MU-NLPC/Calc-aqua_rat huggingface dataset:
How many kg of sugar costing Rs. 9/kg must be mixed with 27kg of sugar costing Rs. 7/ kg so that there may be a gain of 10% the mixture at Rs. 9.24 per kg?	Choose the correct choice from the following choices: A) 51 B) 56 C) 58 D) 62 E) 63

Solution: Selling Price(SP) of 1 kg mixture= Rs. 9.24   Profit = 10%   Cost Price(CP) of 1 kg mixture =100(100+Profit%)×SP   =100(100+10)×9.24=100110×9.24=92.411= Rs.8.4   By rule of alligation,   CP of 1 kg sugar of 1st kind	CP of 1 kg sugar of 2nd kind   Rs. 9	Rs. 7   Mean Price   Rs.8.4   8.4 - 7= 
8.4 - 7 = 1.4
1.4	9 - 8.4= 0.6   i.e., to get a cost price of 8.4, the sugars of kind1 and kind2 should be mixed in the ratio 1.4 : 0.6 = 14 : 6 = 7 : 3   Suppose x   kg of kind1 sugar is mixed with 27 kg of kind2 sugar.   then x : 27 = 7 : 3   ⇒3x=27×7⇒x=9×7=63   63
Answer: E
By how much does the larger root of the equation 2q^2+5q = 12 exceed the smaller root?	Choose the correct choice from the following choices:	A) 5/2	B) 10/3	C) 7/2	D) 14/3	E) 11/2

Solution: For 2q^2+5q = 12 Roots are [-5 + sqrt(25 + 96)]/4 OR [-5 - sqrt(25 + 96)]/4   = 1.5 OR -4   Hence larger root 1.5 is  1.5 - (-4)= 
 1.5 - (-4) = 5.5
5.5= 11/2 greater than smaller root (-4).   Hence option (11/2).
Answer: E
A basketball player succeeds with 80% of her free throws. If she has a set of three free throws, what is the probability that she succeeds at least once?
Choose the correct choice from the following choices:
A) 0.972  B) 0.978  C) 0.984  D) 0.992  E) 0.998

Solution: P(missing all 3 free throws) = 0.2^3 = 0.008   P(succeeding at least once) = 1 - 0.008= 
1 - 0.008 = 0.992
0.992   The answer is 0.992.
Answer: D
What is x if x + 2y = 10 and y = 4?	Select:  A) A)10  B) B)8  C) C)6  D) D)4  E) E)2

Solution: x = 10 - 2y   x = 10 - 8.= 
10 - 8. = 2
2   Answer : 2
Answer: E
A batsman scored 150runs which included 5 boundaries and 5 sixes. What percent of his total score did he make by running between the wickets.	Options.
A) 40%
B) 50%
C) 60%
D) 66.66%
E) 70%

Solution: Explanation:   Number of runs made by running = 150 - (5 x 4 + 5 x 6)   = 150 - (50)= 
150 - (50) = 100
100   Now, we need to calculate 100 is what percent of 150.=> 100/150 * 100 = 66.66 %   Option 66.66%
Answer: D
If shares of two persons in profits are Rs.400 and Rs.600 then ratio of their capitals is Select:	A) 3:4	B) 2:3	C) 4:3	D) 1:3	E) 1:2

Solution: profit=time*capital   so 400:600=2:3   ANSWER:2:3
Answer: B
If the cost of x metres of wire is d rupees, then what is the cost of y metres of wire at the same rate?
Choices:
A) Rs.(yd/U)
B) Rs.(yI/x)
C) Rs.(Od/x)
D) Rs.(yd/x)
E) Rs.(yd/D)

Solution: Cost of x metres = Rs. d.   Cost of 1 metre = Rs. d   x   Cost of y metres = Rs. d	. y = Rs. yd	.   x	x   View Answer Rs.(yd/x)iscuss in Forum   Answer:Rs.(yd/x)
Answer: D
An investor receives a total combined return of 7% on his two different investments. On his $10,000 investment he receives a return of 6%. What is the return on his $20,000 investment?  Choose the correct choice from the following:
A) 7.25%
B) 7.5%
C) 8%
D) 8.5%
E) 9%

