MU-NLPC/Calc-aqua_rat huggingface dataset:
A highway is to be divided into four lanes. For this purpose, three yellow stripes are painted so that stripes divide the highway into four lanes. If 3 gallons of paint cover an area of 2P square feet of highway, how many gallons of paint are needed to paint two stripes x inches wide on a stretch of highway m miles long? (1 mile = 5280 feet and 1 feet = 12 inches)	Options.
A) 1320mx/P
B) 880mx/P
C) 1320P/mx
D) 440P/mx
E) 1980mx/P

Solution: 1 square foot needs 3/2P gallons of paint.   The width of each stripe is x/12 feet.   The length of each stripe is 5280m feet.   The area of each stripe is (5280m)(x/12) = 440mx square feet.   For three stripes, the total area is 1320mx square feet.   The number of gallons needed is (1320mx)*(3/2P) = 1980mx/P gallons.   The answer is 1980mx/P.  (1320  )*(3/2 )= 
  (1320  )*(3/2 ) = 1_980
1980mx/P gallons.   The answer is 1980mx/P.
Answer: E
The ratio of investments of two partners P and Q is 7:5 and the ratio of their profits is 7:10. If P invested the money for 5 months, find for how much time did Q invest the money?
Choose the correct choice from the following:  A) 22  B) 6  C) 17  D) 10  E) 88

Solution: 7*5: 5*x = 7:10   x = 10   Answer:10
Answer: D
A train covers a distance of 12 km in 10 min. If it takes 12 sec to pass a telegraph post, then the length of the train is? Options:
A) 178 m B) 240 m C) 120 m D) 168 m E) 178 m

Solution: Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec   = 20 m/sec.   Length of the train = 20 * 12= 
20 * 12 = 240
240 m.   Answer: 240 m
Answer: B
Calculate the effect changes in dimension of a rectangle will have on its area, if length is increased by 20% and its breadth is decreased by 5%?
Choose one
A) 14 percent increase  B) 5 percent increase  C) 24 percent increase  D) 13 percent increase  E) 11 percent increase

Solution: let L and B be 100 each     100 * 100= 
  100 * 100 = 10_000
10000   L increase by 20%= 120   B decrease by 5% = 95   120 * 95= 
120 * 95 = 11_400
11400   14 percent increase   14 percent increaseNSWER:14 percent increase
Answer: A
A Jar contains 18 balls. 3 blue balls are removed from the jar and not replaced.Now the probability of getting a blue ball is 1/5 then how many blue balls jar contains initially?
Choose the correct choice from the following answers.
A) 2	B) 3	C) 4	D) 5	E) 6

Solution: x/15 = 1/5   x =3   3+3(removed 3 blue balls) = 6   ANSW6R:6
Answer: E
If the two-digit integers A and B are positive and have the same digits, but in reverse order, which of the following could be the sum of A and B?	Answers:  A) 53  B) 54  C) 55  D) 56  E) 57

Solution: A two-digit number "cd" can be expressed algebraically as 10c+d.   The sum of A + B = (10c+d)+(10d+c)=11(c+d).   The only answer that is a multiple of 11 is 55.   The answer is 55.
Answer: C
In how many different ways can the letters of the word ‘POSITIVE’ be arranged ?  Select:
A) 120 B) 720 C) 40320 D) 24 E) 6

Solution: 40320   40320   Required number of arrangements = 8! = 40320
Answer: C
In a certain deck of cards, each card has a positive integer written on it, in a multiplication game a child draws a card and multiplies the integer on the card with the next large integer. If the each possible product is between 15 and 150, then the least and greatest integer on the card would be Pick:  A) 3 and 15  B) 3 and 20  C) 4 and 12  D) 4 and 14  E) 5 and 14

