MU-NLPC/Calc-aqua_rat huggingface dataset:
A courier charges for packages to a certain destination are 65 cents for the first 250 grams and 10 cents for each additional 100 grams or part thereof. What could be the weight in grams of a package for which the charge is $1.75? Choose the correct choice from the following answers
A) 1280
B) 1145
C) 1040
D) 950
E) 260

Solution: The charge is 65 cents for the first 250 grams.   This leaves a charge of $1.75 - $0.65 = $1.10   The charge for the next 1000 grams is $1.00 which leaves a charge of $0.10   The weight is somewhere between 1250 and 1350.   The answer is 1280. 1.75 -  0.65= 
 1.75 -  0.65 = 1.1
$1.10   The charge for the next 1000 grams is $1.00 which leaves a charge of $0.10   The weight is somewhere between 1250 and 1350.   The answer is 1280.
Answer: A
40 liters of a mixture is created by mixing Liquid P and Liquid Q in the ratio 5:3. How many liters of Liquid Q must be added to make the ratio 5:6? Choose the correct answer.
A) 5	B) 8	C) 10	D) 12	E) 15

Solution: Let x be the amount of liquid Q to be added.   (3/8)*40 + x = (6/11)*(40+x)   1320 + 88x = 1920 + 48x   40x = 600   x = 15   The answer is 15.
Answer: E
In a store 6 different CDs are there. If John can buy 2 CDs, how many cases that he can buy are there?
Choose the correct answer
A) 12 B) 15 C) 18 D) 21 E) 24

Solution: Let CDs are A, 15, C, D, E, F   He may choose any pair as mentioned below   A15, AC, AD, AE, AF = 5 cases   15C, 15D, 15E, 15F = 4 cases   CD, CE, CF = 3 cases   DE, DF = 2 cases   EF = 1 case   Total cases = 5+4+3+2+1= 
5+4+3+2+1 = 15
15   Answer: Option 15
Answer: B
What percent of a day is 15 hours?  Choose the correct choice:
A) 37Ã—1/2%  B) 16Ã—1/2%  C) 18Ã—2/3%  D) 22Ã—1/2%  E) None

Solution: Solution   Required percentage	= (15/24Ã—100)%   = (75 / 2)%.   = 37Ã—1/2%.   37Ã—1/2%nswer 37Ã—1/2%
Answer: A
Anil and Suresh are working on a special assignment. Anil needs 6 hours to type 32 pages on a computer and Suresh needs 5 hours to type 40 pages. If both of them work together on two different computers, how much time is needed to type an assignment of 100 pages?	Choose one
A) 8 hours 30 mins B) 8 hours C) 9 hours D) 7 hours E) 6 hours

Solution: Pages typed by 8 hours 30 minsnil in 1 hour = 32/6 = 16/3   Pages typed by Suresh in 1 hour = 40/5= 
40/5 = 8
8   Pages typed by 8 hours 30 minsnil and Suresh in 1 hour= 16/3 + 8 = 40/3   Time taken to type 100 pages when 8 hours 30 minsnil and Suresh work together = 100 × 3 /40 = 75/10   = 7 1/2 hours = 7 hour 30 minutes   8 hours 30 minsnswer is 8 hours 30 mins.
Answer: A
Country X taxes each of its citizens an amount equal to 10 percent of the first $40,000 of income, plus 20 percent of all income in excess of $40,000. If a citizen of Country X is taxed a total of $8,000, what is her income?
Choose the correct choice from the following answers.
A) $40,000
B) $56,000
C) $60,000
D) $66,667
E) $80,000

Solution: Equation is correct, so math must be a problem.   0.10*40,000+0.2*(x-40,000)=8,000 --> 4,000+0.2x-8,000=8,000 --> 0.2x=12,000 --> x=60,000.   Answer: $60,000.
Answer: C
The total weight of eight nougat nuggets is 3 oz. What is the average (arithmetic mean) weight of one such nougat nugget?
Select the correct option
A) 0.18 oz.
B) 0.375 oz.
C) 1.8 oz.
D) 5 oz.
E) 18 oz