Solution: Total investment = $30000   on which he receives 7% = 2100   now,   on his $10000 he receives 6% = $600   remaining $1500   which is (1500/20000)*100= 
(1500/20000)*100 = 15/2 = around 7.5
7.5   ANSWER:7.5%
Answer: B
A train 320 m in length crosses a telegraph post in 16 seconds. The speed of the train is?  Pick.
A) 22 kmph  B) 77 kmph  C) 54 kmph  D) 72 kmph  E) 88 kmph

Solution: S = 320/16 * 18/5= 
320/16 * 18/5 = 72
72 kmph   Answer:72 kmph
Answer: D
P is able to do a piece of work in 5 days and Q can do the same work in 10 days. If they can work together for 3 days, what is the fraction of work completed?  Options.
A) 13/10  B) 4/5  C) 11/10  D) 7/10  E) 9/10

Solution: 9/10xplanation :   Amount of work P can do in 1 day = 1/5   Amount of work Q can do in 1 day = 1/10   Amount of work P and Q can do in 1 day = 1/5 + 1/10 = 3/10   Amount of work P and Q can together do in 3 days = 3 × (3/10) = 9/10   Answer : Option 9/10
Answer: E
If 50 percent of X is 25 percent of Y, then what is the relation between X and Y?  Choose the correct choice from the following answers:	A) X=Y	B) 2X=Y	C) X=2Y	D) 1	E) NONE OF ABOVE

Solution: 50/100(X) = 25/100(Y)   2X=Y..   Option 2X=Y.
Answer: B
In a game of billiards, A can give B 20 points in 60 and he can give C 30 points in 60. How many points can B give C in a game of 100?  Choose the correct choice from the following:
A) 22
B) 28
C) 025
D) 20
E) 11

Solution: A scores 60 while B score 40 and C scores 30.   The number of points that C scores when B scores 100 = (100 * 30)/40 = 25 * 3= 
25 * 3 = 75
75.   In a game of 100 points, B gives (100 - 75)= 
(100 - 75) = 25
25 points to C.   Answer: 025
Answer: C
A dozen bananas and 10 pounds of oranges are currently at the same price. If the price of a dozen bananas rises by 20 percent and the price of oranges rises by 4 %. How much more will it cost to buy a dozen bananas and 10 pounds of oranges. Choose the correct choice from the following answers.
A) 24%	B) 22%	C) 23%	D) 25%	E) 29%

Solution: Say currently both a dozen bananas and 10 pounds of oranges cost $100 (they are at the same price). So, to buy a dozen bananas and 10 pounds of oranges we need $200.   After the increase, the price of a dozen bananas will be $120 and the price of 10 pounds of oranges will be $104. So after the increase, to buy a dozen bananas and 10 pounds of oranges we'll need $224.   Increase = 24%.   24%nswer: 24%.
Answer: A
What is the rate percent when the simple interest on Rs.4000 amount to Rs.640 in 2 Years?  Choose the correct choice from the following answers
A) 8.2% B) 8% C) 8.5% D) 9% E) 9.5%

Solution: Interest for 1 year = 640/2= 
640/2 = 320
320   Interest on Rs 4000 p/a= 320   interest rate = 320/4000*100= 
320/4000*100 = 8
8%   Answer : 8%
Answer: B
If x is divisible by 20, 14, and 70, which of the following must be the least multiple of x?
Choose the correct choice from the following options: A) 70 B) 140 C) 210 D) 350 E) 700

Solution: We are looking for the LCM (which is not 0) of 20 = 2^2*5, 70 = 2*7*5, 14 = 2*7:   2^2 * 5 * 7 = 140   The answer is 140.
Answer: B
The longest side of a triangle is 3 times the shortest side and the third side is 2 cm shorter than the longest side. If the perimeter of the triangle is at least 61 cm,What is the minimum length of the shortest side?	Answers: A) 8cm B) 9cm C) 10cm D) 11cm E) 12cm

