MU-NLPC/Calc-aqua_rat huggingface dataset:
A car mechanic purchased four old cars for Rs. 1 lakh. He spent total 2 lakh in the maintenance and repairing of these four cars. what is the average sale price of the rest three cars to get 50% total profit if he has already sold one of the four cars at Rs. 1.2 lakh?  Choose the correct choice
A) 1.8 lakh B) 1.1 lakh C) 1.9 lakh D) 8.1 lakh E) 6.1 lakh

Solution: Explanation:   Total cost of 4 cars = 1+2= 
1+2 = 3
3 lakh   Total SP of 4 cars= 3 x 1.5 = 4.5 lakh   SP of 1 car = 1.2 lakh   SP of rest 3 cars = 4.5 - 1.2= 
4.5 - 1.2 = 3.3
3.3 lakh   Average SP of all the 3 cars= 1.1 lakh   Answer: 1.1 lakh) 1.1 lakh
Answer: B
For an agricultural experiment, 300 seeds were planted in one plot and 200 were planted in a second plot. If exactly 20 percent of the seeds in the first plot germinated and exactly 35 percent of the seeds in the second plot germinated, what percent of the total number of seeds germinated? Choose the correct choice from the following choices
A) 12%	B) 26%	C) 29%	D) 30%	E) 60%

Solution: In the first plot 20% of 300 seeds germinated, so 0.20 x 300 = 60 seeds germinated.   In the second plot, 35% of 200 seeds germinated, so 0.35 x 200 = 70 seeds germinated.   Since 60 + 70= 
60 + 70 = 130
130 seeds germinated out of a total of 300 + 200= 
300 + 200 = 500
500 seeds, the percent of seeds that germinated is (130/500) x 100%, or 26%.   Answer: 26%.
Answer: B
A not-so-good clockmaker has four clocks on display in the window. Clock #1 loses 10 minutes every hour. Clock #2 gains 15 minutes every hour relative to Clock #1 (i.e., as Clock #1 moves from 12:00 to 1:00, Clock #2 moves from 12:00 to 1:15). Clock #3 loses 20 minutes every hour relative to Clock #2. Finally, Clock #4 gains 20 minutes every hour relative to Clock #3. If the clockmaker resets all four clocks to the correct time at 12 noon, what time will Clock #4 display after 6 actual hours (when it is actually 6:00 pm that same day)?
Choose the most appropriate option: A) 5:00 B) 5:34 C) 5:42 D) 6:00 E) 6:24

Solution: C1 loses 15 minutes every hour. So after 60 minutes have passed, C1 displays that 60-15= 
60-15 = 45
45 minutes have passed.   C2 gains 15 minutes for every 60 minutes displayed on C1. Thus, the time displayed on C2 is 75/60= 5/4 the time displayed on C1. So after 60 minutes have passed, C2 displays the passing of (5/4 * 45) minutes.   C3 loses 20 minutes for every 60 minutes displayed on C2. Thus, the time displayed on C3 is 40/60 = 2/3 the time displayed on C2. So after 60 minutes have passed, C3 displays the passing of (2/3 * 5/4 * 45) minutes.   C4 gains 20 minutes for every 60 minutes displayed on C3. Thus, the time displayed on C4 is 80/60 = 4/3 the time displayed on clock 3. So after 60 minutes have passed, C4 displays the passing of  4/3 * 2/3 * 5/4 * 45= 
 4/3 * 2/3 * 5/4 * 45 = 50
50 minutes.   C4 loses 10 minutes every hour.   In 6 hours, C4 will lose   6*10= 
  6*10 = 60
60 minutes= 1 hour.   Since the correct time after 6 hours will be 6pm, C4 will show a time of 6-1 = 6pm.   The correct answer is 6:00.
Answer: D
Machine X takes 80 hours longer than machine Y to produce 1080 Widgets. Machine Y produces 20 percent more widgets in an hour than machine x does in an hour. How many widgets per hour does machine X produce	Choose the correct choice.
A) 100
B) 65
C) 25
D) 11
E) 2.25