Solution: Average = Total/Number of items   = 3/8 = 0.375.   Hence, 0.375 oz.
Answer: B
Last year a certain bond price with a face value of 5000 yielded 6% of its face value in interest. If that interest was approx 6.5 of the bond's selling price approx what was the bond's selling price? Choose the correct choice from the following answers: A) 4615 B) 5325 C) 5351 D) 6000 E) 6154

Solution: Interest = 0.06*5000 = 0.065*selling price --> selling price = 0.06*5000/0.065 --> selling price = ~4,615   4615nswer: 4615.
Answer: A
On a map, 1 inch represents 28 miles. How many Z inches would be necessary to represent a distance of 383.6 miles?  Select the correct option:	A) 5.2	B) 7.4	C) 13.7	D) 21.2	E) 28.7

Solution: Z inches necessary to represent a distance of 383.6 miles = 383.6/28= 
383.6/28 = 13.7
13.7   Answer 13.7
Answer: C
Three friends A, B and C decided to share a lot of apples. Each of them had half of the total plus half an apple in order. After each of them took their share thrice, no apples were left.How many apples were there?  Choose the correct choice from the following options.
A) 500 B) 510 C) 511 D) 501 E) 504

Solution: Whenever the rate of reduction is 'half of the total and half of it', the answer is always (2^n)-1, where 'n' is the number of times the process is repeated. Here, the process is repeated 9 times. So answer is (2^9)-1=511.   ANSWER:511
Answer: C
4 years ago, Paula was 4 times as old as Karl. In 12 years, Paula will be twice as old as Karl. What is the sum of their ages now? Choose the correct choice from the following answers.
A) 36 B) 40 C) 44 D) 48 E) 52

Solution: P-4 = 4(K-4) and so P = 4K-12   P+12 = 2(K+12)   (4K-12)+12 = 2K+24   K = 12   P = 36   P+K = 48   The answer is 48.
Answer: D
Find the average of the series : 220, 180, 328, 147 and 160?  Pick:
A) 230 B) 200 C) 250 D) 201 E) 207

Solution: Average = (220 + 180 + 328 + 147 + 160)/5   = 1035/5= 
1035/5 = 207
207   Answer: 207
Answer: E
If 20% of a number = 1000, then 120% of that number will be?	Choose the correct choice from the following
A) 20  B) 120  C) 360  D) 6000  E) 820

Solution: Let the number x. Then,   20% of x = 1000   x = (1000 * 100)/20= 
(1000 * 100)/20 = 5_000
5000   120% of x= (120/100 * 5000)= 
(120/100 * 5000) = 6_000
6000.   ANSWER:6000
Answer: D
In a LAB experiment, a 100 ml compound of element X and element Y needs to be increased to 300 ml by adding some quantity of element X, and some quantity of element Y. If the original compound contains 40% of element X, how much (in ml) of element Y must be added so that element X will be exactly one third of the resulting mixture ?
Choose the correct choice from the following answers: A) 40 ml B) 100/3 ml C) 140 ml D) 20/3 ml E) 10 ml

Solution: There are 0.4*100= 
0.4*100 = 40
40 ml of element X in the initial solution.   We need X to be 1/3rd of 300 ml in the resulting solution, so 100 ml. Thus out of 200 ml of solution added, 60 must be X (in order it to become 100 ml) ans the remaining 140 must be Y.   Answer: 140 ml
Answer: C
What is the probability that the position in which the consonants appear remain unchanged when the letters of the word "Math" are re-arranged?  Choose the correct choice from the following choices.
A) 1/4
B) 1/6
C) 1/3
D) 1/24
E) 1/12