Solution: Given: 15<x(x+1)<170.   Now, it's better to test the answer choices here rather than to solve:   If x=4 then x(x+1)=20>15 --> so, the least value is 4. Test for the largest value: if x=12 then   x(x+1)=12*13= 
12*13 = 156
156>150   Answer: 4 and 12.
Answer: C
If a motor bike's wheel is 12 cm diameter and rotating at the rate of x cm/min and another motor bike's wheel is 6 cm diameter rotating at the rate of y cm/min and if both the bikes reach the distance at same time then what is the value of y in terms of x?
Choose the correct answer:
A) 4x/2  B) 3x/6  C) 4x/2  D) 1x/2  E) 2x/3

Solution: t=S1/V1=S2/V2   or 12/x=6/y   or y=6x/12=1x/2   Answer is 1x/2
Answer: D
The diagonal of a rectangle is √41 cm and its area is 20 sq. cm. The perimeter of the rectangle must be:
Choices.
A) 18
B) 28
C) 38
D) 48
E) 58

Solution: Explanation:   l2 + b2 = 41   Also, lb = 20   (l + b)2 = l2 + b2 + 2lb   = 41 + 40= 
41 + 40 = 81
81   (l + b)= 9   Perimeter = 2(l + b) = 18 cm. 18nswer: 18
Answer: A
The ratio of the present ages of Giri and Hari is 5 : 8. 12 years hence, the ratio of their ages will be 11 : 14. Find the difference in their present ages?
Choose the correct option
A) 8  B) 6  C) 5  D) 4  E) 2

Solution: Let the present ages of Giri and Hari be 5x and 8x years respectively.   (5x + 12) / (8x + 12) = 11/14   70x + 168 = 88x + 132 => x= 2   Difference in their ages will be the same at all times.   This difference = Difference of their present ages   = 8x - 5x = 3x 8  - 5= 
8  - 5 = 3
3x= 6 years.   Answer:6
Answer: B
How many multiples of 5 are there between 5 to 95?
Choices:
A) 9
B) 18
C) 17
D) none of these
E) Cannot be determined

Solution: Explanation :   As you know, multiples of 5 are integers having 0 or 5 in the digit to the extreme right (i.e. the units place).   So the numbers are 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90.   Answer : 17
Answer: C
The speed of a boat in still water is 60kmph and the speed of the current is 40kmph. Find the speed downstream and upstream?	Choose the correct answer
A) kmph  B) kmph  C) kmph  D) kmph  E) kmph

Solution: Speed downstream = 60 +40= 
60 +40 = 100
100 kmph   Speed upstream= 60 - 40= 
60 - 40 = 20
20 kmph   Answer:kmph
Answer: D
Jaclyn buys $40 000 worth of debentures in a company. She earns 9.5% p.a. simple interest, paid to her quarterly (that is, every 3 months). If the agreed period of the debenture was 18 months: calculate the amount of interest Jaclyn will earn for each quarter  Choose the correct choice from the following answers.
A) 950  B) 1234  C) 1289  D) 1345  E) None of these

Solution: Explanation:   I=(p x r x t)/100   = 40000*9.5/100*(18/12)^1/6 = 950   950nswer: 950
Answer: A
If S = T/P, -1 < P < 0 and 4 < T, which of the following is correct? Select.
A) S > 4. B) 0 < S <4. C) -4 < S < 0. D) S < -4. E) S < -20.

Solution: T is +veP is -ve   Eliminate AB   For min. value max. numerator and minimize dinominator   take T=4.1S=-0.9   S=4.1/-0.9   S<-4   Ans S < -4.
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?  Choose the correct choice from the following choices: A) 877 m B) 240 m C) 167 m D) 887 m E) 265 m

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 m
Answer: B
Walking at the rate of 8kmph a man cover certain distance in 4hr 45min. Running at a speed of 19 kmph the man will cover the same distance in.
Choose the correct choice from the following answers:
A) 100 min
B) 110 min
C) 140 min
D) 120 min
E) 150 min

