MU-NLPC/Calc-aqua_rat huggingface dataset:
If 3<x<6<y<8, then what is the greatest possible positive integer difference of x and y?  Choose the correct choice from the following choices:
A) 3
B) 4
C) 5
D) 6
E) 7

Solution: 3 < x < 6 < y < 8;   3 < x   y < 8   3 + y < x + 8   y - x < 5.   Positive integer difference is 4 (for example y = 7.5 and x = 3.5)   Answer: 4.
Answer: B
Two Copiers are being used to produce 2400 copies of a 1-page document. One Copier runs at 150% of the speed of the other. How many copies should be made on the faster copier so that both copiers will finish the same time? Choose the correct choice:  A) 1240  B) 1440  C) 1340  D) 1540  E) 1640

Solution: Let the speed of one copier be x   Speed of other copier 150x/100   Ratio of speed = 1:150/100 = 2:3   copies made on faster copier = 3/5 *2400= 
3/5 *2400 = 1_440
1440   ANSWER:1440
Answer: B
The ratio of a compound, by weight, consisting only of substances x, y, and z is 4:6:10,
respectively. Due to a dramatic increase in the surrounding temperature, the composition of the
compound is changed such that the ratio of x to y is halved and the ratio of x to z is tripled. In the
changed compound, if the total weight is 290 lbs, how much does substance x weigh?	Choose the correct choice from the following
A) 48  B) 36  C) 24  D) 52  E) 60

Solution: x:y=4:6   if the ratio is halevd then x:y=2:6   The old ratio of x to z was 4:10. If this ratio is tripled, then the new ratio of x to z is 12:10.   x:y=2:6=12:36 ( multiplied the ration with 6/6 to have a common co eff x in both the rations x:y and x:z)   so x:y:z= 12:36:10   and we know x + y + z = 290 lbs   from the ratio of x ,y and z we have x=12k y=36k z=10K   put it in the equation we have 12k+36k+10k=290   k=5   Hence x=12(5)=60   Ans 60
Answer: E
When a random experiment is conducted, the probability that event A occurs is 1/5. If the random experiment is conducted 5 independent times, what is the probability that event A occurs exactly twice?
Choices:	A) 36/625	B) 48/625	C) 64/625	D) 98/625	E) 128/625

Solution: One case is: 1/5*1/5*4/5*4/5*4/5=64/3125   The total number of possible cases is 5C2 = 10   P(event A occurs exactly twice) = 10*(64/3125) = 128/625   The answer is 128/625.
Answer: E
Two students appeared at an examination. One of them secured 9 marks more than the other and his
marks was 56% of the sum of their marks. The marks obtained by them are
Pick.
A) 42,30	B) 42,31	C) 42,32	D) 42,33	E) None of these

Solution: Explanation:   Let their marks be (x+9) and x.   Then, x+9 = 56/100(x + 9 +x)   => 25(x+9)   => 14 (2x + 9)   => 3x = 99   => x = 33.   So, their marks are 42 and 33   Answer: Option 42,33
Answer: D
12 men and 18 boys working 7.5 minutes an hour complete a particular piece of work in 60 hours. If a boy’s work is half as efficient as a man’s work, how many boys will be needed to help 21 men to achieve twice the work in 50 hours working 9 minutes in an hour. Choose the correct choice from the following choices:
A) 28
B) 77
C) 42.
D) 99
E) 17

Solution: Explanation:   1 man is equivalent to 2 boys in work capacity. 12 men + 18 boys = 12 x 2 + 18 = 42 boys.   Let the required number of boys be x. So Total number of people doing work = 21 men x 2 (according to work capacity) + x boys.   Taking respective ratios as required:   Given:   => Hours 50:60   => Minutes per hour 9: 15/2   => Work 1:2   => People: 42: 42 + x   => 50 x 9 x 1 x (42+x) = 60 x 15/2 x 2 x 42   => 42 +x = 84   x = 42   ANSWER:42.
Answer: C
Find a sum for first 5 prime number's?	Choose the correct choice from the following choices:
A) 24  B) 28  C) 30  D) 32  E) 34