Solution: Machine Y produces 20 percent more widgets in an hour than machine x does in an hour.   So if machine X produces 100 widgets, then machine Y produces 120 widgets.   Ratio of 120/100 = 6/5.   This is their speed of work (Y:X).   i.e. speed of their work (X:Y) = 5/6   Now, time is inversely proportional to speed.   Hence the ratio of the time spent (X:Y)= 6/5   Let us assume that they spend 6x and 5x hours.   Given that 6x-5x = 80   So, x = 80.   Hence 6x = 6*80= 
6*80 = 480
480 hours.   Hence X takes 120 hours to produce 1080 widgets.   So, in 1 hour, it can produce  (1 * 1080)/480= 
 (1 * 1080)/480 = 9/4 = around 2.25
2.25   Hence option (2.25).
Answer: E
Factor 3x3 - x2y +6x2y - 2xy2 + 3xy2 - y3 = Options:
A) (3x - 2y)(x + y)  B) (3x - y)(x + y)(x - y)  C) (3x - y)(x + y)2  D) (3x - y)(x2 + y2)  E) none

Solution: Solution:   3x3 - x2y + 6x2y - 2xy2 + 3xy2 - y3=   x2(3x - y) + 2xy(3x - y) + y2(3x-y) =   (3x - y)(x2 + 2xy + y2)=   (3x - y)(x + y)2   Answer (3x - y)(x + y)2
Answer: C
The maximum number of students among them 1234 pens and 874 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is:  Choose the most appropriate option:
A) 91	B) 2	C) 1001	D) 1911	E) None of these

Solution: Explanation:   Required number of students = H.C.F of 1234 and 874 = 2. Answer: 2
Answer: B
The two trains of lengths 400 m, 600 m respectively, running at same directions. The faster train can cross the slower train in 180 sec, the speed of the slower train is 48 km. then find the speed of the faster train? Choose the correct option:  A) 58 Kmph  B) 68 Kmph  C) 78 Kmph  D) 55 Kmph  E) 65 Kmph

Solution: Length of the two trains = 600m + 400m   Speed of the first train = X   Speed of the second train= 48 Kmph   1000/X - 48 = 180   1000/x - 48 * 5/18 = 180   50 = 9X - 120   X = 68 Kmph   ANSWER:68 Kmph
Answer: B
20 balls are numbered 1 to 20. A ball is drawn and then another ball is drawn without replacement. What is the probability that both balls have even numbers?	Choose the correct option:
A) 7/30
B) 3/14
C) 9/38
D) 4/21
E) 5/26

Solution: P(1st ball is even) = 10/20   P(2nd ball is also even) = 9/19   P(both balls are even) = 10/20 * 9/19 = 9/38   The answer is 9/38.
Answer: C
A man can row downstream at the rate of 10 Km/hr and upstream at 4 Km/hr. Find man's rate in still water and the rate of current?	Select:
A) 9,6  B) 7,3  C) 9,3  D) 6,6  E) None of these

Solution: Explanation:   Rate of still water = 1/2 (10 + 4) = 7 Km/hr   Rate of current = 1/2 (10-4) = 3 Km/hr   Answer: Option 7,3
Answer: B
Two cyclist start on a circular track from a given point but in opposite direction with speeds of 7m/s and 8m/s. If the circumference of the circle is 360meters, after what time will they meet at the starting point? Choose the correct option.
A) 20sec	B) 15sec	C) 30sec	D) 24sec	E) 1min

Solution: They meet every 360/7+8 = 24sec   Answer is 24sec
Answer: D
A can do a piece of work in 4 hours; B and C together can do it in 3 hours, while A and C together can do it in 2 hours. How long will B alone take to do it? Choose the correct choice from the following answers.
A) 12 B) 9 C) 8 D) 6 E) 5

