MU-NLPC/Calc-aqua_rat huggingface dataset:
If 20 typists can type 38 letters in 20 minutes, then how many letters will 30 typists working at the same rate complete in 1 hour? Choose the correct choice.
A) 63	B) 72	C) 144	D) 171	E) 400

Solution: 20 typists can type 38 letters, so 30 typists can type = 38*30/20   38*30/20 letters can be typed in 20 mins. In 60 mins typist can type= 38*30*60/20*20= 171   171 is the answer
Answer: D
What is the greatest prime factor of 4^16 - 2^30?  Choose the correct choice
A) 2
B) 3
C) 5
D) 7
E) 11

Solution: 4^16 - 2^30   =(2^2)^16 - 2^30   = 2^32 - 2^30   = 2^30 (2^2 -1)   = 2^30 * (4-1)   = 2^30 * 3   The greatest prime factor is 3.   The answer is 3.
Answer: B
A research team that must consists of 3 members is to be formed from a pool of 6 scientists. How many different teams are possible?  Select the correct option:  A) 17  B) 10  C) 40  D) 26  E) 20

Solution: Note that the team must consist of 3 members, not at least 3 members. Hence, all you have to do is 6C3 = 20   Answer (20)
Answer: E
Rs 3000 is divided into two parts such that one part is put out at 3% and the other at 5%. If the annual interest earned from both the investments be Rs 144, find the first part. Pick:	A) s 400	B) s 280	C) s 300	D) s 350	E) s 310

Solution: Explanation :   Average rate = (144/3000)*100= 
(144/3000)*100 = 24/5 = around 4.8
4.8   Ratio= 2:18   So, first part = (2/20)*3000= 
(2/20)*3000 = 300
Rs 300.   Answer : s 300
Answer: C
Of the 400 members at a health club, 260 use the weight room and 300 use the pool. If at least 60 of the members do not use either, then the number of members using both the weight room and the pool must be between: Choose the correct choice
A) 40 to 100 B) 80 to 140 C) 160 to 260 D) 220 to 260 E) 220 to 300

Solution: 260-X+X+300-X+GT60 = 400   =>X = GT 620-400   => X = GT 220   => X >= 220 (Here GT means Greater than)   So Min value of X is 220 coming to options 220 to 260/E   X's maximum value cannot exceed 260 as per the venn diagramsince 'W' circle cannot accomodate 'X' More than 260   ANSWER:220 to 260
Answer: D
What annual payment will discharge a debt of Rs. 1030 due in 2 years at the rate of 5% compound interest?
Choose the correct option
A) 553.94 B) 551.25 C) 534.33 D) 543.33 E) 646.33

Solution: Explanation:   Let each installment be Rs. x. Then,   x/(1 + 5/100) + x/(1 + 5/100)2 = 1030   820x + 1030 * 441   x = 553.94   So, value of each installment = Rs. 553.94   553.94nswer: Option 553.94
Answer: A
A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is:  Answers
A) 100
B) 110
C) 120
D) 130
E) 150

Solution: Let the length of the train be x meters and its speed be y m/sec.   They, x / y = 15 => y = x/15   x + 100 / 25 = x / 15   x = 150 m.   Answer: Option 130
Answer: D
The probability of a lottery ticket being a prized ticket is 0.2. When 4 tickets are purchased, the probability of winning a prize on atleast one ticket is ?
Choose the correct option
A) 0.5906
B) 0.5904
C) 0.5902
D) 0.5901
E) 0.5932

Solution: P(winning prize atleast on one ticket)   = 1 - P("Losing on all tickets")   = 1 - (0.8)4 = (1 + (0.8)2)(1 - (0.8)2)   = (1.64)(0.36) = 0.5904.   Answer: 0.5904
Answer: B
12. What is the dividend. divisor 17, the quotient is 9 and the remainder is 10.	Choose one: A) 150 B) 152 C) 154 D) 163 E) 144

