MU-NLPC/Calc-aqua_rat huggingface dataset:
What is the product of the greatest 2 digit multiple of 3 and the greatest 2 digit prime number? Choose the correct choice from the following answers
A) 9,312	B) 9,603	C) 9,506	D) 9,649	E) 9,702

Solution: the greatest 2 digit multiple of 3: 99   the greatest 2 digit prime numebr: 97   97*99.   9603   9,603
Answer: B
If X is the sum of first 30 positive even integers and Y is the sum of first 30 positive odd integers, what is the value of x-y?
Please try to explain your answers	Choose the most appropriate option:  A) 10  B) 25  C) 30  D) 75  E) 100

Solution: First even minus first odd = 2-1= 
2-1 = 1
1;   The sum of first 2 even integers minus the sum of first 2 odd integers= (2+4)-(1+3)= 
(2+4)-(1+3) = 2
2;   The sum of first 3 even integers minus the sum of first 3 odd integers= (2+4+6)-(1+3+5)= 
(2+4+6)-(1+3+5) = 3
3;   We can see the patterns here, so the sum of first 30 positive even integers minus the sum of first 30 positive odd integers will be 30.   Answer: 30.
Answer: C
If 3 persons can do 3 times of a particular work in 3 days, then, 7 persons can do 7 times of that work in ? Choose the correct choice from the following options:
A) 3 days	B) 4 days	C) 4 days	D) 6 days	E) 7 days

Solution: That is, 1 person can do one time of the work in 3 days.   Therefore, 7 persons can do 7 times work in the same 3 days itself.   Option '6 days'
Answer: D
10x + 2y = -6
6x + y = 1
In the system of equations above, what is the value of x?  Select the correct option:
A) 2
B) 3
C) 4
D) 5
E) 6

Solution: 10x + 2y = -6 can be written as 5x + y = -3   Let's subtract the second equation from this equation.   -x = -4   x = 4   The answer is 4.
Answer: C
There are 9color balls at a row. From that how many ways can 9 different color balls be arranged in a row so that black, white, red and green are never together?
Choices:
A) 434562  B) 546563  C) 567343  D) 566748  E) 345600

Solution: Total number of ways in which 9 different colour balls can be arranged in a row   =9! ⋯(A)   Now we will find out total number of ways in which 9 different colour balls can be arranged in a row so that black, white, red and green balls are always together.   We have total 9 balls. Since black, white, red and green balls are always together, group these 4 balls together and consider as a single ball. Hence we can take total number of balls as 6. These 6 balls can be arranged in 6! ways.   We had grouped 4 balls together. These 4 balls can be arranged among themselves in 4! ways.   Hence, total number of ways in which 9 different colour balls be arranged in a row so that black, white, red and green balls are always together   =6!×4! ⋯(B)   From (A) and (B),   Total number of ways in which 9 different colour balls can be arranged in a row so that black, white, red and green balls are never together   =9!–6!×4!=6!×7×8×9−6!×4!=6!(7×8×9–4!)=6!(504–24)=6!×480=720×480=345600   345600
Answer: E
In how many ways can the letters of wordINTELLIGENTbe arranged such that all the Consonants always appear together? Choices
A) 9!	B) 5!*4!	C) 5!*5!	D) 5!*7!	E) 6!*4!

Solution: Let the arrangment be: _ _ _ _ _ _ _ _ _ _ (11 letters, 4 vowels I, E, I, E and 7 consonant N, T, L, L, G, N, T)   For all consonants together, consider them as 1 group {N, T, L, L, G, N, T} I E I E --> this gives us 5! arrangements with {} group considered as 1 . Now {} group can in itself be arranged in 7! ways   Thus total arrangements with all consonants together = 5!*7! --> 5!*7! is the correct answer.
Answer: D
In a garden , there are 10 rows and 12 columns of mango trees. the distance between the two trees is 2 m and a distance of one meter is left from all sides of the boundary of the length of the garden is :  Pick one.
A) 450 sq mtrs
B) 460 sq mtrs
C) 480 sq mtrs
D) 490 sq mtrs
E) 470 sq mtrs