Solution: 120 ministance = Speed * time     8*19/4= 
  8*19/4 = 38
38km   New Speed= 19kmph   Therefore time = 120 min/S = 38/19= 120 min   Answer : 120 min.
Answer: D
A palindrome is a number that reads the same forward and backward, such as 464. How many odd five-digit numbers are palindromes?  Choose the correct choice from the following answers.
A) 40  B) 400  C) 500  D) 5,000  E) 100,000

Solution: 5th digit 1,3,5,7,9   4th digit 0 through 9   3rd digit 0 through 9   i.e 10*10*5 = 500 numbers   first and second digit is going to be same as 4th and 5th. so it would still be 400 numbers.   Answer is 500.
Answer: C
A real estate investor decided to sell five of his apartments at the cost of $168,000, $235,000, $157,000, $ 256,000 and $ 235,000. Due to a bidding war, the price on the most expensive apartment will likely be sold for $15,000 higher than the initial asking price. Which of the following best describes how the mean and median would change as a result of a higher sale price on the most expensive apartment? Select the correct option
A) Both the mean and median will be unchanged.
B) The median will change but the mean remains unchanged.
C) The median will remain the same but the mean will increase.
D) Both the mean and the median will increase by the same percentage.
E) Both the mean and the median will increase by different amounts.

Solution: Soln:   (C) The median will remain the same but the mean will increase.   ANSWER:The median will remain the same but the mean will increase.
Answer: C
There are two circles of different radii. The are of a square is 784 sq cm and its side is twice the radius of the larger circle. The radius of the larger circle is seven - third that of the smaller circle. Find the circumference of the smaller circle?  Choose the correct choice from the following answers:	A) 13	B) 14	C) 12	D) 16	E) 17

Solution: Let the radii of the larger and the smaller circles be l cm and s cm respectively. Let the side of the square be a cm.   a2 = 784 = (4)(196) = (22).(142)   a = (2)(14) = 28   a = 2l, l = a/2 = 14   l = (7/3)s   Therefore s = (3/7)(l) = 6 Circumference of the smaller circle = 2∏s = 12∏ cm.   Answer: 12
Answer: C
A six-sided die is rolled once. What is the probability that the number rolled is an even number greater than 2? Choose the correct choice from the following.
A) 4/5	B) 1/3	C) 2/4	D) 1/5	E) 2/6

Solution: Out of the 6 possible numbers that may rolled, 3 are even: 2, 4 and 6 BUT only 4 and 6 are greater than 2. Hence the probability that the number rolled is an even number greater than 2 is given by   (number of even numbers greater than 2) / 6 = 2 / 6 = 1 / 3   correct answer 1/3
Answer: B
It takes one machine 3 hours to complete a production order and another machine 3 hours to complete the same order. How many hours would it take both amhcines working simultaneously at their respective rates to complete the order?	Select the correct option
A) a) 7/12	B) b) 1 1/2	C) c) 1 5/7	D) d) 3 1/2	E) e) 1 1/2

Solution: RT = W   Given:   R = 1/3 + 1/3 = 2/3   T = ?   W = 1   T = 1 / (2/3) = 3/2 = 1 1/2   Answer: e) 1 1/2
Answer: E
There are 6 tasks and 6 persons. Task 1 cannot be assigned either to person 1 or to person 2; task 2 must be assigned to either person 3 or person 4. Every person is to be assigned one task. In how many ways can the assignment be done?
Choose the correct choice from the following options
A) 144  B) 180  C) 192  D) 360  E) None of these

Solution: Task 1 can not be assigned to either person 1 or 2 i.e.there are 4 options.   Task 2 can be assigned to 3 or 4   So, there are only 2 options for task 2.   So required no. of ways = 2 options for task 2 × 3 options for task 1 × 4 options for task 3 × 3 options for task 4 × 2 options for task 5 × 1 option for task 6.   = 2 × 3 × 4 × 3 × 2 × 1 = 144   144nswer 144
Answer: A
A man purchases 8 pens for Rs.9 and sells 9 pens for Rs.8, how much profit or loss does he make?
Select the correct option
A) 29.98 B) 20.98 C) 20.92 D) 20.96 E) 20.91