Solution: A's 1 hour's work = 1 ;   4   (B + C)'s 1 hour's work = 1 ;   3   (A + C)'s 1 hour's work = 1 .   2   (A + B + C)'s 1 hour's work = ( 1 + 1 ) = 7 .   4 3 12   B's 1 hour's work = ( 7 - 1 ) = 1 .   12 2 12   Therefore 12 alone will take 12 hours to do the work.
Answer: A
A man can row a boat at 20 kmph in still water. If the speed of the stream is 6 kmph, what is the time taken to row a distance of 120 km downstream?	Choose the correct choice from the following choices:
A) 60/18
B) 30/29
C) 60/12
D) 60/13
E) 30/82

Solution: Speed downstream = 20 + 6= 
20 + 6 = 26
26 kmph.   Time required to cover 60 km downstream= d/s = 120/26   = 60/13 hours.   Answer:60/13
Answer: D
There is a truck driver starts from one place to pick another person at
another place. The driver goes to that place by 6 AM and then picking him
he returns back.one day the other person woke a bit early and started
walking towards the first place.one the way he meets truck driver and joins
him and both went back to the first place. This day the other person came
20 min early to the time he usually comes to the first place?Tell the time
when the driver met the second person that day?
Pick.
A) 5.10 AM	B) 5.20 AM	C) 5.40 AM	D) 5.50 AM	E) 5.30 AM

Solution: Given that the first person reaches the first place by 6.00 AM   But,one day the second person reached the place 20 min early.   and met the first person on the way ad reached the stop at 6.00 AM.   Therfore,They would have met at 5.50 AM.   ANSWER:5.50 AM
Answer: D
The length of a rectangular plot is thrice its width. If the area of the rectangular plot is 675 sq meters, then what is the width (in meters) of the rectangular plot? Choices
A) 12  B) 15  C) 18  D) 21  E) 24

Solution: Area = L*W = 3W^2 = 675   W^2 = 225   W = 15   The answer is 15.
Answer: B
How many different positive integers exist between 10^9 and 10^10, the sum of whose digits is equal to 2?	Select the correct option:
A) 6  B) 7  C) 5  D) 8  E) 10

Solution: So, the numbers should be from 1,000,000,000 to 10,000,000,000   The following two cases are possible for the sum of the digits to be 2:   1. Two 1's and the rest are 0's:   1,000,000,001   1,000,000,010   1,000,000,100   1,000,001,000   1,000,010,000   1,000,100,000   1,001,000,000   1,010,000,000   1,100,000,000   9 numbers.   2. One 2 and the rest are 0's:   2,000,000,000   1 number.   Total = 10 numbers.   Answer: 10
Answer: E
List K consists of 14 consecutive integers. If -4 is the least integer in list K, what is the range of the positive integers in list K?
Answers
A) 5  B) 6  C) 7  D) 8  E) 12

Solution: Answer = 8 = 8   If least = -4, then largest = 9   Range = 9 - 1= 
9 - 1 = 8
8
Answer: D
A, B and C are partners. A receives 2/3 of profits, B and C dividing the remainder equally. A's income is increased by Rs.200 when the rate to profit rises from 5 to 7 percent. Find the Capital of B?	Select the correct option:
A) 18 B) 99 C) 77 D) 66 E) 25

Solution: 1500 ---- 270   100 ---- ? => 18%   18nswer: 18
Answer: A
A professional athlete was offered a three-year contract to play with Team K that provided for an annual salary of $120,000 in the first year, an increase in annual salary of 20% over the previous year for the next two years, and a bonus of $50,000 on signing. Team L offered a three-year contract providing for an annual salary of $150,000 in the first year, an increase in annual salary of 10% over the previous year for the next two years, and no signing bonus. If he accepts the offer of Team L and fulfills the three-year contract terms, the athlete will receive how much more money by choosing Team L over Team K ?
Select:
A) $3,500  B) $5,000  C) $2,500  D) $9,700  E) $10,000