Solution: length of garden = 1+2*11+1= 
1+2*11+1 = 24
24 m   breadth of garden= 1+9*2+1= 
1+9*2+1 = 20
20 m   area= 24*20= 
24*20 = 480
480 sq mtrs   ANSWER:480 sq mtrs
Answer: C
Caleb and Frank are partners in a business. Caleb runs the business and receives 8% of the profit for managing the business, the rest is divided in proportion of their capitals. Caleb invested Rs.5000 and Frank invested Rs.10000. the rest is divided in proportion of their capitals. Out of a total profit of Rs.6000, how much did Caleb receive?
Choose the correct choice from the following options
A) 1197.6 B) 3097.6 C) 1097.6 D) 5097.6 E) 2097.6

Solution: ratio of their investments Rs.5000:10000=1:2   8% of the profit for managing the business =8/100*6000= 
8/100*6000 = 480
480   remaining profit=6000-480= 
6000-480 = 5_520
5520   share profit in ratio of investment 5520/3=323.52   Moses's ratio share=5*323.52= 
5*323.52 = 1_617.6
1617.6   total money Moses collects=1617.6+480= 
1617.6+480 = 2_097.6
2097.6   Answer: 2097.6
Answer: E
34.	The side surface of a cylinder can is rolled with a rectangular plate. If the height of a cylinder tank is 8 feet and the perimeter of the circular base Is 6 feet, what is the diagonal of the rectangular plate?  Answers
A) 10	B) 12	C) 8	D) 14	E) 9

Solution: Think of a can. If you took off the bottom and top and cut a slit down the length, it would flatten to a rectangle. The dimensions of the rectangle are the height of the can and the circumference of the circle. Since you know both, use pythagoreans theorem or properties of 3-4-5 triangles to solve for the hypothenuse, 10. (Correct answer: 10)
Answer: A
If a randomly selected positive single digit multiple of 3 is multiplied by a randomly selected prime number less than 20, what is the probability W that this product will be a multiple of 45?  Choices
A) 1/32	B) 1/28	C) 1/24	D) 1/16	E) 1/14

Solution: There are 3 single digit multiple of 3, that is, 3,6,9.   There are 8 prime nos less than 20 - 2,3,5,7,11,13,17,19   Total outcome - 8*3 = 24   Favourable outcome = 1 (9*5)   Hence required probability W= 1/24. Answer 1/24.
Answer: C
If the money was put in for the same duration of time by A,B and C, three business partners and four times A’s capital is equal to 6 times B’s capital is equal to 10 times C’s capital. Determine that out of a total profit of Rs 4650 what is C’s share?
Select:
A) Rs 9008  B) Rs 906  C) Rs 900  D) Rs 905  E) Rs 901

Solution: Explanation:   It is given that business partnership is independent of time in this case as all the investors have invested their money for same amount of time.   Let A’s capital be x, B’s capital be y and C’s capital be z.   =>x+y+z = 4650   => 4x = 6y = 10z   =>C’s share is z so let us solve the question w.r.t. z   =>x = 5z/2   =>y = 5z/3   =>(5z/2)+(5z/3)+(z) = 4650   =>31z = 4650*6   =>z = 900   ANSWER:Rs 900
Answer: C
Which of the following is equal to (x-1)!/(x-2)!?  Choose the most appropriate option:
A) x-1
B) 1+(1/x)
C) 1
D) x+1
E) x-1

Solution: (x - 1)! = (x - 2)! * (x-1)   (x - 1)!/(x-2)! = x - 1   Answer: x-1
Answer: E
A sum was put at simple interest at a certain rate for 10 years . Had it been put at 5% higher rate , it would have fetched Rs.150 more. What was the Sum?  Choose the correct choice from the following answers.
A) s.120 B) s.130 C) s.140 D) s.150 E) s.300