Solution: Explanatory Answer   Step 1: Compute denominator   In any probability question, the denominator represents the total number of outcomes for an event. The numerator represents the number of favorable outcomes.   The total number of ways in which the word MATH can be re-arranged = 4! = 4*3*2*1= 
4*3*2*1 = 24
24 ways.   Step 2: Compute numerator and the probability   If the positions in which the consonants appear do not change, the first, third and the fourth positions are reserved for consonants and the vowel A remains at the second position.   The consonants M, T and H can be re-arranged in the first, third and fourth positions in 3!= 6 ways so that the positions in which the positions in which the consonants appear remain unchanged.   Therefore, the required probability 6/24=/14   Choice 1/4
Answer: A
Of the 3,600 employees of Company X, 1/3 are clerical. If the clerical staff were to be reduced by 1/4, what percent of the total number of the remaining employees would then be clerical? Answers
A) 25%	B) 28.1%	C) 20%	D) 12.5%	E) 11.1%

Solution: Welcome, just post the question and the choices   Let's see, the way I did it was   1/3 are clerical out of 3600 so 1200 are clerical   1200 reduced by 1/4 is 1200*1/4   so it reduced 300 people , so there is 900 clerical people left   but since 300 people left, it also reduced from the total of 3600 so there are 3300 people total   since 900 clerical left / 3200 people total   Answer : 28.1%
Answer: B
You have a bag of 9 letters: 3 Xs, 3 Ys and 3 Zs. You are given a box divided into 3 rows and 3 columns for a total of 9 areas. How many different W ways can you place one letter into each area such that there are no rows or columns with 2 or more of the same letter? Select the correct option
A) 5	B) 6	C) 9	D) 12	E) 18

Solution: Consider one particular arrangement of the first row: XYZ, then we can construct only two boxes with so that no rows or columns have 2 or more of the same letter:   XYZ   YZX   ZXY   And:   XYZ   ZXY   YZX   Now, the first row itself can be arranged in 3!=6 ways (since there are three distinct letter), hence the total number of boxes possible W is   2*6= 
  2*6 = 12
12.   Answer: 12.
Answer: D
{-10, -6, -5, -4, -2.5, -1, 0, 2.5, 4, 6, 7, 10}
A number is to be selected at random from the set above. What is the probability that the number selected will be a solution of the equation (x-5)(x+10)(2x-5) = 0?  Pick one
A) 1/12 B) 1/6 C) 1/4 D) 1/3 E) 1/2

Solution: Roots of the equation (x-5)(x+10)(2x-5)=0 are x=5, x=-10 and x=5/2=2.5. So, two solutions present in our set of 12 distinct numbers, therefore P=2/12=1/6.   Answer: 1/6.
Answer: B
At a certain high school, the senior class is twice the size of the junior class. If 7/8 of the seniors and 1/2 of the juniors study Japanese, what fraction of the students in both classes study Japanese?  Choose one
A) 3/4	B) 1/2	C) 1/4	D) 3/8	E) 5/16

Solution: Start by deciding on a number of students to represent the number of students in the senior class. For this example I will choose 200 students. That would make the number of students in the junior class 100. Then we can find out how many students are taking Japanese in each grade and add them together. (7/8)*200=175 and   (1/2)*100= 
  (1/2)*100 = 50
50. 175+50=225. There are a total of 300 students in the junior class and senior class combined (100+200=300), and there are 225 total students in Japanese, so 225 students in Japanese / 300 total students equals 3/4 of the students in both classes that study Japanese.   3/4nswer: 3/4
Answer: A
A bat is bought for Rs.400 and sold at a gain of 20% find its selling price?  Choose the correct choice from the following answers.
A) Rs.430/-	B) Rs.440/-	C) Rs.480/-	D) Rs.490/-	E) Rs.500/-

Solution: 100 % ------> 400 (100 * 4 = 400)   120 % ------> 480 (120 * 4 = 480)   Selling price = Rs.480/-   Rs.480/-
Answer: C
The ratio of two quantities is 5 : 8. If each of the quantities is increased by 10, what is the ratio of the new quantities?  Pick:
A) 5:8
B) 50:78
C) 2:3
D) It cannot be determined from the information given.
E) 6:7