Solution: 163 = d * Q + R   163 = 17 * 9 + 10   163 = 153 + 10   163 = 163   ANSWER 163
Answer: D
A furniture dealer purchased a desk for $140 and then set the selling price equal to the purchase price plus a markup that was 30% of the selling price. If the dealer sold the desk at the selling price, what was the amount of the dealer's gross profit from the purchase and the sale of the desk?  Choose the correct choice from the following options
A) $40
B) $60
C) $80
D) $90
E) $100

Solution: Purchase price = 140   Selling price = x   140 + 0.3*x = x   0.7*x = 140   x = 200   Profit = 200 - 140= 
200 - 140 = 60
60   ANSWER:$60
Answer: B
Lisa and Robert have taken the same number of photos on their school trip. Lisa has taken 3 times as many photos as Claire and Robert has taken 10 more photos than Claire. How many photos has Claire taken?  Choose the correct choice from the following:
A) 5
B) 8
C) 11
D) 12
E) 14

Solution: L = R   L = 3C   R = C + 10   3C = C + 10   C = 5   The answer is 5.
Answer: A
If a person walks at 14 km/hr instead of 10 km/hr, he would have walked 20 km more. The actual distance travelled by him is:  Select:  A) 50 Km  B) 55 Km  C) 45 Km  D) 35 Km  E) 40 Km

Solution: Let the actual distance travelled be x km.   Then,	x /10=x + 20 / 14   14x = 10x + 200   4x = 200   x = 50 km.   50 KmNSWER : 50 Km
Answer: A
Abhay's age after six years will be three -seven of his father 's age . TTen years ago, the ratio of heir ages was 1 : 5. What is Abhay's fathers age at present ? Answers.
A) 45 years B) 48 years C) 49 years D) 50 years E) 52 years

Solution: Explanation :   Sol. Let the ages of Abhay and his father 10 years ago be xand5xxand5x years respectively . Then   Abhay's age after 6 years = (x+10)+6 =(x+16)(x+10)+6 =(x+16) years   Father's age after 6 years = (5x+10) +6=(5x+16)(5x+10) +6=(5x+16) years   âˆ´âˆ´ (x+16)=37(5x+16)(x+16)=37(5x+16)   â‡” 7(x+16)=3(5x+16   â‡” 7x+112=15x+48   â‡” 8x=64   â‡” x=8   Hence , Abhay's father's present age = (5x+10)(5x+10) = 50 years   ANSWER IS 50 years
Answer: D
In a group of ducks and cows, the total number of legs are 22 more than twice the no. of heads. Find the total no.of buffaloes.
Choose the correct choice
A) 11	B) 12	C) 13	D) 15	E) 16

Solution: Let the number of buffaloes be x and the number of ducks be y   => 4x + 2y = 2 (x + y) + 22   => 2x = 22 => x = 11   11
Answer: A
A certain restaurant offers 5 kinds of cheese and 2 kinds of fruit for its dessert platter. If each dessert platter contains an equal number of kinds of cheese and kinds of fruit, how many different dessert platters could the restaurant offer?	Choose the correct choice from the following answers.
A) 8 B) 12 C) 15 D) 21 E) 20

Solution: As dessert platter should contain equal number of kinds of cheese and fruits, desert can contain:   A. 2 kinds of cheese and 2 kinds of fruits --> 5C2*2C2=10*1= 
10*1 = 10
10   B. 1 kind of cheese and 1 kind of fruit --> 5C1*2C1=5*2= 
5*2 = 10
10   A+B=10+10= 
10+10 = 20
20   Answer: 20.
Answer: E
Tom, working alone, can paint a room in 16 hours. Peter and John, working independently, can paint the same room in 8 hours and 4 hours, respectively. Tom starts painting the room and works on his own for two hour. He is then joined by Peter and they work together for two hour. Finally, John joins them and the three of them work together to finish the room, each one working at his respective rate. What fraction of the whole job was done by Peter?	Options
A) 4/7
B) 5/7
C) 2/7
D) 1/7
E) 3/7