Solution: At 5% more rate, the increase in S.I for 10 years = Rs.150 (given)   So, at 5% more rate, the increase in SI for 1 year = 150/10 = Rs.15/-   i.e. Rs.15 is 5% of the invested sum   So, 1% of the invested sum = 15/5   Therefore, the invested sum = 15 × 100/5 = Rs.300 Answer: s.300
Answer: E
A cylindrical water tower with radius 14 m and height 20 m is 3/4 full at noon. Every minute, .08π m3 is drawn from tank, while .03π m3 is added. Additionally, starting at 1pm and continuing each hour on the hour, there is a periodic drain of 4π m3. From noon, how many hours will it take to drain the entire tank? Choose one
A) 420 2/7  B) 420 6/7  C) 421  D) 421 3/7  E) 420

Solution: initial volume = (3/4)×∏×14²×20 = 2940∏   Relative Drain/ min = .08∏ - .03∏ = .05∏ m³/min drain   Relative drain / hour .08  - .03= 
.08  - .03 = 0.05
.05∏ m³/min drain   Relative drain / hour= .05∏×60 = 3∏ m³/ hr   Every one hour starting from 1pm, 4∏ m³ of water is drained. It means that only at the hour the water is drained and NOT “in that 1 hour“   So after 1 hr the relative drain would be 3∏ + 4∏ = 7∏m³ of water drain   What i did initially was formed an equation 2940∏   3  + 4= 
  3  + 4 = 7
7∏m³ of water drain   What i did initially was formed an equation 2940∏= 7∏×n (n is the number of hrs) so ended up with 420. 420
Answer: E
50^51^52 /11
Choose one
A) 6  B) 4  C) 7  D) 3  E) 5

Solution: We know that 6^1=6 or 6^2=36 so for all power of 6 unit digit is 6 now que is 50^51^52 now if we divide 50/11 then rem is 6 means 6^51=6 at unit place same for 6^52 salso give 6 at unit place now finally 50^51^52 gives 6 at unit place now 6/11=6   6NSWER:6
Answer: A
If there are only 2 wheelers and 4 wheelers parked in a school located at the heart of the city, find the number of 4 wheelers parked there if the total number of wheels is 66?
Choose the correct choice from the following.
A) 11	B) 12	C) 13	D) 16	E) 17

Solution: four wheeler=16*4= 
16*4 = 64
64(max)   2 wheel=1   so no of 4 wheeler=16   ANSWER:16
Answer: D
There are 5 married couples and a group of three is to be formed out of them; how many arrangements are there if a husband and wife may not be in the same group?
Choose one:
A) 70	B) 75	C) 80	D) 85	E) 90

Solution: Total ways of selecting 3 people out of 10 = 10C3 = 10*9*8/3*2 = 120   So final answer cannot be greater than 120.   In 3 people only 1 couple is possible. So way of selecting 1 couple out of 5 = 5801 = 5   Way of selecting 1 person out of remaining 8 = 8801 = 8   Total ways when there will be 1 couple and 1 different person = 8*5= 
8*5 = 40
40   Total number of ways in which no people will be from same couple= 120 - 40= 
120 - 40 = 80
80 ANS"80
Answer: C
A bat is bought for Rs.400 and sold at a gain of 20% find its selling price	Choose the correct option
A) Rs.460/-	B) Rs.470/-	C) Rs.480/-	D) Rs.500/-	E) Rs.520/-

Solution: 100 % ------> 400 (100 * 4 = 400)   120 % ------> 480 (120 * 4 = 480)   Selling price = Rs.480/-   Rs.480/-
Answer: C
On dividing 181 by a number, the quotient is 9 and the remainder is 1. Find the divisor?	Choose the correct choice from the following answers
A) A)12  B) B)15  C) C)16  D) D)17  E) E)20

Solution: d = (D-R)/Q   = (181 - 1)/9   = 180/9= 
180/9 = 20
20   20)
Answer: E
Renuka bought an electric drill at 90% of the regular price. She paid $450 for the drill. What was the regular price?	Choose the correct choice from the following choices
A) $400 B) $500 C) $300 D) $200 E) $100