Solution: Required sum = (2 + 3 + 5 + 7 + 11)= 
(2 + 3 + 5 + 7 + 11) = 28
28   Note: 1 is not a prime number   Option 28
Answer: B
The number of new words that can be formed by rearranging the letters of the word 'OF' is
Select.
A) 5 B) 8 C) 1 D) 3 E) 4

Solution: Explanation:   Number of words which can be formed = 2! - 1 = 2- 1= 
2- 1 = 1
1.   Answer: 1
Answer: C
A student travels from his house to school at 10 km/hr and reaches school 2 hours late. The next day he travels 15 km/hr and reaches school 1 hour early. What is the distance between his house and the school?  Choose the correct choice from the following options.
A) 60	B) 70	C) 80	D) 90	E) 100

Solution: Let x be the distance from his house to the school.   x/10 = x/15 + 3   6x = 4x + 180   2x = 180   x = 90 km   The answer is 90.
Answer: D
How many positive integers less than 7,000 are there in which the sum of the digits equals 5?  Select the correct option:
A) 52	B) 54	C) 56	D) 58	E) 60

Solution: Basically, the question asks how many 4 digit numbers (including those in the form 0XXX, 00XX, and 000X) have digits which add up to 5. Think about the question this way: we know that there is a total of 5 to be spread among the 4 digits, we just have to determine the number of ways it can be spread.   Let X represent a sum of 1, and | represent a seperator between two digits. As a result, we will have 5 X's (digits add up to the 5), and 3 |'s (3 digit seperators).   So, for example:   XX|X|X|X = 2111   ||XXX|XX = 0032   etc.   There are 8C3 ways to determine where to place the separators. Hence, the answer is 8C3 = 56.   56
Answer: C
The value of a scooter depreciates in such a way that its value of the end of each year is 3/4 of its value of the beginning of the same year. If the initial value of the scooter is Rs.40,000, what is the value at the end of 1 year?	Pick one:  A) 3277  B) 2977  C) 30000  D) 6077  E) 17112

Solution: Explanation: 40,000*(3/4)^1   Answer:30000
Answer: C
For integers x, y, and z, if (3^x) (4^y) (5^z) = 13,107,200,000 and x + y + z = 16, what is the value of xy/z?	Choose the correct answer:  A) undefined  B) 0  C) 3  D) 5  E) 7

Solution: The number 13,107,200,000 is not divisible by 3. (We can verify this by adding the digits of the number to see that the sum is not a multiple of 3.)   Thus x = 0 and xy/z = 0.   The answer is 0.
Answer: B
A does a work in 20 days and B does the same work in 30 days. In how many days they together will do the same work ?	Choose the correct choice from the following:
A) 5 days
B) 6 days
C) 9 days
D) 12 days
E) None of these

Solution: Explanation:   Firstly we will find 1 day work of both A and B, then by adding we can get collective days for them,   So,   A's 1 day work = 1/20   B's 1 day work = 1/30   (A+B)'s 1 day work =   (1/20+1/30)=1/12   So together they can complete work in 12 days.   Answer: 12 days
Answer: D
A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? Select the correct option:	A) 246	B) 240	C) 88	D) 76	E) 121

Solution: Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train = (15 x 20)m = 300 m. Let the length of the platform be x meters. Then, (x + 300)/36 = 15 ==> x + 300 = 540 ==> x = 240 m.   Answer:240
Answer: B
A rectangular grass field is 75 m * 55 m, it has a path of 2.5 m wide all round it on the outside. Find the area of the path and the cost of constructing it at Rs.6 per sq m?
Choose the correct choice from the following choices.
A) 675, Rs.1350
B) 575, Rs.1350
C) 1350, Rs.675
D) 1450, Rs.775
E) 675, Rs.4050