Solution: 81 ---- 17   100 ----- ? è 20.98%loss   Answer:20.98
Answer: B
For integers x and y, if 91x = 8y, which of the following must be true?
I. y > x
II. y/7 is an integer
III. The cube root of x is not necessarily an integer	Choose the correct choice.
A) I only
B) II only
C) III only
D) I and II
E) II and III

Solution: Statement 1: y>x   When y=x=0, equation holds but y is not greater than x   When x=-8 and y=-91, equation again holds but x>y   NOT TRUE   Statement 2: y/7 is an integer   Since x and y are integers, 91x and 8y must also be integers.   It is given that 91x=8y   or 13*7*x = 8 y   or 13x = 8y/7   To balance the equation, y/7 must be an integer   TRUE   Statement 3: The cube root of x is an integer   x can be equal to 2*2*2*3 and for this value of x,y will be 13*7*3   So, x may or may not be a cube root.   TRUII and III   Answer:-II and III
Answer: E
A $500 investment and a $1,500 investment have a combined yearly return of 8.5 percent of the total of the two investments. If the $500 investment has a yearly return of 7 percent, what percent yearly return does the $1,500 investment have?  Options.
A) 9% B) 10% C) 105/8% D) 11% E) 12%

Solution: The equation we can form the question :   Return on Total Investment = Sum of individual Investments   (500+1500)(8.5)=(500∗7)+(1500x), where x is the return on investment of 1500.   Solving the equation, we get x = 9% ( Option 9% )	9%NSWER:9%
Answer: A
How much interest can a person get on Rs. 8800 at 17.5% p.a. simple interest for a period of two years and six months?
Select the correct option.
A) 3587.58
B) 3587.59
C) 3587.5
D) 3587.52
E) 3850

Solution: I = (8800 * 2.5 * 17.5)/100 = (8800 * 5 * 35)/(100 * 2 * 2) = Rs. 3850.Answer: 3850
Answer: E
A box contains 4 blue marbles, 3 red, 6 green marbles and two yellow marbles. If two marbles are picked at random, what is the probability that they are either blue or yellow?  Choose the correct choice from the following choices
A) 5/10  B) 4/10  C) 1/10  D) 2/10  E) 3/10

Solution: Given that there are 4 blue marbles, 3 red marbles, 6 green marbles and 2 yellow marbles. Probability that both marbles are blue = 41/10â‚‚/Â¹âµ1/10â‚‚ = (3 * 2)/(15 * 14) = 2/35   Probability that both are yellow = Â²1/10â‚‚/Â¹âµ1/10â‚‚ = (1)/(15 * 14) = 1/210   Probability that one blue and other is yellow = (41/10â‚ * Â²1/10â‚)/Â¹âµ1/10â‚‚ = (4*2)/(15 * 14) = 4/105   Required probability = 2/35 + 1/210 + 4/105   = 1/10   Answer:1/10
Answer: C
Three numbers are in the ratio 5 : 6 : 7. The sum of its longest and smallest numbers equals the sum of the third number and 37. Find the third number? Choose the correct answer
A) A)37 B) B)85 C) C)48 D) D)43 E) E)84

Solution: Let the numbers be 5x, 6x, 7x.   Largest number = 7x.   Smallest number = 5x.   Third number = 6x.   7x + 5x = 6x + 37   6x = 48 => third number is 37.   37nswer: Option 37
Answer: A
A person has to cover a distance of 6km in 45 minutes. If he covers one half of the distance in two-thirds of the total time; to cover the remaining distance in the remaining time, his speed must be?
Select the correct option:
A) 12km per hr
B) 10km/hr
C) 15km/hr
D) 20km/hr
E) 18km/hr