Solution: Let the time when all three were working together be t hours. Then:   Tom worked for t+4 hour and has done 1/16*(t+4) part of the job;   Peter worked for t+2 hour and has done 1/8*(t+2) part of the job;   John worked for t hours and has done 1/4*t part of the job:   1/16*(t+4)+1/8*(t+2)+1/4*t=1 --> multiply by 16 --> (t+4)+(2t+2)+4t=16 --> t=10/7;   Hence Peter has done 1/8*(10/7+2)=1/8 *24/7=3/7   Answer: 3/7
Answer: E
Three guests check into a hotel room. The clerk says the bill is $30, so each guest pays $10. Later the clerk realizes the bill should only be $25. To rectify this, he gives the bellhop $5 to return to the guests. On the way to the room, the bellhop realizes that he cannot divide the money equally. As the guests didn’t know the total of the revised bill, the bellhop decides to just give each guest $1 and keep $2 for himself.
Now that each of the guests has been given $1 back, each has paid $9, bringing the total paid to $27. The bellhop has $2. If the guests originally handed over $30, what happened to the remaining $1?	Options.
A) $30 B) $20 C) $10 D) $40 E) $50

Solution: There is no missing dollar. A dollar only goes "missing" because the statement "each man paid $9 for the room" is wrong - each of three men paid out a total of $9, but that $9 included both the room charge and the bellboy's tip. All in all, each man paid out a total of $9 and had $1 left over, completely accounting for the $30 they started with.. Hotel - $25 Bellhop - $2 Customers - $1 each $25 + $2 + $3 = $30   $30nswer $30 25 +  2 +  3= 
 25 +  2 +  3 = 30
$30   $30nswer $30
Answer: A
If X is to be chosen at random from the integers between 1 to 6, inclusive, and Y is to be chosen at random from the integers between 7 and 10, inclusive, what is the probability that X + Y will be even? Select the correct option:	A) 1/2	B) 2/3	C) 3/4	D) 4/5	E) 5/6

Solution: X+Y will be even if X and Y are both even or both odd.   P(X and Y are both even) = 3/6*2/4 = 1/4   P(X and Y are both odd) = 3/6*2/4 = 1/4   P(X+Y is even) = 1/4 + 1/4 = 1/2   The answer is 1/2.
Answer: A
If X is invested in a bank at a rate of simple interest of y% p.a. for two years, then the interest earned is 800. if X is invested at y% p.a., for two years when the interest is compounded annually, the interest is 820. What is the value of X?
Choices
A) 8000 B) 6000 C) 5000 D) 4000 E) 3000

Solution: Simple way to solve this question is to use options.   From SI, we know that X*y=40,000.   Now, put the value of X = 8000, we will have y = 5%   To calculate CI,   Now, we know 1st year Amount= 8000+5% of 8000= 8400.   2nd year, Amount = 8400 + 5% of 8400 = 8820.   We can see after 2 years Interest = 8820-8000= 
8820-8000 = 820
820. hence, it satisfies the question. Hence 8000 is the correct answer
Answer: A
Rob also compared the Empire State Building and the Petronas
Towers. What is the height difference between the two if the Empire
State Building is 356m tall and the Petronas Towers is 370m tall?	Choose the correct choice from the following answers:
A) 14
B) 17
C) 23
D) 45
E) 12

Solution: 370-356=14.14nswer is 14.
Answer: A
In the third grade of Windblown School there are 90 students, one third of them failed the math test and 1/6 failed that literature test. At least how many students failed both tests?
Select the correct option: A) 0. B) 6. C) 8. D) 10. E) 12.