Solution: Team K's contract = $120,000 + $120,000*1.2 + $120,000*1.2*1.2 + $50,000 = $486,800   Team L's contract = $150,000 + $150,000*1.1 + $150,000*1.1*1.1 = $496,500   The difference = $9,700.   Answer: $9,700.
Answer: D
At what price must an article costing Rs.47.50 be marked in order that after deducting 5% from the list price. It may be sold at a profit of 25% on the cost price? Choose the correct choice from the following choices:
A) 62.5
B) 62.3
C) 62.7
D) 62.2
E) 62.9

Solution: CP = 47.50   SP = 47.50*(125/100)= 
47.50*(125/100) = 59.375
59.375   MP*(95/100)= 59.375   MP = 62.5   62.5nswer:62.5
Answer: A
If each side of a square is increased by 6%, find the percentage change in its area?  Choose the correct choice from the following answers.
A) 10.68%  B) 8.72%  C) 9.28%  D) 12.36%  E) 11.91%

Solution: let each side of the square be a , then area = a x a   New side = 106a / 100 = 53a /50   New area =(53a x 53a) / (50 x 50) = (2809a²/2500)   increased area== (2809a²/2500) - a²   Increase %= [(309a²/2500 ) x (1/a² ) x 100]% = 12.36%   answer :12.36%
Answer: D
In x-y plane, there is a right triangle ABC (∠B=90o). If the length of AC is 100 and the slope of line segment AC is 4/3, what is the length of AB? Pick:	A) 12	B) 18	C) 24	D) 28	E) 80

Solution: Slope = Change in Vertical Direction/Change in Horizontal Direction = 4/3   Change in Vertical Direction = 4x = AB   Change in Horizontal Direction = 3x = BC   AB^2 + BC^2 = 100^2   16x^2 + 9x^2 = 10000   25x^2 = 400   x^2 = 400   x = 20   Therefore AB = 20*4= 
20*4 = 80
80   Answer: 80
Answer: E
A cricketer has a certain average for 10 innings. In the eleventh inning, he scored 108 runs, there by increasing his average by 7 runs. His new average is:	Choose the correct choice from the following choices:  A) 38 runs  B) 37 runs  C) 39 runs  D) 40 runs  E) 41 runs

Solution: Let average for 10 innings be x. Then,   (10x + 108)/11 = x + 7   = 11x + 77 = 10x + 108   = x = 31.   New average = (x + 7) = 38 runs.   38 runsnswer:38 runs
Answer: A
Two men starting from the same place walk at the rate of 5 kmph and 5.5 kmph respectively. What time will they take to be 8.0 km apart, if they walk in the same direction?
Select: A) 12 hrs B) 14 hrs C) 15 hrs D) 16 hrs E) None

Solution: Sol.   to be 0.5 km apart, they take 1 hour.   To be 8.0 km apart, they take [1/0.5 * 8.0= 
1/0.5 * 8.0 = 16
16 hrs.   Answer 16 hrs
Answer: D
If 50% of (x-y) = 30% of (x+y) then what percent of x is y?  Select:	A) 15	B) 20	C) 18	D) 26	E) 25

Solution: 50% of (x-y)=30% of(x+y) ==> (50/100)(x-y)=(30/100)(x+y)   ==>5(x-y)=3(x+y) ==> 2x=8y => x=4y   therefore required percentage =((y/x) X 100)% = ((y/4y) X 100) =25%   Answer 25.
Answer: E
A train speeds past a pole in 15 sec and a platform 100 m long in 25 sec, its length is? Choose the correct choice from the following choices:
A) 388	B) 150	C) 288	D) 269	E) 271

Solution: Let the length of the train be x m and its speed be y m/sec.   Then, x/y = 15 => y = x/15   (x + 100)/25 = x/15 => x = 150 m.   Answer:150
Answer: B
Find the value of a/b + b/a, if a and b are the roots of the quadratic equation x2 + 9x +3 = 0?
Select: A) 28.3 B) 1.45 C) 2.78 D) 6.84 E) 7.23