Solution: Regular price = 450/90*100= 
450/90*100 = 500
500   Answer : $500
Answer: B
A train running at the speed of 60 km/hr crosses a pole in 9 seconds. Find the length of the train?
Choose the correct answer
A) 150 meter B) 876 meter C) 167 meter D) 719 meter E) 169 meter

Solution: Speed = 60*(5/18) m/sec = 50/3 m/sec   Length of Train (Distance) = Speed * Time     (50/3) * 9= 
  (50/3) * 9 = 150
150 meter   150 meternswer: 150 meter
Answer: A
X can finish a work in 25 days. Y can finish the same work in 20 days. Y worked for 12 days and left the job. how many days does X alone need to finish the remaining work?
Choose the correct choice from the following answers.
A) 2	B) 5	C) 6	D) 7	E) 8

Solution: Work done by X in 1 day = 1/25   Work done by Y in 1 day = 1/20   Work done by Y in 12 days = 12/20 = 3/5   Remaining work = 1 – 3/5 = 2/5   Number of days in which X can finish the remaining work = (2/5) / (1/20)= 
(2/5) / (1/20) = 8
8   8
Answer: E
A tap can fill a tank in 6 hours. After half the tank is filled three more similar taps are opened. What is the total time taken to fill the tank completely?	Select
A) 3 hrs 45 min B) 3 hrs 45 min C) 3 hrs 42 min D) 3 hrs 65 min E) 3 hrs 35 min

Solution: Time taken by one tap to fill the tank = 3 hrs.   Part filled by the taps in 1 hour = 4 * 1/6 = 2/3   Remaining part = 1 - 1/2 = 1/2   2/3 : 1/2 :: 1 : x   x = 1/2 * 1 * 3/2 = 3/4 hrs. i.e., 45 min   So, total time taken = 3 hrs 45 min.   Answer:3 hrs 45 min
Answer: B
What percent of the different arrangements of the letters of the word AFACUT are those in which the vowels appear together? Choose the correct answer:
A) 25%
B) 20%
C) 30%
D) 40%
E) 50%

Solution: let's determine the number of total possibilities in arranging the letters. There are six spaces, so the total number of arrangements is 6!, or 360.   Next, we need to figure out how to determine the number of ways that we can arrange the 3 vowels together - simply place them together (as in AAU) and call that a single place.   Next, we must determine the number of ways to arrange the now 4 units (i.e., AAU, B, C, S). Like above, there are 4 units and 4 places so the number of arrangements is 4!, or 24.   Finally, we need to account for the number of ways we can arrange AAU. We can either write out each unique iteration (AAU, AUA and UAA) or calculate as 3!/2! and get 3.   Putting this all together, we get the number of ways to arrange the letters so that the vowels are together is 4! x 3 ==> 72   the number of total arrangements of all the letters is 6! ==> 360   72/360 = 1/5, or 20%   Correct answer is 20%
Answer: B
How many bricks, each measuring 100 cm x 11.25 cm x 6 cm, will be needed to build a wall of 8 m x 6 m x 22.5 cm?
Select:
A) 1600 B) 2400 C) 5500 D) 7400 E) 3400

Solution: Number of bricks = Volume Of the wall / Volume of 1 brick = (800 x 600 x 22.5) / (100 x 11.25 x 6) = 1600   1600NSWER:1600
Answer: A
The average (arithmetic mean) of the integers from 100 to 400, inclusive, is how much greater than the average of the integers from 50 to 250, inclusive?
Choose the correct choice from the following
A) 100  B) 175  C) 200  D) 125  E) 300