Solution: let the shortest measurement be x cm   then the largest side will be 3x cm   and the third side will be (3x-2)cm   now according to the problem   x+3x+3x-2 >=61   7x-2 >= 61   7x >= 63   therefore x>=9cm   ANSWER:9cm
Answer: B
Let the function T(n) represent the product of the first n prime numbers, where n > 0. If x = T(n) + 1, which of the following must be true?
(i) x is always odd
(ii) x is always prime
(iii) x is never the square of an integer
Choose one.
A) ii only B) iii only C) i and ii only D) i and iii only E) ii and iii only

Solution: T(n) is always even, because the first prime is 2 and no matter what n is, 2 always will be a divisor of T(n). Thus, T(n) + 1 = even + 1 = odd. So, (i) is always true.   Now, use logic:   If (ii) is true (so if x is always prime), then (iii) must automatically be true: no prime is the square of an integer. So, the correct answer must be i only; i, ii, and iii only; or i and iii only. since onlyi and iii onlyis among the options, then it must be true.   Or, since (i) is always true, then from options the answer must be either C or D. C cannot be correct because if (ii) is true, then so must be (iii). Thus only D remains.   Answer: i and iii only.
Answer: D
A rower can row upstream at 15 kph and downstream at 35 kph. What is the speed of the rower in still water? Choose the correct option:
A) 22  B) 23  C) 24  D) 25  E) 26

Solution: Let V be the rower's speed in still water.   Let S be the speed of the current in the stream   V-S = 15   V+S = 35   When we add the two equations, we get: 2V = 50   Then V = 25 kph.   The answer is 25.
Answer: D
A university cafeteria offers 5 flavors of pizza - pork,pepperoni, chicken, Hawaiian and vegetarian. If a customer has an option (but not the obligation) to add extra cheese, mushrooms or both to any kind of pizza, how many different pizza varieties are available ?	Select: A) 4 B) 8 C) 12 D) 25 E) 32

Solution: 5 flavours * 5 choices = 5C1*5C1 = 5*5= 
5*5 = 25
25=25
Answer: D
A man goes from A to B at a speed of 20 kmph and comes back to A at a speed of 30 kmph. Find his average speed for the entire journey?
Choose the correct choice from the following options
A) 24 kmph	B) 22 kmph	C) 23 kmph	D) 21 kmph	E) 25 kmph

Solution: 24 kmph   24 kmph   Distance from 24 kmph and B be 'd'   24 kmphverage Speed = total distance/total time   24 kmphverage Speed = (2d)/[(d/20) + (d/30)]   = (2d)/[5d/60) => 24 kmph.
Answer: A
A certain car can travel 40 kilometers on a liter of fuel. If the fuel tank’s contents decrease by 3.9 gallons over a period of 5.7 hours as the car moves at a constant speed, how fast is the car moving, in miles per hour? (1 gallon = 3.8 liters; 1 mile = 1.6 kilometers)
Choose the correct choice:
A) 52 B) 65 C) 78 D) 91 E) 104

Solution: Fuel used 3.9 gallons ;convert to liters--> 3.9 x 3.8 liters   Time = 5.7 hours   1 mile = 1.6 kilometers ;convert to miles--> 1km = 1/1.6 mile   Speed (km/hour)  --  1= 
  --  1 = 1
1/1.6 mile   Speed (km/hour)= D/T = 40 (km*) x 3.9 x 3.8 / 5.7   replace (km*) to miles ; multiply by 1/1.6 mile   Speed (miles/hour)= 40 x 3.9 x 3.8 / 5.7 x 1.6 = 78 miles/hour   Ans :C   PS :i felt the factors were easy to cancel out ,so didn't require much rounding off   = 40 x 3.9 x 3.8 / 5.7 x 1.6   = 65   65
Answer: B
An area of a circularplace is 17 hectares. Find the cost of fencing it at the rate of Rs. 3 permeter approximately. Choose the correct choice from the following options:
A) Rs. 4000  B) Rs. 4450  C) Rs. 4457  D) Rs. 4560  E) Rs. 5457