Solution: Remaining distance = 3km   Remaining time = 1/3 * 45= 
1/3 * 45 = 15
15min= 1/4 hour   Required speed = 3*4= 
3*4 = 12
12km/hr   12km per hrnswer is 12km per hr
Answer: A
Two men A and B start from place X walking at 4 ½ kmph and 5 ¾ kmph respectively. How many km apart they are at the end of 3 ½ hours if they are walking in the same direction?	Select the correct option
A) 4 3/9 km
B) 5 3/8 km
C) 4 3/8 km
D) 6 3/8 km
E) 7 3/8 km

Solution: RS = 5 ¾ - 4 ½ = 1 ¼   T = 3 ½ h.   D = 5/4 * 7/2 = 35/8 = 4 3/8 km   Answer:4 3/8 km
Answer: C
What amount does an investor receive if the investor invests $7000 at 10% p.a. compound interest for two years, compounding done annually?  Choose the correct choice from the following options:
A) $8080
B) $8130
C) $8260
D) $8320
E) $8470

Solution: A = (1 + R/100)^n * P   (1.1)^2 * 7000 = 1.21 * 7000= 
1.21 * 7000 = 8_470
8470   The answer is $8470.
Answer: E
If 16 men can reap 80 hectares in 24 days , then how many hectares can 36 men reap in 30 days?  Pick:  A) 127  B) 225  C) 287  D) 450  E) 281

Solution: Explanation:   Let the required no of hectares be x. Then   Men --- Hectares---Days   16---------80---------24   36---------x---------30   More men, More hectares (Direct proportion)   More days, More hectares (Direct proportion)   x=36/16*30/24*80= 
36/16*30/24*80 = 225
225   Answer: 225
Answer: B
If p is a positive integer, and r is the units digit of 3^4p×5^5p×6^6p×7^7p then r + 2 is divisible by which of the following?	Pick: A) 2 B) 3 C) 5 D) 7 E) 9

Solution: The number will be an even number as it contains 6 as a term in its product, so units digit will be even..   EVEN +2 will be another EVEN and will be div by 2..   2NSWER:2
Answer: A
A reduction of 18% in the price of oil enables a house wife to obtain 8kgs more for Rs.1080, what is the reduced price for kg? Pick:	A) 72.15	B) 27.24	C) 24.25	D) 28.46	E) 20.9

Solution: 1080*(18/100) = 194 ---- 8   ? ---- 1 => Rs.24.25   Answer:24.25
Answer: C
Due to 10% decrease in the price of sugar and John can buy 5kg more sugar in Rs100 , then find the CP of sugar?  Pick: A) Rs.2(1/9) B) Rs.2(2/9) C) Rs.3(1/9) D) Rs.1(1/9) E) Rs.2(2/5)

Solution: Here r = 10 % ,x = 100 and A = 5 kg   Actual price of sugar = 10*100/((100-10 )*5) = Rs.2(2/9)   Rs.2(2/9)
Answer: B
A man went into a bank to cash a check. In handing over the money the cashier, by mistake, gave him dollars for cents and cents for dollars. He pocketed the money without examining it, and spent a nickel on his way home. He then found that he possessed exactly twice the amount of the check. He had no money in his pocket before going to the bank. What was the exact amount of that check?
Choose the correct option:
A) $31.63 B) $35.63 C) $32.63 D) $37.63 E) $33.63

Solution: A   $31.63   The amount must have been $31.63. He received $63.31. $31.63fter he had spent a nickel there would remain the sum of $63.26, which is twice the amount of the check.
Answer: A
Lorna invests $7000, with some at 6% annual interest and some at 11% annual interest. If she receives a total of $580 from these investments at the end of a year, how much was invested at the 6% interest rate? Options:
A) $160
B) $1,600
C) $2,200
D) $1,400
E) $5,840

