 200 and 500 that are divisible by 25?  Choose the correct choice from the following options.
A) 20  B) 25  C) 14  D) 15  E) 18

Solution: 125, 150, 175, ..., 450,475   This is an equally spaced list; you can use the formula:   n = (largest - smallest) / ('space') + 1 = (475- 125) / (25) + 1 = 350/25 + 1 = 14+ 1= 
14+ 1 = 15
15   Answer is 15
Answer: D
If Rs.400 amount to Rs.540 in 4 years, what will it amount to in 6 years at the same rate % per annum?	Options
A) s.575 B) s.595 C) s.590 D) s.610 E) s.585

Solution: 80 = (400*4*R)/100   R = 8.75%   I = (400*6*8.75)/100= 
(400*6*8.75)/100 = 210
210   400 + 210= 
400 + 210 = 610
610   ANSWER:s.610
Answer: D
A car runs 10,000 miles using 5 tyres interchangeably. to have equal worn out by all tyres,how many miles each tyre should have run?  Select the correct option
A) 5000 B) 8000 C) 4000 D) 3000 E) 7000

Solution: for 5 tyres running interchangeably 10,000 miles the car runs   for 1 tyre=10000/5= 
10000/5 = 2_000
2000   as you all know i suppose the car has 4 tyre   to have equal worn out by 4 tyres we need=2000*4= 
2000*4 = 8_000
8000   ANSWER:8000
Answer: B