Solution: a/b + b/a = (a2 + b2)/ab = (a2 + b2 + a + b)/ab   = [(a + b)2 - 2ab]/ab   a + b = -9/1 = -9   ab = 3/1= 
3/1 = 3
3   Hence a/b + b/a= [(-9)2 - 2(3)]/3 = 56/4 = 28.3.   28.3)
Answer: A
If Rahul rows 15 km upstream in 3 hours and 21 km downstream in 3 hours, then the speed of the stream is	Select the correct option
A) 5 km/hr
B) 4 km/hr
C) 2 km/hr
D) 1 km/hr
E) 3 km/hr

Solution: Explanation:   Rate upstream = (15/3) kmph   Rate downstream (21/3)= 
(21/3) = 7
7 kmph.   Speed of stream (1/2)(7 - 5)kmph= 1 kmph   Option 1 km/hr
Answer: D
Two trains one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 16 hours and 25 hours respectively. The ratio of their speeds is  Choose the most appropriate option.
A) 2 : 3  B) 4 : 3  C) 6 : 7  D) 9 : 8  E) 5 : 4

Solution: Sol.   Let us name the trains as A and B. Then,   (A's speed) : (B's speed) = √b : √a   = √25 : √16   = 5 : 4.   Answer 5 : 4
Answer: E
How many factors of 2475 are odd numbers greater than 1?	Choose the correct option
A) 3  B) 4  C) 17  D) 6  E) 7

Solution: prime factors of 330 are 2^1,3^2,5^2 and 11^1   total divisors = (power if a prime factor+1)   total no. of odd factors(3,5,11) = (2+1)(2+1)(1+1) =18   since we need odd divisors other than 1 =>18-1= 
18-1 = 17
17 odd divisors   17 is the answer
Answer: C
A 1200 m long train crosses a tree in 120 sec, how much time will I take to pass a platform 700 m long?  Choose the correct choice from the following answers:
A) 11
B) 190
C) 188
D) 177
E) 121

Solution: L = S*T   S= 1200/120= 
1200/120 = 10
10 m/Sec.   Total length (D)= 1900 m   T = D/S   T = 1900/10= 
1900/10 = 190
190 Sec ,Answer:190
Answer: B
By selling 100 pencil, a trader gains the cost of 20 Pencil. Find his gain percentage?
Select.
A) 26 1/3%	B) 51 1/3%	C) 20%	D) 53 1/3%	E) 34 1/3%

Solution: C   20%   Let the CP of each pencil be Rs. 1.   CP of 100 pens = Rs. 100   Profit = Cost of 20 pencil = Rs. 20   Profit% = 20/100 * 100= 
20/100 * 100 = 20
20%
Answer: C
If the personal income tax rate is lowered from 45% to 30%, what is the differential savings for a tax payer having an annual income before tax to the tune of $48000?  Choose the correct answer.
A) $3500
B) $5000
C) $3150
D) $7200
E) $10000

Solution: Saving = (45-30)% of 48000 = 7200.   Answer:$7200
Answer: D
When p is divided by W, the remainder is 4. All of the following are possible values of W, except for which of the following?	Choose the correct answer:
A) 13
B) 31
C) 49
D) 57
E) 67

Solution: The number can be expressed in the form of 9x+4 where x can 0,1,2,3,4....   by evaluating the answer choices carefully we can clearly observe that 57 is the only number which can't be W expressed in the form of 9x+4   In other words we can also say that the (answer - 4) will not be divisible by 9.57 is the number which doesn't follow this condition   Correct Answer - 57
Answer: D
There arr 4 prime numbers in ascending order. The multiplication of 1st 3 is 385 and that of last 3is 1001. what is the last number is Choose the most appropriate option
A) 8
B) 10
C) 12
D) 13
E) 15

Solution: Explanation:   abcbcd=3851001=>ad=513   abcbcd=3851001=>ad=513   So d = 13   13
Answer: D
If n is an integer, then the least possible value of |33 - 5n| is?	Pick:
A) 0
B) 1
C) 2
D) 3
E) 4