Solution: Area = (l + b +2d) 2d   = (75 + 55 +2.5 * 2) 2*2.5 => 675   675 * 6 = Rs.4050   ANSW675, Rs.4050R:675, Rs.4050
Answer: E
If 4 (A's capital) = 8 (B's capital) = 10 (C's capital). Then the ratio of their capitals is?	Choose the most appropriate option.
A) 10:5:5 B) 10:5:8 C) 10:5:2 D) 10:5:4 E) 10:5:1

Solution: 4A = 8B = 10 C   A:B:C = 1/4:1/8:1/10   = 10:5:4   Answer: 10:5:4
Answer: D
Frank the Fencemaker needs to fence in a rectangular yard. He fences in the entire yard, except for one full side of the yard, which equals 40 feet. The yard has an area of 200 square feet. How many feet offence does Frank use?	Choose the correct choice from the following.
A) 14  B) 47  C) 50  D) 180  E) 240

Solution: Area = Length x Breadth   200 = 40 x Breadth   So, Breadth = 5 Units   Fencing required is -   Breadth + Breadth + Length    5 + 5 + 40= 
 5 + 5 + 40 = 50
> 50 feet   Answer must be (50) 50
Answer: C
If n is an even negative integer, which of the following must then be an odd positive integer? Choices
A) 2n B) -2n + 1 C) -(n^2) D) 2n - 1 E) n^3

Solution: Answer: -2n + 1   A: 2n = even negative   -2n + 1: -2n + 1 = odd positive   C: -(n^2) = even negative   D: 2n - 1 = odd negative   E: n^3 = odd negative   Answer: -2n + 1
Answer: B
A store purchased a pair of pants for $210 and was selling it at a price that equaled the purchase price of the pants plus a markup that was 25 percent of the selling price. After some time a store owner decided to decrease the selling price by 20 percent. What was the store's gross profit on this sale?
Choose the correct choice from the following options:
A) $14
B) $2
C) $10
D) $6
E) $8

Solution: Sale Price(SP) = 210 + Markup(MP)   --> Mp = SP-210   and given MP=SP/4 ( 25% is 1/4th)   so SP/4= SP-210   3SP/4= 210   SP=280   Now a discount of 20% is given so NEW SP is .8 *280= 
.8 *280 = 224
224   Profit=224-210= 
224-210 = 14
14   $14nswer is $14
Answer: A
There were two clock one is getting slow by two minutes/hr and another one is gaining 1 minute every hour and exactly after how many hours there two clock has a 1hr difference.
Choose the correct choice.
A) 10 Hours B) 15 Hours C) 20 Hours D) 25 Hours E) 28 Hours

Solution: Assume x as the current time.   After an hour:   Time in Clock1=x+58mins   Time in Clock2=x+61= 
+61 = 61
61-58= 
61-58 = 3
3 mins   3 mins of time difference happens in 1 hour   therefore 60 min (i.e. 1 hour) of time diffrence will happen in= 1/3 *60= 
1/3 *60 = 20
20 Hours   ANSWER:20 Hours
Answer: C
Jerry left a job paying $75,000 per year to accept a sales job paying $45,000 per year plus 15 percent commission. If each of his sales is for $750, what is the least number of sales he must make per year if he is not to lose money because of the change? Choose the correct choice from the following choices:	A) 40	B) 200	C) 266	D) 267	E) 600

Solution: In order not to lose money because of the change Jerry's total commission must beat least$75,000-$45,000=$30,000, so total sales must beat least$30,000/0.15=$200,000. Which means that he must makeat least$200,000/750=800/3=266.6 sales, so 267 sales.   Answer: 267.
Answer: D
Mathematics, physics, and chemistry books are stored on a library shelf that can accommodate 25 books. Currently, 20% of the shelf spots remain empty. There are twice as many mathematics books as physics books and the number of physics books is 4 greater than that of the chemistry books. Ricardo selects 1 book at random from the shelf, reads it in the library, and then returns it to the shelf. Then he again chooses 1 book at random from the shelf and checks it out in order to read at home. What is the probability Ricardo reads 1 book on mathematics and 1 on chemistry?  Pick one:
A) 3%	B) 6%	C) 12%	D) 20%	E) 24%