Solution: Since the ratio is 5:8 we can put the quantities as 5K and 8K.   Moreover increasing quantities implies that the quantities become 5K+10 and 8K+10. So the ratio is (5K+10):(8K+10). The ratio value depend on the value of K. So It cannot be determined from the information given.   The answer is It cannot be determined from the information given.
Answer: D
$364 is divided among A, B, and C so that A receives half as much as B, and B receives half as much as C. How much money is C's share?  Choices
A) $200
B) $204
C) $208
D) $212
E) $216

Solution: Let the shares for A, B, and C be x, 2x, and 4x respectively.   7x = 364   x = 52   4x = 208   The answer is $208.
Answer: C
If the tens digit of positive integers q, y are 6, how many values of the tens digit of 2(q+y) can be there?	Choose the most appropriate option
A) 2
B) 3
C) 4
D) 5
E) 6

Solution: If the tens digit of positive integers q, y are 6, how many values of the tens digit of 2(q+y) can be there?   A. 2   B. 3   C. 4   D. 5   E. 6   -> If q=y=60, 2(q+y)=240 is derived. If q=y=69, 2(q+y)=276 is derived, which makes 4,5,6,7 possible for the tens digit. Therefore, the answer is 4.
Answer: C
The difference between a number and its three-fifth is 50. What is the number ? Options:
A) 75
B) 100
C) 125
D) none of these
E) 95

Solution: Let the number be x. Then, x-(3/5)x=50   =>(2/5)*x=50   =>x=(50*5)/2= 
(50*5)/2 = 125
125   Answer :125
Answer: C
In the equation 2x â€“ cy = 18, c is a constant. If the value of y is 2 when x is 6, what is the value of x when y is 2 ?  Choose the correct choice.
A) âˆ’9/2	B) -4	C) -3	D) 6	E) 9/2

Solution: 2x - cy = 18   x=6, y=2;   12-2c=18   c=-3   2x-cy=18   when y=3, c=-3, x=   x=6   ANSWER:6
Answer: D
A man can row a distance of 5 km in 60 min with the help of the tide. The direction of the tide reverses with the same speed. Now he travels a further 25 km in 10 hours. How much time he would have saved if the direction of tide has not changed? Choose the correct choice from the following options:  A) 2  B) 5  C) 1  D) 6  E) 7

Solution: Explanation:   He covered 5 km in 1 hour , so he might cover 25 km in 5 hours.   But he took 10 hours.   He would have saved 10 â€“ 5 = 5 hours.   Answer: 5
Answer: B
Five machines at a certain factory operate at the same constant rate. If four of these machines, operating simultaneously, take 35 hours to fill a certain production order, how many fewer hours does it take all five machines, operating simultaneously, to fill the same production order?  Pick
A) 3	B) 5	C) 7	D) 16	E) 24

Solution: Total work = 4*35 machine hrs   Time taken = 4* 35 /5= 
4* 35 /5 = 28
> 28 hours...   Thus all five machines, operating simultaneously will take ( 35 - 28 ) 7 hours..   Answer will be (7) 7
Answer: C
What least number must be added to 9879, so that the sum is completely divisible by 10 ?  Choose the correct choice from the following: A) 3 B) 4 C) 1 D) 2 E) 6

Solution: If we divide 9879 by 10 remainder is 9   10-9= 
10-9 = 1
1   Answer : 1
Answer: C
IN Common Wealth Games an athlete runs 200 meters in 24 seconds. Hisspeed is ? Choose the correct choice from the following options:
A) 25 km/hr B) 27 km/hr C) 30 km/hr D) 32 km/hr E) None of these