Solution: Total = 90   failed in math = 90/3= 
90/3 = 30
30   failed in literature=90/6= 
90/6 = 15
15   the least failed in both can be 0   while max can be 15   0.nswer 0.
Answer: A
Arun purchased 30 kg of wheat at the rate of Rs. 11.50 per kg and 20 kg of wheat at the rate of 14.25 per kg. He mixed the two and sold the mixture. Approximately what price per kg should be sell the mixture to make 20% profit? Pick one:
A) 15.12 B) 16.33 C) 16.35 D) 16.3 E) 16.32

Solution: C.P. of 50 kg wheat = (30 * 11.50 + 20 * 14.25) = Rs. 630.   S.P. of 50 kg wheat = 120% of Rs. 630 = 120/100 * 630 = Rs. 756   S.P. per kg = 756/50 = Rs. 15.12   15.12nswer: 15.12
Answer: A
An analyst will recommend a combination of 2 industrial stocks, 2 transportation stocks, and 2 utility stocks. If the analyst can choose from 6 industrial stocks, 5 transportation stocks, and 4 utility stocks, how many different combinations of 6 stocks are possible?
Select: A) 1200 B) 900 C) 600 D) 180 E) 720

Solution: 6C2 * 5C2 * 4C2 = 15*10*6= 
15*10*6 = 900
900.   Answer: 600
Answer: C
If the LCM and HCF of 8 and another number is 24 and 4 respectively. Find the other number ?
Choose one:
A) 11  B) 12  C) 14  D) 15  E) 16

Solution: HCF x LCM = Product of Numbers   4 x 24 = 8 x the other number   other number = (4 x 24) / 8   other number = 12   ANSWER : 12
Answer: B
A big container is 30% full with water. If 45 liters of water is added, the container becomes 3/4 full. What is the capacity of the big container?  Options.
A) 36 liters
B) 40 liters
C) 45 liters
D) 54 liters
E) 100 liters

Solution: A big container is 30% full with water and after 45 liters of water is added, the container becomes 75% full. Hence these 45 liters account for 45% of the container, which means that the capacity of it is  45/0.45= 
 45/0.45 = 100
100 liters.   OR: if the capacity of the container is x liters then: 0.3x+45=0.75x --> x=100 liters.   Answer:100 liters.
Answer: E
The average temperature of the town in the first four days of a month was 58 degrees. The average for the second, third, fourth and fifth days was 61 degrees. If the temperatures of the first and fifth days were in the ratio 7 : 8, then what is the temperature on the fifth day ?
Choices.
A) 96 degrees	B) 64 degrees	C) 65 degrees	D) 66 degrees	E) 67 degrees

Solution: Explanation:   Sum of temperatures on 1st, 2nd, 3rd and 4th days = (58 * 4)= 
(58 * 4) = 232
232 degrees ... (1)   Sum of temperatures on 2nd, 3rd, 4th and 5th days - (61 * 4)= 244 degrees ....(2)   Subtracting (1) From (2), we get :   Temp, on 5th day - Temp on 1st day = 12 degrees.   Let the temperatures on 1st and 5th days be 7x and 8x degrees respectively.   Then, 8x - 7x = 12 or x = 12. 96 degreesnswer: 96 degrees   Temperature on the 5th day = 8x = 96 degrees.
Answer: A
A call center has two teams. Each member of Team A was able to process 3/5 calls as compared to each member of Team B. If Team A has 5/8 as many number of call center agents as Team B, what fraction of the total calls was processed by Team B? Choose the correct answer:
A) 3/2
B) 3/4
C) 8/11
D) 1/2
E) 1/5

Solution: Let team B has 8 agents, so team A has 5 agents   Let each agent of team B picked up 5 calls, so total calls by team B = 40   So, each agent in Team A picked up 3 calls, so total calls for team A = 15   Fraction for team B = 40/(40+15) =8/11 = Answer = 8/11
Answer: C
Four of the five parts numbered (a), (b), (c), (d) and (e) are exactly equal. Which of the parts is not equal to the other four? The number of that part is the answer. Choose the correct choice from the following answers.
A) 16.80 × 4.50 + 4.4  B) 1600 ÷ 40 + 16 × 2  C) 5.5 × 8.4 + 34.6  D) 1620 ÷ 20 – 1  E) 1856.95 – 1680.65 – 96.3