Solution: Area = (17.56 x 10000) m2= 175600 m2.   ΠR2 = 175600 ⇔ (R)2 = (175600 x (7/22)) ⇔ R = 236.37 m.   Circumference = 2ΠR = (2 x (22/7) x 236.37) m =1485.78 m.   Cost of fencing = Rs. (1485.78 x 3) = Rs. 4457.   Rs. 4457
Answer: C
A 12 month project had a total budget of $18,000. After five months, the project had spent $6,400. At this point, how much was the project under budget?
Pick one.
A) $1000	B) $1100	C) $1200	D) $1300	E) $1400

Solution: Each month, the project should spend $18,000 / 12 = $1500.   In 5 months, the project should spend 5*$1500=$7500.   The project is under budget by $7500 - $6400   5* 1500= 
  5* 1500 = 7_500
$7500.   The project is under budget by $7500 - $6400 = $1100.   The answer is $1100.  7500 -  6400= 
  7500 -  6400 = 1_100
$1100.   The answer is $1100.
Answer: B
Dana borrows 6500 pounds annually for her college education. If Dana gives her parents 3% of that amount back each month, how much will she still owe her parents after four years of college?	Choose one
A) 16240	B) 16340	C) 16440	D) 16540	E) 16640

Solution: dana borrows 6500 and returns 3% per month.   so returns 195 per month. and 2340 per year.   so dana owes  6500-2340= 
 6500-2340 = 4_160
4160 per year.   after 4 years she will owe 16640.   Ans (16640)
Answer: E
A work could be completed in 100days by x workers. However, due to the absence of 10workers, it was completed in 110days. The original no.of workers was:	Choose the correct choice from the following options:
A) 90
B) 100
C) 110
D) 134
E) 154

Solution: sax Letlheo g alnumberofworkers hex   x workers can do the wor - 100 days   (x — 10) workers can do the work in 110 days   4 100x 1u1x— 10)   1100 Q x 110   110
Answer: C
When m is divided by 9, the remainder is 4. When m is divided by 13, the remainder is 10. If 1 < m < 200, what is the greatest possible value of m?	Choose one:
A) 47
B) 65
C) 103
D) 117
E) 166

Solution: Looking at the choices, options BD can be eliminated as they are divisible by 13   Starting from the highest number 164;   166 = 162 + 4 (162 divisible by 9)   166 = 156 + 10 (156 divisible by 13)   it fits the result   Answer = 166
Answer: E
Tough and Tricky questions: Exponents.
If a and b are positive integers and x = 24^a and y = 9^b, which of the following is a possible units digit of xy?
Pick: A) 1 B) 6 C) 5 D) 7 E) 8

Solution: Only Units digit of X and Y contribute to the Units digit of XY.   Finding all values ofXfor positive values ofa   When,   a=1; X=24   a=2; X=576   a=3; X=13824........ Units digit repeat in a cycle of 4,6,4,6......   Similarly, Finding all values ofYfor positive values ofb   When,   b=1; Y=9   b=2; Y= 81   b=3; Y= 729....... Units digit repeat in cycle of 9,1,9,1....   So, possible value of Units digit of XY can be found by considering all possibilities of Units digit of X and Y   When X=4 and Y=9: Units digit of XY = 6   When X=4 and Y=1: Units digit of XY = 4   When X=6 and Y=9: Units digit of XY = 4   When X=6 and Y=1: Units digit of XY = 6   Only two possibilities for Units digit of XY i.e. 4 and 6.   Only 6 is given in answer choices, therefore answer is 6
Answer: B
Alex has $246,713 dollars in his savings account. What is the least amount of money (in whole number of dollars) that he must remove from his account if he wants to split this money evenly among his 6 children?
Choices:  A) $1  B) $2  C) $3  D) $4  E) $5