Solution: Explanation :   (200/1000)/(24/3600)= 
(200/1000)/(24/3600) = 30
30 km/hr   Answer : 30 km/hr
Answer: C
There are two examinations rooms A and B. If 10 students are sent from A to B, then the number of students in each room is the same. If 20 candidates are sent from B to A, then the number of students in A is double the number of students in B. The number of students in room A is: Pick
A) 20
B) 30
C) 40
D) 50
E) 10

Solution: A   20   Let the number of students in rooms A and B be x and y respectively.   Then, x - 10 = y + 10 x - y = 20 .... (i)   and x + 20 = 2(y - 20) x - 2y = -60 .... (ii)   Solving (i) and (ii) we get: x = 100 , y = 80.   The required answer 20 = 100.
Answer: A
Anand and Deepak started a business investing Rs. 6,000 and Rs. 7,000 respectively. Out of a total profit of Rs. 1,300. Deepak's share is?  Select.
A) s. 650	B) s. 780	C) s. 800	D) s. 760	E) s. 700

Solution: Ratio of their shares = 6000 : 7000 = 7 : 13   Deepak's share = Rs. (1300 * 7/13) = Rs. 700 ANSWs. 700R "s. 700
Answer: E
An art gallery owner is hanging paintings for a new show. Of the seven paintings she has to choose from, she can only hang three on the main wall of the gallery. Assuming that she hangs as many as possible on that wall, in how many ways can she arrange the paintings?	Choose one.
A) 18 B) 30 C) 64 D) 120 E) 210

Solution: Arrangment means permutations questions..   7P3 = 7!/3! = 210.   IMO option 210 is correct answer..
Answer: E
If a2 - b2 = 10 and a*b = 5, find a4 + b4.	Options: A) 50 B) 100 C) 150 D) 92 E) 25

Solution: a2 - b2 = 10 : given   a4 + b4 - 2a2b2 = 102 : square both sides and expand.   a*b = 5 : given   a2b2 = 52 : square both sides.   a4 + b4 - 2(25) = 100 : substitute   a4 + b4 = 150   correct answer 150
Answer: C
A numberais squared and then multiplied by negative 3. The result of this operation T is equal to three times the sum of three timesaand two. What is one possible value ofa? Choose the most appropriate option
A) -3	B) -2	C) 1	D) 2	E) 3

Solution: T=-3*a^2=3(3a+2)   a= -2 or -1   a=-2=-2
Answer: B
Ramu rides his bike at an average speed of 45 km/hr and reaches his desitination in four hours. Somu covers the same distance in six hours. If Ramu covered his journey at an average speed which was 9 km/hr less and Somu covered his journey at an average speed which was 10 km/hr more, then the difference in their times taken to reach the destination would be (in minutes).
Answers:  A) 22 min  B) 30 min  C) 87 min  D) 26 min  E) 11 min

Solution: Explanation:   Distance travelled by Ramu = 45 x 4 = 180 km   Somu travelled the same distance in 6 hours.   His speed = 180/6= 
180/6 = 30
30 km/hr   Hence in the conditional case, Ramu's speed= 45 - 9= 
45 - 9 = 36
36 km/hr and Somu's speed= 30 + 10= 
30 + 10 = 40
40km/hr.   Therefore travel time of Ramu and Somu would be 5 hours and 4.5 hours respectively.   Hence difference in the time taken= 0.5 hours = 30 minutes.   Answer: 30 min
Answer: B
If 40 percent of the members of a certain organization are women and 4/8 of the members of the organization are married men, which of the following statements concerning the membership must be true?
I. The number of women in the organization is greater than the number of married men in the organization.
II. The number of women in the organization is greater than the number of unmarried men in the organization.
III. The number of married men in the organization is greater than the number of unmarried men in the organization.
Choose the correct choice from the following answers.
A) I,II
B) III
C) II,III
D) II
E) I