Solution: Others equal 80 whereas (c) equals 80.8.   Answer 5.5 × 8.4 + 34.6
Answer: C
If |u+v|=|u-v|, then u*v must be equal to:  Answers.
A) 2
B) 0
C) -3
D) 3
E) -2

Solution: Solution 1: Distance perspective   |u-v| = |u+s| ==> The distance of u and v is equal to the distance of u and -v.   <=======(-v)=======0=======(v)======>   Only 0 is the value that has a distance equal to v and -v.   Solution 2:   |u-v| = |u+v| (square both)   u^2 -2uv + v^2 = u^2 + 2uv + v^2   4uv = 0   uv = 0   Answer: 0
Answer: B
What positive number, when squared, is equal to the cube of the positive square root of 12?  Pick
A) 64  B) 32  C) 8  D) 4  E) 2

Solution: Let the positive number be x   x^2 = ((12)^(1/2))^3   =>x^2 = 4^3 = 16   => x = 4   Answer 4
Answer: D
Evaluate
3.6×0.48×2.50 / 0.12×0.09×0.5	Options
A) 80  B) 800  C) 8000  D) 80000  E) None of these

Solution: Explanation:   3.6×0.48×2.50 / 0.12×0.09×0.5   =36×48×250 / 12×9×5=800   Option 800
Answer: B
An aircraft company has 20 planes in its fleet. Every year it retires 5 of its planes and replaces then with 6 newer planes. How many years will it take the company, starting from 2010, to reduce the number of it s old planes to less than half of its fleet?
Pick
A) 2	B) 1	C) 3	D) 4	E) 5

Solution: Total fleet--20   End of year 2010 -- (retires 5 and buys 6) total fleet--21(15 old 6 new).   End of year 2011 -- (retires 5 and buys 6) total fleet--22(10 old 12 new).   End of year 2012 -- (retires 5 and buys 6) total fleet--23(5 old 18 new).   2nswer is 2--after 2 years the company has a total of 22 planes (10 old 12 new).
Answer: A
Mario and Nina each have a bag of marbles, each of which contains 4 blue marbles, 10 red marbles, and 6 white marbles. If Mario and Nina each select one marble from their respective bags, what is the probability that either Mario or Nina select a red marble? Answers:  A) 3/4  B) 2/4  C) 1/4  D) 1/8  E) 1/16

Solution: Mario and Nina each select one marble from their respective bags.   Probability that either Mario or Nina select a red marble = Probability that Mario selects a red marble + Probability that Nina selects a red marble   Probability that either Mario or Nina select a red marble = (10/20)*(10/20) + (10/20)*(10/20) = 2*(1/4)   Probability that either Mario or Nina select a red marble = 1/2   Answer would be 2/4.
Answer: B
A can do a piece of work 40 days. B can do work in 60 days. In how many days they will complete the work together?
Choose the correct choice from the following answers:  A) 15 days  B) 16 days  C) 19 days  D) 17 days  E) 24 days

Solution: LCM = 120, Ratio= 40:60=2:3   No of days= 120/(2 + 3) = 90/5 = 24 days   ANSW24 daysR:24 days
Answer: E
If mn > 0, which of the following must be negative? Choose the correct choice from the following answers.
A) m +n B) |m| + n C) m^2 D) -m/n E) mn

Solution: Given mn> 0 So both will be the positive integers. If both are positive, then A,B,C,E also positive.   Answer :-m/n
Answer: D
If it takes 4 identical printing presses exactly 4 hours to print 6,000 newspapers, how long would it take 2 of these presses to print 5,000 newspapers?
Select the correct option:
A) 6 hrs 50 mins
B) 6 hrs 40 mins
C) 6 hrs 30 mins
D) 6 hrs 20 mins
E) 6 hrs 10 mins