Solution: Shelf can accommodate 25 books but 20% of it is empty so there are in all 20 books.   If no of 12%hem books = x, number of Physics book = x+4, number of Math books = 2(x+4)   x + x+4 + 2(x+4) = 4x + 12 = 20   x = 2   12%hem books = 2, Phy books = 6, Math books = 12   Probability of picking a Math book = 12/20   Probability of picking a 12%hem book = 2/20   Total Probability = Pick Math first and then 12%hem + Pick 12%hem first and then Math   = (12/20) * (2/20) + (2/20) * (12/20) = 12/100 = 12%   Answer:12%
Answer: C
A number increased by 20% gives 600. The number is  Answers
A) 250  B) 400  C) 450  D) 500  E) 520

Solution: Formula = TOTAL=100% ,INCRESE = "+" 500ECREASE= "-"   A number means = 100 %   That same number increased by 20 % = 120 %   120 % -------> 600 (120 × 5 = 600)   100 % -------> 500 (100 × 5= 500)   500)
Answer: D
.
On dividing a number by 357, we get 38 as remainder. On dividing the same number 17, what will be the remainder ?	Choose the correct choice from the following answers: A) 0 B) 3 C) 4 D) 8 E) 11

Solution: Let x be the number and y be the quotient. Then,   x = 357 x y + 38   = (17 x 21 x y) + (17 x 2) + 4   = 17 x (21y + 2) + 4)   Required remainder = 4.   Answer: Option 4
Answer: C
The average age of a husband and a wife is 23 years when they were married five years ago but now the average age of the husband, wife and child is 18 years(the child was born during the interval). What is the present age of the child?  Pick one:
A) 13 years  B) 9 years  C) 6 years  D) 4 years  E) 5 years

Solution: 28 * 2= 
28 * 2 = 56
56   23 * 3= 
23 * 3 = 69
69   -----------   13 years   13 yearsnswer: 13 years
Answer: A
There are 8 digit mobile numbers. From that how many 8 digit mobile numbers can be formed if any digit can be repeated and 0 can also start the mobile number?	Choose the most appropriate option:  A) 9^2  B) 7^3  C) 10^8  D) 11^9  E) 12^3

Solution: Here the digits(0,1,2,3,4,5,6,7,8,9) can be repeated and 0 can also be used to start the mobile number. Hence, any of the 10 digits can be placed at each place of the 8 digit number.   10	10	10	10	10	10	10	10   Hence, required number of 8 digit mobile numbers   =10^8   10^8
Answer: C
Let y = 2m + x^2 and m = 5x + 1.
If m^2 = 36, then which of the following can be a value of 2y + 3m?	Choose the correct choice from the following choices:
A) 100  B) 130  C) 141  D) 142  E) 44

Solution: m^2 = 36 => m=6   6= 5x+1 => x=1   y= 2*6+1^2 = 13   2y+3m = 2*13+3*6= 
2*13+3*6 = 44
44   Answer : 44
Answer: E
A man whose speed is 4.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph, find his average speed for the total journey?	Choose the correct option.
A) 4 B) 5 C) 6 D) 7 E) 8

Solution: M = 45   S = 1.5   DS = 6   US = 3   4S = (2 * 6 * 3) /9= 
(2 * 6 * 3) /9 = 4
4   4nswer: 4
Answer: A
Find two numbers whose sum is 26 and whose product is 165.
Select.
A) 11 and 12	B) 11 and 13	C) 11 and 15	D) 11 and 16	E) 11 and 19