Solution: We have that 'x' invested at 6%   We also have that '6000-x' invested at 11%   Now then 580/7000 is approx 10%   Therefore, -4x+7000-x=0   5x=7000   x=1400 approximately. Probably higher   Only $1,400 matches
Answer: D
By travelling at 70 kmph, a person reaches his destination on time. He covered two-third the total distance in one-third of the total time. What speed should he maintain for the remaining distance to reach his destination on time?
Pick:
A) 25 kmph
B) 20 kmph
C) 28 kmph
D) 35 kmph
E) 32 kmph

Solution: Let the time taken to reach the destination be 3x hours. Total distance = 70 * 3= 
70 * 3 = 210
210x km   He covered 2/3 * 210= 
2/3 * 210 = 140
140x km in 1/3 * 3x= x hours So, the remaining 70x km, he has to cover in 2x hours. Required speed = 70x/2x   =35 kmph.   Answer: 35 kmph70 /2= 
70 /2 = 35
35 kmph.   Answer: 35 kmph
Answer: D
The profit earned by selling an article for $ 832 is equal to the loss incurred when the same article is sold for $ 448. What should be the sale price for making 50% profit?  Choose the correct choice from the following:	A) $480	B) $450	C) $960	D) $870	E) $660

Solution: C   $ 960   Let C.P. = $ x.   Then, 832 - x = x - 448   2x = 1280 => x = 640   Required S.P. = 150% of $ 640 = 150/100 * 640= 
150/100 * 640 = 960
$ 960.
Answer: C
Carmelo and LeBron participate in a seven-person footrace on the basketball court during All-Star Weekend. If all seven contestants finish (including Charles Barkley) and there are no ties, how many different arrangements of finishes are there in which Carmelo defeats LeBron? Select the correct option
A) 5040  B) 2520  C) 720  D) 120  E) 42

Solution: 7! = 5040   5040/2= 
5040/2 = 2_520
2520 half the time carmelo is in front, vice versa   Answer:   (2520) 2520
Answer: B
A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 32, the how old is B?  Choose the correct choice from the following answers:
A) 7  B) 9  C) 8  D) 11  E) 12

Solution: Explanation:   Let C's age be x years. Then, B's age = 2x years. A's age = (2x + 2) years.   (2x + 2) + 2x + x = 32   ⇒ 5x = 30   ⇒ x = 6.   Hence, B's age = 2x = 12 years.   Answer: 12
Answer: E
Anand and Deepak started a business investing Rs.22,500 and Rs.35,000 respectively. Out of a total profit of
Rs. 13,800. Deepak's share is
Pick
A) Rs 9600	B) Rs 8500	C) Rs 8450	D) Rs 8400	E) None of these

Solution: Explanation:   Ratio of their shares	= 22500 : 35000   =9 : 14   Deepak's share	= Rs.(13800×14/23)   = Rs. 8400   Option Rs 8400
Answer: D
A man performs 1/2 of his journey by rail, 2/5 by bus and the remaining 10 km on foot. His total journey is? Select:
A) 40km
B) 50km
C) 60km
D) 70km
E) 100km

Solution: Let the total journey be x km   x/2 + 2x/5 + 10 = x   9x+50 = 10x   x = 50 km   Answer is 50km
Answer: B
A straight pipe 1 yard in length was marked off in fourths and also in fifths. If the pipe was then cut into separate pieces at each of these markings, which of the following gives all the different lengths of the pieces, in fractions of a yard?  Choose the correct option
A) 1/6 and 1/4 only	B) 1/4 and 1/3 only	C) 3/20, 1/5 and 1/10	D) 1/12, 1/6 and 1/4	E) 1/20, 3/20, 1/5 and 1/10