Solution: 4 presses - 6,000 newspapers - 4 hours ;   2 presses - 3,000 newspapers - 4 hours ; (240 mins)   2 presses - 5,000 newspapers - 240/3000*5000 = 400 mins = 6 hrs 40 mins   Answer : 6 hrs 40 mins
Answer: B
What will be the fraction of 6%	Options
A) 1/20
B) 3/50
C) 1/75
D) 1/25
E) None of these

Solution: Explanation:   6*1/100 = 3/50.   Option 3/50
Answer: B
How many times in a day the hands of a clock are straight?
Choose the correct choice from the following answers:	A) 21	B) 27	C) 24	D) 22	E) 25

Solution: In 12 hours, the hands coincide or are in oppesite direction 22 times.   In 24 hours, they are at right angles 22 times.   Answer is 22.
Answer: D
Sushil got thrice as many marks in English as in Science. His total marks in English, Science and Maths are 152. If the ratio of his marks in English and Maths is 1:5, find his marks in Science?	Select the correct option:
A) 8
B) 77
C) 66
D) 55
E) 31

Solution: S:E = 1:3   E:M = 1:5   ------------   S:E:M = 1:3:15   1/19 * 152= 
1/19 * 152 = 8
8   8nswer: 8
Answer: A
Pam and Stanley packed several boxes with reams of paper. While both packed, Pam packed 80% of the boxes. After Pam stopped, Stanley packed the same number of boxes that he had packed while working with Pam. What is the ratio of the number of boxes Pam packed to the number of boxes Stanley packed?	Choose the correct choice from the following choices:	A) 1 to 4	B) 1 to 3	C) 3 to 5	D) 3 to 4	E) 2 to 2

Solution: Correct Answer: E   Solution: E. We know that when Pam and Stanley were both working, the ratio was 4 boxes by Pam to 1 boxes by Stanley. We also know that Stanley continued working after Pam stopped. He packed as many boxes alone as he had packed whlie working with Pam, effectively doubling his number of boxes. Thus, the ratio of Pam's boxes to Stanley's boxes is 4 to 2. Answer 2 to 2 is correct.
Answer: E
Ginger over the course of an average work-week wanted to see how much she spent on lunch daily. On Monday and Thursday, she spent $5.43 total. On Tuesday and Wednesday, she spent $3.54 on each day. On Friday, she spent $4.89 on lunch. What was her average daily cost? Choose the correct option: A) a. $3.19 B) b. $3.75 C) c. $3.48 D) d. $4.08 E) e. $4.23

Solution: On Monday and Thursday, she spent $5.43total.   On Tuesday and Wednesday, she spent $3.54on each day.   On Friday, she spent $4.89 on lunch.   The average = (5.43 + 2*3.54 + 4.89)/5 = 4.08.   Answer: c. $3.48.
Answer: C
The volume of a rectangular swimming pool is 840 cubic meters and water is flowing into the swimming pool. If the surface level of the water is rising at the rate of 0.5 meters per minute, what is the rate R, in cubic meters per minutes, at which the water is flowing into the swimming pool?
Choose the correct choice from the following.
A) 0.125  B) 0.25  C) 0.5  D) 0.75  E) Not enough information to determine the rate

Solution: The correct answer is E.   There are not enough info to answer the question.   A 840 cubic meters rectangle is built from: height*length*width.   From the question we know the volume of the pool and the filling rate.   A pool can have a height of 10*width8.4*length10 and have a volume of 840 cubic meters, and it can have a height of 1 meter, width of 100 meters and length of 8.4. In both cases the pool will fill up in a different rate = Not enough information to determine the rate
Answer: E
The ratio of investments of two partners A and B is 7:5 and the ratio of their profits is 7:10. If A invested the money for 5 months, find for how much time did B invest the money ?  Select
A) 11 months
B) 9 months
C) 7 months
D) 10 months
E) 12 months