Solution: |33 - 5n| represents the distance between 33 and 5n on the number line. Now, the distance will be minimized when 5n, which is multiple of 5, is closest to 33. Multiple of 5 which is closest to 33 is 35 (for n = 7), so the least distance is 2: |33 - 35| = 2.   Answer: 2.
Answer: C
An error 2% in excess is made while measuring the side ofa square. The % of error in the calculated area of the square is?  Options:  A) 4.14%  B) 4.04%  C) 4.23%  D) 4.67%  E) 4.89%

Solution: 100 cm is read as 102 cm.   A1 = (100 x 100) cm2 and A2 (102 x 102) cm2.   (A2 - A1) = [(102)2 - (100)2]   = (102 + 100) x (102 - 100)   = 404 cm2.   Percentage error = 404 x 100 % = 4.04%   100 x 100   4.04%
Answer: B
A single discount equivalent to the discount series of 25%, 20% and 15% is?	Options.
A) 31.8 B) 31.1 C) 31.6 D) 49 E) 31.9

Solution: Explanation:   100*(75/100)*(80/100)*(85/100)= 
100*(75/100)*(80/100)*(85/100) = 51
51   100 - 51= 
100 - 51 = 49
49   Answer: 49
Answer: D
In a certain archery competition, points were awarded as follows: the first place winner receives 11 points, the second place winner receives 7 points, the third place winner receives 5 points and the fourth place winner receives 2 points. No other points are awarded. John participated several times in the competition and finished first, second, third, or fourth each time. The product of all the points he received was 15400. How many times did he participate in the competition?	Pick
A) 5  B) 6  C) 7  D) 8  E) 9

Solution: 15400 = 2*2*2*5*5*7*11   John participated 7 times.   The answer is 7.
Answer: C
How many different 9 digit numbers can be formed from the number 223355888 by re-arranging its digits so that the odd digits occupy even position?	Choose the correct choice from the following answers:
A) 22
B) 776
C) 26
D) 28
E) 60

Solution: Odd places are 4 and these are occupied by 3355. So this can be done in 4!/ (2! 2!) = 6   There are 5 even numbers which have to be placed at 5 odd places. So 5!/(2!3!) = 10 ways   so total number of ways of arranging all these numbers are  10 * 6= 
 10 * 6 = 60
60 ways   Answer:60
Answer: E
The mass of the sun is approximately 4 × 10^30 kg and the mass of the moon is approximately 8 × 10^12 kg. The mass of the sun is approximately how many times the mass of the moon?	Choose the correct answer:  A) 4.0 × 10^(−18)  B) 2.5 × 10^17  C) 5 × 10^17  D) 2.5 × 10^19  E) 4.0 × 10^42

Solution: Mass of sun = x * Mass of moon   x = Mass of sun / Mass of moon = (4 × 10^30) / (8 × 10^12) = 2^2*2^-3*10^18 = 10^18/2= 5*10^17   Ans. 5 × 10^17) 2.5 × 10^17
Answer: C
One train is traveling 45 kmph and other is at 10 meters a second. Ratio of the speed of the two trains is?
Choose the correct option.
A) 5:4 B) 9:4 C) 5:6 D) 5:0 E) 2:4

Solution: Explanation:   45 * 5/18 = 10   25:20 => 5:4   5:4nswer: Option 5:4
Answer: A
The scoring system in a certain football competition goes as follows: 3 points for victory, 1 point for a draw, and 0 points for defeat. Each team plays 20 matches. If a team scored 14 points after 5 games, what is the least number of the remaining matches it has to win to reach the 40-point mark by the end of the tournament? Select the correct option: A) 6 B) 7 C) 8 D) 9 E) 10

Solution: To get 40 points as end of season we need another 26 points or more from remaining 15 matches:   Option 6= 6*3+9*1= 
6*3+9*1 = 27
27   hence option 6-6
Answer: A
y = x^2 + bx +64 cuts the x axis at (h, 0) and (k, 0). If h and k are integers, what is the least value of b?	Choices
A) -65
B) -64
C) -32
D) 32
E) 64