Solution: In order to divide the sum into 6 parts, the amount must be divisible by 6.   Divisibility rule of 6: A number is divisible by 6 if it is divisible by both 2 and 3   Divisibility rule of 3: A number is divisible by 3 if the sum of the digits is divisible by 3   We need to make this number even in order for it to be divisible by 2.   Sum of digits 246,713 = 23 and 21 is divisible by 3. Subtracting 2 does not yields an even number.   Sum of digits 246,713 = 23 and 18 is divisible by 3. Subtracting 5 yields an even number.   Hence, we need to subtract 5 from this number for it to be divisible by 6.   Correct Option: $5
Answer: E
An inspector rejects 0.008% of the meters as defective. How many will be examine to project ?	Choose the correct choice from the following choices:	A) 2000	B) 230	C) 2700	D) 25000	E) 250

Solution: Let the number of meters to be examined be x.   Then, 0.008% of x =2   [(8/1000)*(1/100)*x] = 2   x = [(2*100*1000)/8= 
(2*100*1000)/8 = 25_000
25000   Answer is 25000.
Answer: D
In a school of 850 boys, 44% of Muslims, 32% Hindus, 10% Sikhs and the remaining of other communities. How many belonged to the other communities?  Choose the correct option:  A) A)125  B) B)119  C) C)153  D) D)721  E) E)159

Solution: 44 + 32 + 10= 
44 + 32 + 10 = 86
86%   100 – 84= 14%    850 * 14/100= 
 850 * 14/100 = 119
119   Answer:119
Answer: B
An office supply store stocks two sizes of notebooks, each in six colors: orange, blue, green, yellow, red, or pink. The store packs the notebooks in packages that contain either 4 notebooks of the same size and the same color or 4 notebooks of the same size and of 4 different colors. If the order in which the colors are packed is not considered, how many different packages of the types described above are possible? Choose the correct choice from the following answers:  A) 20  B) 24  C) 32  D) 36  E) 42

Solution: First let's consider the small notebooks.   There are 6 ways to choose notebooks of the same color.   The number of ways to choose four notebooks with different colors is 6C4=15.   There are 21 different packages we can make with the small notebooks.   We can use the same process to find 21 different packages with large notebooks.   The total number of different packages is 42.   The answer is 42.
Answer: E
On the x-y coordinate plane there is a parabola, y=x(6-x). Which of the following points is in the region that is enclosed by this parabola and the x-axis?
I. (1, 1) II. (4, 4) III. (6, 6)  Choices.
A) I only B) II only C) III only D) I and II E) I, II, and III

Solution: Since co-efficient of x^2 is negative, the parabola will be downward facing. So the parabola and the x axis will enclose some points where the y-values of the parabola are positive.   When x = 1, y = 5 lies on the parabola, so (1, 1) will be enclosed by the parabola and x axis.   When x = 4, y = 8 lies on the parabola, so (4, 4) will be enclosed by the parabola and x axis.   When x = 6, y = 0 lies on the parabola, so (6, 6) will not be enclosed by the parabola and x axis.   The answer is I and II.
Answer: D
Bradley owns b video game cartridges. If Bradley’s total is one-fifth the total owned by Andrew and four times the total owned by Charlie, how many video game cartridges do the three of them own altogether, in terms of b?	Choose the correct option:
A) 16b / 3	B) 17b / 4	C) 13b / 4	D) 19b / 12	E) 25b / 4

Solution: b = Bradley’s total   5b = Andrew’s total   b/4 = Charlie’s total   The total number of cartridges is:   b + 5b+ b/4 = (4b + 20b + b) / 4 = 25b / 4   The answer is 25b / 4.
Answer: E
The length of a rectangle is halved, while its breadth is tripled. Watis the % change in area?
Select
A) 30%	B) 40%	C) 50%	D) 60%	E) 65%