Solution: Explanation:   7x5: 5xk = 7:10   k = 10 months   ANSWER IS 10 months
Answer: D
In a market, a dozen eggs cost as much as a pound of rice, and a half-liter of kerosene costs as much as 6 eggs. If the cost of each pound of rice is $0.33, then how many cents does a liter of kerosene cost? [One dollar has 100 cents.]	Choose the correct choice from the following answers.
A) 0.33	B) 0.44	C) 33	D) 44	E) 55

Solution: A dozen eggs cost as much as a pound of rice --> 12 eggs = 1 pound of rice = 33 cents;   A half-liter of kerosene costs as much as 6 eggs --> 6 eggs = 1/2 liters of kerosene.   How many cents does a liter of kerosene cost --> 1 liter of kerosene = 12 eggs = 12/12*33= 
12/12*33 = 33
33 cents.   Answer: 33.
Answer: C
A sum of money amounts to Rs. 9800 after 5 years and Rs. 12005 after 8 years at the same rate of simple interest. The rate of interest per annum is: Choose the correct choice from the following options.
A) 22 B) 88 C) 12 D) 73 E) 29

Solution: Explanation:   S.I. for 3 years = Rs. (12005 - 9800) = Rs. 2205.   S.I. for 5 years = Rs. = Rs.3675   Principle = Rs.(9800-3675) = Rs.6125   Hence, Rate = =12%   Answer: 12) 12%
Answer: C
At a dinner party 3 people are to be seated around a circular table. Two sitting arrangements are considered different only when the positions of the people are different relative to each other.What is the total number of possible sitting arrangements or the group?
Choices:	A) 2	B) 10	C) 24	D) 32	E) 120

Solution: Hi there,   You can treat this as an ordering question except thatfor a circular arrangement you need to divide by the number of spaces.So in this case:   3!/3=2   If you spin the circle to right, that doesn't count as a new arrangement. Dividing by the number of spaces takes that into consideration.   Happy Studies,   HG.   2
Answer: A
Find the lowest common multiple of 24, 36 and 42.  Pick
A) 360  B) 504  C) 510  D) 320  E) 280

Solution: LCM=2*2*2*3*3*7= 
2*2*2*3*3*7 = 504
504.   Answer is 504
Answer: B
Ray writes a two digit number. He sees that the number exceeds 4 times the sum of its digits by 3. If the number is increased by 18, the result is the same as the number formed by reversing the digits. Find the sum of the digits of the number. Choose the correct choice
A) 2  B) 8  C) 9  D) 3  E) 5

Solution: Let the two digit number be xy.   4(x + y) +3 = 10x + y - - - (1)   10x + y + 18 = 10 y + x - - - (2)   Solving 1st equation,   4x + 4y + 3 = 10x + y   3y + 3 = 6x   6x – 3y   3  + 3= 
  3  + 3 = 6
6x   6x – 3y= 3   Therefore, 2x – y = 1 - - - (3)   Solving 2nd equation,   xy + 18 = yx   ⇒⇒ (10x + b) + 18 = 10y + x   ⇒⇒ 18 = 9y – 9x   ⇒⇒ 2 = y – x   we get y - x = 2 - - - (4)   adding 3 and 4, we get x = 3   By substituting in (4), we get y = 5   So the given number is 35. Sum of the digits = 8.   Answer:8
Answer: B
In what ratio should a variety of rice costing Rs. 6 per kg be mixed with another variety of rice costing Rs. 8.75 per kg to obtain a mixture costing Rs. 7.50 per kg?
Options:  A) 5 : 6  B) 3 : 4  C) 7 : 8  D) 8 : 9  E) None of these

Solution: Explanation:   Let us say the ratio of the quantities of cheaper and dearer varieties = x : y   By the rule of allegation, x/y = (87.5 - 7.50) / (7.50 - 6) = 5/6   5 : 6NSWER IS 5 : 6
Answer: A