Solution: Let the two numbers be a and b and use the sum and product to write two equations with two unknowns   a + b = 26 and a b = 165   Solve the first equation for b   b = 26 - a   Substitute b in the equation a b = 165 by 26 - a   a (26 - a) = 165   Write the above equation in standard form   - a 2 + 26 a - 165 = 0   Solve the above equation for a   a = 11 and a = 15.   Use b = 26 - a to find b   when a = 11 , b = 15 and when a = 15 , b = 11.   The two numbers are 11 and 15.   Answer 11 and 15
Answer: C
Pure milk costs 3.60 per litre. A milkman adds water to 25 litres of pure milk and sells the mixture at 3 per litre. How many litres of water does he add?  Choices.
A) 2 litres  B) 5 litres  C) 7 litres  D) 11 litres  E) None of these

Solution: In mixture,   Quantity of pure milk /Quantity of water=3−0/3.6−3=3/0.6= 
3/0.6 = 5
5/1   Since in every 5 litres of milk, he adds 1 litre of water.   ∴ In every 25 litres of milk, he adds 5 litres of water.   Answer 5 litres
Answer: B
If y = x^2 + mx + n, y is minimum when x is:	Choose the most appropriate option:
A) m/n B) -m/n C) -m/2 D) -n/2 E) n/m

Solution: We're given the equation Y = X^2 + mX + n.   IF.. we use a simple Classic Quadratic....   m = 2   n = 1   Y = X^2 + 2X + 1   We can then go about finding the answer that yields the MINIMUM result when X = ...   Answer A: m/n = 2/1= 
2/1 = 2
2 --> 4+4+1= +9   Answer B: -m/n = -2/1 = -2 --> 4-4+1 = +1   Answer -m/2: -m/2 = -2/2 = -1 --> 1-2+1 = 0   Answer D: -n/2 = -1/2 -->(1/4)-1+1 = +1/4   Answer E: n/m = 1/2 --> (1/4)+1+1 = +2 1/4   From these results, we can see the minimum result:   -m/2
Answer: C
Find the value of 3 x [(3.6 x 0.48 x 2.50) / (0.12 x 0.09 x 0.5)]	Choose one:
A) 800 B) 500 C) 900 D) 1600 E) 2400

Solution: Answer   3 x [(3.6 x 0.48 x 2.50) / (0.12 x 0.09 x 0.5)]   = 3 x [(36 x 48 x 250) / (12 x 9 x 5)]   = 3 x 4 x 4 x 50 = 2400   Correct Option: 2400
Answer: E
A dishonest dealer professes to sell goods at the cost price but uses a weight of 850 grams per kg, what is his percent? Select.
A) 2%
B) 25%
C) 22%
D) 17.65%
E) 45%

Solution: 850 --- 150   100 --- ? => 17.65%   Answer:17.65%
Answer: D
The sale price sarees listed for Rs.340 after successive discount is 20% and 15% is? Choose the most appropriate option
A) 298	B) 231	C) 342	D) 876	E) 291

Solution: 340*(80/100)*(85/100)   = 231   Answer: 231
Answer: B
If 2|2 –w| = 5, what is the sum of all the possible values for w ?  Choices.
A) 1/2  B) 2  C) 5/2  D) 4  E) 5

Solution: if w<2, then 2-w=5/2; w=-1/2   if w>2 , then w-2=5/2; w=9/2   9/2-1/2=8/2= 
8/2 = 4
4=4
Answer: D
Let the polynomials be:
P1(x)=3x2−7x+5,
P2(x)=−5x2−4x+2,
P1(x)+P2(x)= Choose the correct choice from the following options
A) 2x2 + 11x - 7 B) -2x2 - 11x + 7 C) -2x2 - 11x + 6 D) 2x2 - 9x + 7 E) None of these

Solution: Solution:   P1(x)+P2(x)=(3x2−7x+5)+(−5x2−4x+2)=P1(x)+P2(x)=(3x2−7x+5)+(−5x2−4x+2)=   3x2−7x+5−5x2−4x+2=3x2−7x+5−5x2−4x+2=   −2x2−11x+7   Answer -2x2 - 11x + 7
Answer: B
5^100 is divided by 18. Then what is the remainder?  Choose the most appropriate option.
A) 10	B) 11	C) 13	D) 15	E) 16