Solution: Generally fast way to solve such problem is writing the different marks in ascending/descending order with same denominator:   Here 4th : 0/4, 1/4, 2/4, 3/4, 4/4   and 5th : 0/5, 1/5, 2/5, 3/5 , 4/5, 5/5   Now with understood common denominator 20 write the numbers : for 4th : 0,5,10,15,20 and for 5th : 0,4,8,12,16,20   Now comine : 0,4,5,8,10,12,15,16,20   Now find the cut with denominator 20 (Substracrt adjacent terms : 1/5, 1/20, 3/20, 1/10,1/10,3/20,1/20,1/5 i.e. 1/5, 1/20 ,3/20 and 1/10 after removing duplicates.   Answer : 1/20, 3/20, 1/5 and 1/10
Answer: E
If n is a positive integer, which of the following expressions must be even?  Select the correct option:
A) (n − 3)( n + 1)
B) (n − 8)( n + 1)
C) (n − 4)( n + 4)
D) (n − 5)( n + 1)
E) (n − 5)( n + 5)

Solution: Whether n is even or odd, (n-8)(n+1) will have one odd factor and one even factor.   The product will be even.   The answer is (n − 8)( n + 1).
Answer: B
The average age of three boys is 25 years and their ages are in the proportion 3 : 5 : 7. The age of the youngest boy is:
Choose the correct option:	A) 21 years	B) 18 years	C) 15 years	D) 9 years	E) None of these

Solution: Total age of 3 boys = (25 × 3) years = 75 years. Ratio of their ages = 3 : 5 : 7.   Age of the youngest = (75 × 3⁄15) years = 15 years.   Answer 15 years
Answer: C
List I: { y, 2, 4, 7, 10, 11}
List II: {3, 3, 4, 6, 7, 10}
If the median T of List I is equal to the sum of the median of list II and the mode of list II, then y equals	Choose the correct choice:
A) 5
B) 7
C) 8
D) T=9
E) 10

Solution: mode of list ii =3   median T of list ii =4+6/2 =5   sum of mode + mean = 3+ 5= 
3+ 5 = 8
8   now to make 8 as the median we need to find a value of y such that if the no. of terms in list 1 are odd then y=8 else if even then 7+y /2=8   here its even so   7+y/2=8 from this y= 9 (T=9)
Answer: D
The value of a machine depreciates at 20% per annum. If its present value is Rs. 1,50,000, at what price should it be sold after two years such that a profit of Rs. 27,000 is made?	Choose the correct choice from the following answers:
A) Rs. 1,10,000 B) Rs. 1,23,000 C) Rs. 1,24,000 D) Rs. 1,21,000 E) None of these

Solution: The value of the machine after two years = 0.8 * 0.8 * 1,50,000 = Rs. 96,000   SP such that a profit of Rs. 24,000 is made = 96,000 + 27,000 = Rs. 1,23,000   ANSWER:Rs. 1,23,000
Answer: B
If two integers x,y (x>y) are selected from -5 to 6 (inclusive), how many cases are there? Answers.
A) 62	B) 66	C) 70	D) 74	E) 78

Solution: There are 12 integers from -5 to 6 inclusive.   12C2 = 66.   The answer is 66.
Answer: B
Six animals of a circus has to be placed inside in six cages one in each cage. If 4 of the cage are too small for 6 of the animal then find the number of ways of caging the animal. Choose one
A) A.240  B) B.808250  C) C.502450  D) D.784200  E) E.302400

Solution: ways for cages that are too small = 5*4*3*2= 
5*4*3*2 = 120
120   since we have 2 cages and 2 animal left therefore ways for 2 cages=2!   total ways =120*2!=604800   A.240nswer A.240
Answer: A
How many two-digit whole numbers yield a remainder of 3 when divided by 10 and also yield a remainder of 3 when divided by 4?
Options:
Answers.
A) ONE	B) TWO	C) THREE	D) FOUR	E) FIVE

Solution: Numbers giving remainder 3 when divided by 10 = 13,23, 33,43, 53,63, 73,83, 93   Numbers giving remainder 3 when divided by 4 = Alternate numbers (coloured in red) = 4   Correct Option:	FOUR
Answer: D