Solution: For an AP the mean or average of series is average of first and last term.   So, average of numbers between 100 to 400, inclusive = (100+400)/2= 
(100+400)/2 = 250
250   average of numbers between 50 to 250, inclusive= (50+250)/2= 
(50+250)/2 = 150
150   difference= 250 - 150= 
250 - 150 = 100
100   100nswer is 100
Answer: A
If log10 2 = 0.3010, then log2 10 is equal to:  Answers.
A) 1000/301  B) 1000/500  C) 966/301  D) 0.301  E) 0.966

Solution: log2 10 =	1/log10 2 = 1/0.3010 = 10000/3010 = 1000/301   1000/301NSWER 1000/301
Answer: A
The ages of Patrick and Michael are in the ratio of 3 : 5 and that of Michael and Monica are in the ratio of 3 : 5. If the sum of their ages is 98, what is the difference between the ages of Patrick and Monica?
Choose the correct choice from the following answers:
A) 32
B) 48
C) 45
D) 72
E) 18

Solution: Ages of P and Mi=3x:5x   Ages of Mi and Mo=3x:5x   Rationalizing their ages. ratio of their ages will be 9x:15x:25x   Sum=49x=98   x=2   Difference if ages of Pa and Mo=25x-9x=16x25 -9= 
25 -9 = 16
16x=16*2= 
16*2 = 32
32   32nswer 32
Answer: A
At what rate percent per annum will the simple interest on a sum of money be 2/5 of the amount in 10 years?
Pick
A) 4%  B) 74%  C) 64%  D) 74%  E) 94%

Solution: Let sum = x. Then, S.I. = 2x/5, Time = 10 years.   Rate = (100 * 2x) / (x * 5 * 10) = 4%   4%nswer: 4%
Answer: A
The perimeter of one square is 48 cm and that of another is 20 cm. Find the perimeter and the diagonal of a square which is equal in area to these two combined?
Choose the correct choice from the following.
A) 12√2	B) 13√2	C) 13√3	D) 13√1	E) 13√1

Solution: 4a = 48 4a = 20   a = 12 a = 5   a2 = 144 a2 = 25   Combined area = a2 = 169 => a = 13   d = 13√2   Answer:13√2
Answer: B
Machine–A produces 40% of the total output and Machine-B produces 60% of the total output. An average of nine units out of a thousand goods manufactured by Machine-A and one unit of 200 units produced by Machine-B prove to be defective. What is the probability that a unit chosen at random from the total daily output of the factory is defective?  Choose the correct option
A) 0.6	B) 0.06	C) 0.0066	D) 0.0006	E) 6.0e-05

Solution: Let total Production be 10000 units....   A produces 4000 units and 36 units are defective   B produces 6000 units and 30 units are defective   So, Out of total 10,000 units 66 units are defective...   So the required probability = 66/10000= 
66/10000 = 33/5_000 = around 0.0066
> 0.0066   Answer will be (0.0066)
Answer: C
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?
Answers:
A) 2877 B) 1299 C) 8400 D) 2799 E) 2698

Solution: Ratio of their shares = 22500 : 35000 = 9:14   Deepak's share = 13800 * 14/23   = Rs.8400.   Answer: 8400
Answer: C
The area of a circle is four times its circumference. What is the diameter of the Circle?
Select
A) 4π  B) 16  C) 8  D) 12  E) 8π

Solution: pi*r^2 = 4*2*pi*r   r*pi(8 - r) = 0   r = 8   Diameter = 2r = 16   16
Answer: B
X starts a business with Rs.45000. Y joins in the business after 3 months with Rs.36000. What will be the ratio in which they should share the profit at the end of the year?  Choose the correct choice from the following:
A) 20:9
B) 2:1
C) 3:2
D) 2:3
E) 5:3

Solution: Ratio in which they should share the profit   = Ratio of the investments multiplied by the time period   =45000×12:36000×9   =45×12:36×9   =15×12:9×9   =20:9   20:9nswer is 20:9.
Answer: A
Sonika deposited Rs.8000 which amounted to Rs.9200 after 3 years at simple interest. Had the interest been 1% more. She would get how much?  Choose the correct choice from the following options:
A) 9440  B) 96288  C) 26667  D) 1662  E) 2882