Solution: 4/10 (40%) of the members are women and 4/8 of the members are married men. Let the total numbers of members is 80 (the LCM of 10 and 8). Then there are:    4/10*80= 
 4/10*80 = 32
32 women;    80 - 32= 
 80 - 32 = 48
48 men;     4/8*48= 
  4/8*48 = 24
24 married men;    48 - 24= 
 48 - 24 = 24
24 unmarried men.   So, option I,II is true.   I,IInswer: I,II
Answer: A
What is the remainder when (71)(73) is divided by 9?
Pick
A) 1 B) 2 C) 4 D) 6 E) 8

Solution: (71)(73) = (72-1)(72+1) = 72^2 - 1 which is 1 less than a multiple of 9.   Then the remainder will be 8.   The answer is 8.
Answer: E
A boat having a length 3 m and breadth 2 m is floating on a lake. The boat sinks by 1 cm when a man gets on it. The mass of the man is: Choose the correct option.
A) 40 kg	B) 42kg	C) 50kg	D) 58kg	E) 60 kg

Solution: Volume of water displaced	= (3 x 2 x 0.01) m3   = 0.06 m3.   Mass of man   = Volume of water displaced x Density of water   = (0.06 x 1000) kg   = 60 kg.   answer : 60 kg
Answer: E
Look at this series: 70, 71, 76, 70, 81, __, 70, 91, ... What number should fill the blank? Answers.
A) 70	B) 86	C) 82	D) 77	E) 52

Solution: 86   86   In this series, 5 is added to the previous number; the number 70 is inserted as every third number.
Answer: B
The average age of students of a class is 15.8 years. The average age of boys in the class is 16.4 years and that of the girls is 15.4 years. The ration of the number of boys to the number of girls in the class is? Pick:
A) 2:7 B) 2:3 C) 2:1 D) 2:9 E) 2:2

Solution: Let the ratio be k : 1. Then,   k * 16.4 + 1 * 15.4 = (k + 1) * 15.8   = (16.4 - 15.8)k = (15.8 - 15.4)   = k = 0.4/0.6 = 2/3   Required ratio = 2/3 : 1 = 2:3.   Answer: Option B   Explanation:   Let the ratio be k : 1. Then,   k * 16.4 + 1 * 15.4 = (k + 1) * 15.8   = (16.4 - 15.8)k = (15.8 - 15.4)   = k = 0.4/0.6 = 2/3   Required ratio = 2/3 : 1 = 2:3.   Answer: 2:3
Answer: B
What is the smallest positive integer X such that (X+1)^2 is divisible by 28, 98, 242, and 308?	Choose the correct option:  A) 153  B) 308  C) 121  D) 96  E) 511

Solution: 28 = 2 * 2 * 7   98 = 2 * 7 * 7   242 = 2 * 11 * 11   308 = 2 * 2 * 7 * 11   So (X+1)^2 = 2 * 2 * 7 * 7 * 11 * 11, which means (X+1) = 2 * 7 * 11= 
2 * 7 * 11 = 154
154, which means X= 153, which is option 153
Answer: A
The area of a right-angled triangle is two-thirds of the area of a rectangle. The base of the triangle is 80 percent of the breadth of the rectangle. If the perimeter of the rectangle is 200 cm, what is the height of the triangle?
Choose the most appropriate option.
A) 20 cm B) 30 cm C) 15 cm D) Data inadequate E) None of these

Solution: Let the base and height of triangle, and length and breadth of rectangle be L and h, and L1 and b1 respectively.   Then 1⁄2 × L × h = 2⁄3 × L1 × b1 .....(i)   L = 4⁄5b1 .....(ii)   and L1 + b1 = 100 .....(iii)   In the above we have three equations and four unknowns. Hence the value of ‘h’ can’t be determined.   Answer Data inadequate
Answer: D
If t and g are distinct prime numbers less than 10, which of the following cannot be the product of t and g?	Choose the correct choice from the following:
A) 6 B) 9 C) 10 D) 14 E) 15