Solution: As the curve cuts the x-axis at (h,0) and (k,0). Therefore h,k are the roots of the quadratic equation.   For the quadratic equation is in the form ofax^2+bx+c=0,   The product of the roots =c/a= 64/1=256 and the sum of the roots =-b/a=-b   64 can be expressed as product of two numbers in the following ways:   1 * 64   2 * 32   4 * 16   The sum of the roots is maximum when the roots are 1 and 64 and the maximum sum is 1 + 64= 
1 + 64 = 65
65.   The least value possible for b is therefore -65.   -64
Answer: B
In a covering a certain distance, the speeds of A and B are in the ratio of 3:4. A takes 30 minutes more than B to reach the destination. The time taken by A to reach the destination is?  Choose the correct choice from the following options:
A) 32 hrs  B) 8 hrs  C) 2 hrs  D) 6 hrs  E) 7 hrs

Solution: Ratio of speeds = 3:4   Ratio of times taken = 4:3   Suppose A takes 4x hrs and B takes 3x hrs to reach the destination.   Then, 4x - 3x = 30/60 => x = 1/2   Time taken by A = 4x hrs = 4 * 1/2= 
4 * 1/2 = 2
2 hrs.   Answer: 2 hrs
Answer: C
A board of length L feet is cut into two pieces such that the length of piece A is 4 feet less than twice the length of piece B. Which of the following is the length, in feet, of piece A?	Choose the correct choice from the following choices
A) (L - 4)/3	B) (2L + 4)/3	C) (L + 4)/3	D) (2L + 2)/3	E) (2L - 4)/3

Solution: A+B = L so we know that B = L - A.   A = 2B-4   A = 2(L-A) - 4   3A = 2L - 4   A = (2L-4) / 3   The answer is (2L - 4)/3.
Answer: E
A license plate in the country Kerrania consists of four digits followed by two letters. The letters A, B, and C are used only by government vehicles while the letters D through Z are used by non-government vehicles. Kerrania's intelligence agency has recently captured a message from the country Gonzalia indicating that an electronic transmitter has been installed in a Kerrania government vehicle with a license plate starting with 79. If it takes the police 60 minutes to inspect each vehicle, what is the probability that the police will find the transmitter within three hours? Select.
A) 18/79  B) 1/6  C) 1/300  D) 1/50  E) 1/900

Solution: So there are 900 cars that they have to search.. Each takes 60mins, total of 54000 mins.. Have to find in 180 mins.. Prob180/54000 = 1/300 (ANSWER 1/300)
Answer: C
Shekar scored 76, 65, 82, 67 and 95 marks in Mathematics, Science, Social studies, English and Biology respectively. What are his average marks?  Choose the correct choice
A) 65	B) 77	C) 75	D) 85	E) 90

Solution: Explanation :   Average= (76+65+82+67+95)/5 = 385/5= 
385/5 = 77
77   Hence average=77   Answer : 77
Answer: B
On average, Machine A will produce a completed item once every three minutes, and Machine B will produce a completed item once every thirteen minutes. The number of items Machine A produces in a 24-hour period is approximately what percent greater than the number of items Machine B would produce in that same period? Choose the correct choice from the following
A) 500%  B) 133%  C) 100%  D) 166%  E) 333%

Solution: Machine A: 1 item in 3 minutes --> 1/3 items in 1 minute;   Machine B: 1 item in 13 minutes --> 1/13 items in 1 minute.   In the same time period, Machine A produces (1/3-1/13)/(1/13)*100=~133% more items than machine B.   Answer: 333%.
Answer: E
The sum of the numbers is 330. If the first number be twice the second and third number be one-third of the first, then the second number is: Choose the most appropriate option.
A) 48	B) 54	C) 72	D) 84	E) 90

Solution: Let the second number be x. Then, first number = 2x and third number = 2x/3.   2x + x + 2x/3 = 330   11x/3 = 330   x = 90   ANSW90R:90
Answer: E