Solution: Let original length = x and original breadth = y.   Original area = xy.   New length = x .   2   New breadth = 3y.   New area = x x 3y = 3 xy.   2 2   Increase % = 1 xy x 1 x 100 % = 50%.   2 xy   50%
Answer: C
♠n denotes the number obtained when n is rounded to the nearest tenth. For example ♠4.31 = 4.3
♠0.098 - ♠1.125 =  Choose the correct choice from the following answers: A) -1.1 B) 1.04 C) -1.05 D) -1.0 E) -0.1

Solution: ♠0.098 - ♠1.125 =   0.1 - 1.1 = -1.1   -1.1nswer : -1.1
Answer: A
A customer pays 20 dollars for a coffee maker after a discount of 20 dollars
What is the original price of the coffee maker?  Options.
A) 50	B) 40	C) 70	D) 60	E) 20

Solution: Let x be the original price.   x - 20 = 20   x - 20 + 20 = 20 + 20   x + 0 = 40   x = 40   Answer is 40
Answer: B
John makes $60 a week from his job. He earns a raise and now makes $90 a week. What is the % increase?
Choose the correct option
A) 16%	B) 50%	C) 17%	D) 17.61%	E) 17.56%

Solution: Increase = (30/60)*100 = (3/6)*100= 
(3/6)*100 = 50
50%.   50%
Answer: B
How much space, in cubic units, is left vacant when maximum number of 4x4x4 cubes are fitted in a rectangular box measuring 10x12x16 ?  Choose the correct answer:
A) 0
B) 36
C) 180
D) 216
E) 384

Solution: No of cubes that can be accommodated in box = (10*12*16)/(4*4*4)   12*16 in numerator can be perfectly divided by 4*4 in denominator.   side with length 10 can't be perfectly divided by 4 and hence is the limiting factor. Closet multiple of 4 less that 10 is 8. so vacant area in cube =   =12*16*(10-8)   =12*16*2= 
12*16*2 = 384
384   ANSW384R:384
Answer: E
The function f is defined for all positive integers n by the following rule: f(n) is the product of the distinct prime factors of n. If f(n) < 30 and n is not prime, what is the greatest possible value of f(n)?	Choose the correct choice
A) 28
B) 26
C) 20
D) 18
E) 15

Solution: Since we need the largest value of f (n), we will start with the largest option.   Option A: 28 = 2*2*7. This is not a product of distinct prime numbers. Hence incorrect   Option B: 26 = 2*13. This is a product of distinct prime numbers.   Rest all the options are smaller that 26.   Correct Option: 26
Answer: B
On dividing a certain number by 5, 7 and 8 successively, the remainders obtained are 2, 3 and 4 respectively. When the order of division is reversed and the number is successively divided by 8, 7 and 5, the respective remainders Q will be:[/b]
Choose the most appropriate option.
A) Q=3, 3, 2 B) Q=3, 4, 2 C) Q=5, 4, 3 D) Q=5, 5, 2 E) 6, 4, 3

Solution: Let the original number be X. Then by the successive dividing we have followings :   X=5A+2   A=7B+3   B5 +2= 
5 +2 = 7
7B+3   B=8C+4.   So we have A=7*(8C+4)+3=7*8C+31, and X=5*(7*8C + 31)+2 = 5*7*8C + 157.   Now by dividing X by 8, 7, 5 successively we have followings :   X=8*(5*7C+19)+5   5*7C+19=7*(5C+2) + 5   5C+2=5C+2.   The remainders are, therefore, 5, 5, 2.   The answer is (Q=5, 5, 2).
Answer: D
One-fourth of a tank holds 135 litres of water. What part of the tank is full if it contains 180 litres of water?
Select the correct option
A) 1/2
B) 1/3
C) 1/5
D) 1/6
E) 1/4

Solution: 135 litres = 1/4 of tank   180 litres = 1/4 x 180/135 = 1/3   Answer 1/3.
Answer: B
The average age of husband, wife and their child 3 years ago was 27 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is? Choose the correct choice from the following options:	A) 87 years	B) 40 years	C) 19 years	D) 16 years	E) 18 years