Solution: Here N = 18=2×32   ϕ(18)=18(1−12)(1−13) = 6   So 56 when divided by 18, remainder is 1.   So we can write the given expression 5100=(56)16×54 = (1)16×54 = 52×52=7×7=49   Now 49 when divided by 18, remainder is 13.   13
Answer: C
If an investor puts $1000 in a savings account that earns 10 percent annual interest compounded semiannually, how much money will be in the account after one year?  Select:
A) $1100.25
B) $1100.75
C) $1101.25
D) $1101.75
E) $1102.50

Solution: 1.05*1.05*1000= 
1.05*1.05*1000 = 1_102.5
$1102.50   The answer is $1102.50.
Answer: E
A problem is given to three students whose chances of solving it are 1/2, 1/3 and 1/4 respectively. What is the probability that the problem will be solved?
Answers:
A) 3/0 B) 3/1 C) 3/4 D) 3/8 E) 3/40

Solution: Let A, B, C be the respective events of solving the problem and be the respective events of not solving the problem. Then A, B, 3/4 are independent events   are independent events   Now, P(A) = 1/2 , P(B) = 1/3 and P(3/4)=1/4   P( none solves the problem) = P(not A) and (not B) and (not 3/4)   =   = =   =   Hence, P(the problem will be solved) = 1 - P(none solves the problem)   Answer: 3/4) 3/4
Answer: C
If x is real, find the maximum value of the expression -2x^2 + 11x + 13. Choices:  A) 16.125  B) 20.125  C) 24.125  D) 28.125  E) 32.125

Solution: This is an equation of a downward facing parabola.   The maximum value is the top point of the parabola.   -2x^2+11x+13 = (-2x+13)(x+1)   The roots are 13/2 and -1.   The maximum value must be when x is halfway between these two points.   x = 2.75   The maximum value is -2(2.75)^2+11(2.75)+13 = 28.125   The answer is 28.125.
Answer: D
A family of 7 queue to get ice cream from a an ice cream van. What is the probability that the father will be standing right in front of the mother in the queue?
Pick one
A) 5%
B) 10%
C) 15%
D) 21%
E) 25%

Solution: Possible Sitting position is 7! = 120   Father standing next to mother is 7 Combination 2   =7!/2!(7-2)!   =5040/2(120)   =5040/240= 
5040/240 = 21
21   Answer= 21%
Answer: D
Find the area of trapezium whose parallel sides are 24 cm and 18 cm long, and the distance between them is 15 cm.  Pick:
A) 227	B) 299	C) 315	D) 161	E) 212

Solution: Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them)   = 1/2 (24 + 18) * (15)   = 315 cm2   Answer: 315
Answer: C
In a group of 800 people, 3/5 play at least one instrument, 96 play two or more. What is the probability that one student play exactly one instrument?
Answers:	A) 2/125	B) 12/25	C) C)2/25	D) 3/25	E) 1/5

Solution: P(playing 2 or more instruments) = 96/800 = 3/25.   Then, the probability of playing exactly one instrument is given by:   P(playing 1 or more instruments) - P(playing 2 or more instruments) = 3/5 - 3/25 = 12/25.   Answer 12/25.
Answer: B
The amount of principal Rs.8000 at compound interest at the ratio of 5% p.a. for 5 years is Choose the correct answer
A) s.9621
B) s.6921
C) s.10210
D) s.6261
E) s.6361

Solution: c.i=p(1+r/100)^n   =8000(1+5/100)^5   =Rs10210   ANSWER:s.10210
Answer: C
Two trains running in opposite directions cross a man standing on the platform in 37 seconds and 27 seconds respectively and they cross each other in 29 seconds. The ratio of their speeds is:	Choose the correct choice from the following answers: A) 3 : 1 B) 3 : 2 C) 3 : 8 D) 3 : 25 E) 1 : 4