Solution: If t and g are distinct prime numbers less than 10 prime numbers less than 10 are 2, 3, 5, 7   all except 9 is product of any two numbers picked from above set.   Ans: 9
Answer: B
A rectangular cube has a volume of 10 cubic feet. If a similar cube is twice as long, twice as wide, and twice as high, then the volume, in cubic feet of such cube is?
Choices  Select:
A) 24	B) 48	C) 64	D) 80	E) 100

Solution: Lets say the sides of the rectangular cube are x, y and z. Problem states volume is 10.   i.e,   x*y*z = 10 .   If every side is increased twice as before. then new volume is   2x*2y*2z = 8*(x*y*z)  2 *2 *2= 
 2 *2 *2 = 8
8*(x*y*z)= 8*10= 
8*10 = 80
80.   Answer is 80
Answer: D
In 2008, a certain factory produced 40% more widgets than it did in 2007, and its production in 2009 was 120% of its production in 2008. By approximately what percent would its production need to decrease the following year for the factory to produce the same number of widgets it did in 2007? Choose the most appropriate option:
A) 25.5%
B) 30.5%
C) 36.5%
D) 40.5%
E) 48.5%

Solution: Let P be the original level of production in 2007.   Let x be the rate of production in 2010 compared to 2009.   x*1.2*1.4*P = P   x = 1/1.68 = 0.595 which is a decrease of 40.5%.   The answer is 40.5%.
Answer: D
Find the first term of an AP whose 8th and 12th terms are respectively 39 and 59.
Select the correct option.
A) 5	B) 6	C) 4	D) 3	E) 7

Solution: Solution: 1st Method:   8th term = a+7d = 39 ........... (i)   12th term = a+11d = 59 ........... (ii)   (i)-(ii);   Or, a+7d-a-11d = 39-59; Or, 4d = 20;   Or, d = 5;   Hence, a+7*5 = 39;   Thus, a = 39-35= 
39-35 = 4
4.   2nd Method (Thought Process):   8th term= 39;   And, 12th term = 59;   Here, we see that 20 is added to 8th term 39 to get 12th term 59 i.e. 4 times the common difference is added to 39.   So, CD = 20/4= 
20/4 = 5
5.   Hence, 7 times CD is added to 1st term to get 39. That means 4 is the 1st term of the AP.   Answer: Option 4
Answer: C
If x, 2, 3, 4 are there and the range and median of them are the same, what is the value of x?  Choose the correct option: A) 0 B) 1 C) 2 D) 3 E) 4

Solution: Try taking the values of x as you suggested and then see if the median and the range are equal.   Once you do that, you will get the answer yourself.   Tried substituting values starting with 2, 3, 4...   only x = 3 satisfies the condition.   3
Answer: D
A shopkeeper has 280 kg of apples. He sells 30% of these at 20% profit and remaining 60% at 30% profit. Find his % profit on total.	Choose the correct option
A) 24%  B) 25%  C) 26%  D) 28%  E) 35%

Solution: If the total quantity was 100   Then 30X 20% + 60 X30%= 24   This profit will remain same for any total quantity unless the % of products remains the same. Hence '24%' is the answer
Answer: A
A man standing at a point P is watching the top of a tower, which makes an angle of elevation of 30º with the man's eye. The man walks some distance towards the tower to watch its top and the angle of the elevation becomes 60º. What is the distance between the base of the tower and the point P?
Choose the most appropriate option:
A) 43 units	B) 8 units	C) 12 units	D) Data inadequate	E) None of these

Solution: One of AB, AD and CD must have given.   So, the data is inadequate.   ANSWER:Data inadequate
Answer: D
David and Rachel are getting married. The extended family wants to have its picture taken, but David's father is unwilling to stand next to Rachel's mother. How many options does the photographer have to arrange the 10 family members in a row for the picture?	Pick:
A) 9!  B) 9×8!  C) 8×9!  D) 10!/2!  E) 10!

Solution: Total - Restriction =   = 10! - 9!*2! =   = 9!(10 - 2!) =   = 8*9!.   Answer: 8×9!
Answer: C