Solution: (8000*3*1)/100= 
(8000*3*1)/100 = 240
240   9200   --------   9440   9440nswer:9440
Answer: A
QUANT 4-PACK SERIES Problem Solving Pack 4 Question 2 For every positive integer n...
For every positive integer n that is greater than 1, the function t(n) is defined to be the sum of all of the odd integers from 1 to n, inclusive. The t(n) could have any of the following units digits except…? Choose the correct choice.
A) 1
B) 2
C) 4
D) 6
E) 9

Solution: For every positive integer n that is greater than 1, the function t(n) is defined to be the sum of all of the odd integers from 1 to n, inclusive. The t(n) could have any of the following units digits except…?   Used brute force on this one to calculate. Not sure if there is a quicker way.   1+3= 
1+3 = 4
4 C is out   1+3+....15= 81 A is out   1+3+5+7= 
1+3+5+7 = 16
16 D is out   1+3+5= 
1+3+5 = 9
9 E i out   Answer: 2
Answer: B
10% of a number is added to 45, the result is the same number. Find the number? Choose the correct answer.
A) 50	B) 288	C) 270	D) 129	E) 281

Solution: (10/100) * X + 45 = X   9X = 450   X =50   50nswer:50
Answer: A
Which of the following leads to the correct mathematical solution for the number of ways that the letters of the word BOOK could be arranged to create a four-letter code?	Select:
A) 4!
B) 4! − ( 2!)
C) 4! − (3! × 2!)
D) 4!/( 2!)
E) 4!/(3! × 2!)

Solution: BOOK - four letters can be arranged in 4! ways   since 'O' repeats 2 times we need to divide the 4! ways by 2! to adjust repetition.   4!/(2!)   Ans. 4!/( 2!)) 4!/( 2!)
Answer: D
A certain sum is invested at simple interest at 15% p.a. for two years instead of investing at 12% p.a. for the same time period. Therefore the interest received is more by Rs. 720. Find the sum?
Choose the correct choice from the following choices
A) s. 7000	B) s. 9000	C) s. 14000	D) s. 12000	E) s. 27000

Solution: Let the sum be Rs. x.   (x * 15 * 2)/100 - (x * 12 * 2)/100 = 720   => 30x/100 - 24x/100 =720   => 6x/100 = 720   => x = 12000.   ANSWER:s. 12000
Answer: D
In a group of 4 boys and 6 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be selected?	Choose the correct choice from the following:
A) 135	B) 155	C) 175	D) 195	E) 215

Solution: Number of ways to select four children is 10C4 = 210   Number of ways to choose only girls is 6C4 = 15   Number of ways that at least one boy is selected is  210 - 15= 
 210 - 15 = 195
195   The answer is 195.
Answer: D
A committee is reviewing a total of 20x black-and-white films and 8y color films for a festival. If the committee selects y/x% of the black-and-white films and all of the color films, what fraction of the selected films are in color?	Choose one: A) 40/41 B) 20/41 C) 30/41 D) 60/41 E) 80/41

Solution: Say x=y=10. In this case we would have:   20x=200 black-and-white films;   8y=80 color films.   y/x%=10/10= 
10/10 = 1
1% of the black-and-white films, so 2 black-and-white films and all 80 color films, thus total of 82 films were selected.   Color films thus compose 80/82=40/41 of the selected films.   40/41nswer: 40/41
Answer: A
Complete the numerical series by replacing the question mark with the correct numbers.
5+3+2 = 151022
9+2+4 = 183652
8+6+3 = 482466
5+4+5 = 202541
9+5+5 = ??????  Pick one
A) 454585 B) 454583 C) 456685 D) 454588 E) 456585