Solution: Let the speeds of the two trains be x m/sec and y m/sec respectively. Then, length of the first train = 37 x meters, and length of the second train = 27 y meters. (37 x + 27 y) / (x + y) = 29==>   37 x + 27 y = 29 x + 29 y ==> 8 x = 2 y ==> x/y = 2/8 = 1/4   Answer: Option 1 : 4
Answer: E
If a man lost 4% by selling oranges at the rate of 12 a rupee at how many a rupee must he sell them to gain 44%?
Select the correct option
A) 1
B) 8
C) 2
D) 7
E) 4

Solution: 96% ---- 12   144% ---- ?     96/144 * 12= 
  96/144 * 12 = 8
8   Answer: 8
Answer: B
Working alone, machine X can manufacture 1,200 nails in 12 hours. Working together, machines X and Y can manufacture 1,200 nails in 6 hours. How many hours does it take machine Y to manufacture 1,200 nails working alone?
Choose the correct choice from the following
A) 3 9/17	B) 5 1/3	C) 7	D) 10 1/5	E) 12

Solution: rate of machine x = 1200/12   (1200/12 + y)6=1200   y=100   100 * t = 1200   t=12   12.
Answer: E
A store sells seven different kinds of shirts. If we want to buy two different kinds of shirts, how many possible combinations of two shirts can we buy? Choose the correct choice from the following answers.
A) 21	B) 22	C) 23	D) 24	E) 25

Solution: 7C2=21.   The answer is 21.
Answer: A
In how many ways can a four-letter password be chosen, using the letters A, B, C, D, E, and/or F, such that at least one letter is repeated within the password?
Select the correct option.
A) 720	B) 864	C) 900	D) 936	E) 1,296

Solution: Total number of four letter passwords = 6*6*6*6= 
6*6*6*6 = 1_296
1296 ------(1)   Total number of passwords in which no letter repeats= 6C4*4!= 15*24= 
15*24 = 360
360------(2)   therefore required value= (1)-(2)= 1296-360= 
1296-360 = 936
936   ANSWER:936
Answer: D
In a mixture of milk and water, the proportion of milk by weight was 80%. If, in a 180 gm mixture, 36 gms of pure milk is added, what would be the percentage of milk in the mixture formed? Choose the correct answer
A) 83.39%
B) 83.83%
C) 83.93%
D) 82.33%
E) 83.33%

Solution: Percentage of milk in the mixture formed   = [80/100 (180) + 36] / (180 + 36) * 100% = (144 + 36)/216 * 100%   = 5/6 * 100% = 83.33%.   Answer:83.33%
Answer: E
Three persons invested Rs.9000 in a joint business. The second person invested Rs.1000 more than the first and the third Rs.1000 more than second. After two years, they gained Rs.5400. How much third person will get? Choose the correct choice from the following choices:
A) 2400	B) 2499	C) 2779	D) 2729	E) 2791

Solution: First persons investment = x   Second persons investment = x + 1000   Third persons investments = x + 2000   x + x + 1000 + x + 2000 = 9000   3x = 6000   x = 2000   Ratio = 2000 : 3000 : 4000   2:3:4   4/9 * 54000 = 2400   2400nawer:2400
Answer: A
10% of the inhabitants of a village having died of cholera, a panic set in, during which 25% of the remaining inhabitants left the village. The population is then reduced to 4050. Find the number of original inhabitants. Select
A) 5000
B) 6000
C) 7000
D) 8000
E) None of these

Solution: Let the total number of original inhabitants be x. Then,   (100 – 25)% of (100 –10)% of x = 4050   ⇒ (75/100×90/100×x) = 4050 ⇒ 27⁄40x = 4050   ⇒ x = 4050×40/27=6000   ∴ Number of original inhabitants = 6000.   Answer 6000
Answer: B