Solution: Sum of the present ages of husband, wife and child   = (27 * 3 + 3 * 3)= 
(27 * 3 + 3 * 3) = 90
90 years.   Sum of the present age of wife and child= (20 * 2 + 5 * 2)= 
(20 * 2 + 5 * 2) = 50
50 years.   Husband's present age= (90 - 50)= 
(90 - 50) = 40
40 years.   Answer: 40 years
Answer: B
15 men take 21 days of 8 hours each to do a piece of work. How many days of 6 hours each would 21 women take to do the same. If 3 women do as much work as 2 men? Choose the most appropriate option:  A) 33  B) 77  C) 30  D) 88  E) 12

Solution: 3W = 2M   15M ------ 21 * 8 hours   21 W ------ x * 6 hours   14 M ------ x * 6   15 * 21 * 8 = 14 * x * 6   x = 30   Answer: 30
Answer: C
The average of 35 students in a class is 18 years. The average age of 25 students is 16. What is the average age of remaining 10 students? Choose the correct choice from the following options.
A) 21 years  B) 23 years  C) 22 years  D) 20 years  E) 24 years

Solution: Sum of the ages of 14 students   = (18 * 35) - (16 * 25) = 630 - 400= 
630 - 400 = 230
230   Required average= (230/10)= 
(230/10) = 23
23 years.   Answer:23 years
Answer: B
What is the median from the below series 93, 88, 95, 88, 97, 87, and 98
Choose the correct answer
A) 80	B) 82	C) 92.14	D) 98	E) 100

Solution: Ordering the data from least to greatest, we get:   87, 88, 88, 93, 95, 96, 98   The median quiz score was 92.14 (Four quiz scores were higher than 92.14 and four were lower.)   92.14
Answer: C
There are 380 doctors and nurses in a hospital. If the ratio of the doctors to the nurses is 8 : 11, then how many nurses are there in the hospital? Answers:
A) 152 B) 209 C) 57 D) 171 E) 220

Solution: Given,   The ratio of the doctors to the nurses is 8 : 11   Number of nurses = 11/19 x 380 = 220   ANSW220R:220
Answer: E
What is the greatest 6-digit number when divided by 7 ,8 , 9, and 10 leaves a remainder of 5, 6, 7, and 8 respectively?  Choose the correct choice from the following choices: A) 456788 B) 678910 C) 997479 D) 997919 E) 997920

Solution: When you divide a positive integer by 10, the remainder will just be the units digit. We know the remainder is 8 when we divide by 10, so 456788 is the only possible answer.
Answer: A
A train after traveling for 50km meets with an accident and then proceeds at 3/4 of its former speed and arrives at its destination 35 minutes late . Had the accident occurred 24 km farther, it would have reached the destination only 25 minutes late. What is the speed R of the train.  Answers: A) a) 45 B) b) 33 C) c) 48 D) d) 55 E) e) 61

Solution: Let y be the balance distance to be covered and x be the former speed.   A train after traveling for 50km meets with an accident and then proceeds at 3/4 of its former speed and arrives at its destination 35 minutes late   so, y/(3x/4) - y/x = 35/60   4y/3x - y/x = 7/12   y/x(4/3-1)=7/12   y/x*1/3=7/12   y/x=7/4   4y-7x=0 ........ 1   Had the accident occurred 24 km farther, it would have reached the destination only 25 minutes late   so, (y-24)/(3x/4) - (y-24)/x = 25/60   4(y-24)/3x - (y-24)/x = 5/12   (y-24)/x (4/3-1) = 5/12   (y-24)/x *1/3 = 5/12   (y-24)*12 = 3x*5   (y-24)*4 = 5x   4y-5x = 96 ....... 2   eq2 - eq1   2x=96   x=48=R   Ans = c) 48
Answer: C
Find the average of all the numbers between 6 and 34 which are divisible by 5
Options
A) 18	B) 20	C) 24	D) 30	E) 40

Solution: Exp. Multiples of 5 between 6 and 34 are 10,15,20,25,30   Average = (10+15+20+25+30)/5 =5(10+30)/2*5 = 40/2= 
40/2 = 20
20   Answer:20
Answer: B