Solution: 454585   454585   Explanation:   Number is formed as (num454585*numB)(numB*numC)(numC*num454585)   Following the formular, 1st row will be like   5+3+2 => 5*3 3*2 2*5 => 151022   Simillarly   (9*5)(9*5)(9*5+9*5-5) => 454585
Answer: A
The current of a stream runs at the rate of 4 kmph. A boat goes 6 km and back to the starting point in 2 hours, then find the speed of the boat in still water?	Choose the correct answer:
A) 3
B) 7
C) 8
D) 5
E) 1

Solution: S = 4   M = x   DS = x + 4   US = x - 4   6/(x + 4) + 6/(x - 4) = 2   x = 8   Answer:8
Answer: C
The following list follows a peculiar pattern. Can you find it out and guess the next number?
2, 12, 36, 80, 150, 252, ?  Choose the correct choice from the following answers:
A) 383	B) 321	C) 392	D) 651	E) 823

Solution: C   The next number is 392.   The first number = (Square of 1 + 392ube of 1)   The second number = (Square of 2 + 392ube of 2)   The third number = (Square of 3 + 392ube of 3)   The fourth number = (Square of 4 + 392ube of 4)   The fifth number = (Square of 5 + 392ube of 5)   The sixth number = (Square of 6 + 392ube of 6)   Therefore, the seventh number will be   Square of 7 + 392ube of 7 = 392.
Answer: C
If log1087.5 = 3.9421, then the number of digits in (875)10 is? Choose the correct choice from the following options:
A) 30 B) 28 C) 27 D) 50 E) 25

Solution: X = (875)10 = (87.5 x 10)10   Therefore, log10X = 10(log1087.5 + 1)   = 10(3.9421 + 1)   = 10(4.9421) = 49.421   X = antilog(49.421)   Therefore, number of digits in X = 50.   ANSWER:50
Answer: D
If a and b are positive integers, and a=5b+20, the greatest common divisor of a and b CANNOT be	Pick one: A) 2 B) 4 C) 5 D) 6 E) 10

Solution: If b is 2, 4, 5, or 10, then GCD of a and b is 2, 4, 5, and 10 respectively. So, by POE the answer must be D.   Still: if b is a multiple of 6, then a is 20 greater than a multiple of 6, so not a multiple of 6, so both of them cannot be divisive by 6.   Answer: 6.
Answer: D
The length of a rectangular plot is thrice its breadth. If the area of the rectangular plot is 867 sq m, then what is the breadth of the rectangular plot?  Choose one.
A) 66 m  B) 17 m  C) 87 m  D) 65 m  E) 43 m

Solution: Let the breadth of the plot be b m.   Length of the plot = 3 b m   (3b)(b) = 867   3b2 = 867   b2 = 289 = 172 (b > 0)   b = 17 m.   Answer:17 m
Answer: B
Median C of price of the car is 52,000. which could be the median of the other two.
35000, 44000, x, y, 57000.  Select the correct option.
A) 38000  B) 47000  C) 48000  D) 51,000  E) 56,000

Solution: Median of the car is 52,000 therefore 52,000 is the middle number. Assuming Y >= X, X will have to be the median value i.e. 52,000. Therefore the remaining value would have to be between 52,000 and 57,000 inclusive. The only answer choice that fits is C 56,000.56,000
Answer: E
A car travelling with 5/7 of its actual speed covers 42 km in 1 hr 40 min 48 sec. Find the actual speed of the car.
Pick.
A) 17 6/7 km/hr B) 25 km/hr C) 30 km/hr D) 35 km/hr E) 45 km/hr

Solution: Time taken = 1 hr 40 min 48 sec = 1 hr 40 4/5 min. = 126/75 hrs.   Let the actual speed be x km/hr.   Then, (5/7)x X 126/75 = 42   --> x = 35 km/hr.   Answer : 35 km/hr.
Answer: D
In how many different number of ways 5 boys and 4 girls can sit on a bench?
Options:
A) 700  B) 710  C) 720  D) 362880  E) 740

Solution: npn = n!   9p9 = 9 X 8 X 7 X 6 Ã— 5 Ã— 4 Ã— 3 Ã— 2 Ã— 1 = 362880   362880
Answer: D