MU-NLPC/Calc-aqua_rat huggingface dataset:
A certain cube floating in a bucket of water has between 80 and 85 percent of its volume below the surface of the water. If between 8 and 15 cubic centimeters of the cube's volume is above the surface of the water, then the length of a side of the cube is approximately  Select.
A) 3  B) 4  C) 7  D) 8  E) 9

Solution: If sides are 7, vol=7^3=343   80%= 274.4, 85%=291.55   so vol above water, between 68.6 and 51.45 -->too big   If side are 4, vol = 64   80%=51.2, 85%=54.4   vol above water between 12.8 and 9.6   So 4 should be the answer.   Check option C,   If sides are 5, vol = 125   80%= 100, .85%=106.25   vol above water between 18.75-25   (Sides are 4 cubic centimeters)   4
Answer: B
How many three digit numbers contain the digit 5 at least once?	Options.
A) 52  B) 128  C) 252  D) 648  E) 900

Solution: The question is basically asking how many numbers between 100-999 contain at least one digit as 5.   Let ABC be a 3 digit number A can be filled with 9 digits, B can be filled with 10 digits and C can be filled with 10 digits. (because hundredth digit can only be between 1-9= 9 digits)   Therefore total number of ways we can form 3 digit number=9*10*10= 
9*10*10 = 900
900 ways (100-999)   Number of ways we can form a 3 digit number without the digit 5= 8*9*9= 
8*9*9 = 648
648 ways   ANSWER:648
Answer: D
A set of numbers has the property that for any number t in the set, t + 2 is in the set. If -1 is in the set, which of the following must also be in the set?
I. 5
II. 1
III. -5	Choose the correct choice from the following answers:  A) I only  B) II only  C) I and II only  D) II and III only  E) I, II, and III

Solution: The question is which of the following must be in the set, not could be in the set.   If -1 is in the set so must be   -1+2= 
  -1+2 = 1
1, as 1 is in the set so must be   1+2= 
  1+2 = 3
3, as 3 is in the set so must be   3+2= 
  3+2 = 5
5 and so on. So basically knowing that -1 is in the set we can say that ALL odd numbers more than -1 are also in the set.   Answer: I and II only.
Answer: C
There are two decks of 10 cards each. The cards in each deck are labeled with integers from 11 to 22 inclusive. If we pick a card from each deck at random, what is the probability that the product of the numbers on the picked cards is a multiple of 6?  Choose the correct choice from the following answers.
A) 0.23	B) 0.36	C) 0.4	D) 0.42	E) 0.46

Solution: If 6 is a multiple, we need 2 and 3 as a factor of the number. If we factor the numbers 11 through 20 we have:   11 = 11   12 = 2*2*3   13 = 13   14 = 7*2   15 = 5*3   16 = 2*2*2   17 = 17   18 = 3*2*3   19 = 19   20 = 5*2*2   Combos that have a 2 and a 3 as factors (first + second card):   12 + anything - 19 of these possibilities (we count 12 + 12 only once)   14 + 15 - 2 of these possibilities   15 + 16 - 2 of these possibilities   15 + 20 - 2 of these possibilities   18 + anything (except 12, since that is counted in our first option) - 17 of these possibilities   Total possibilities that will be a multiple of 6: 42   Total possibilites:   10*10= 
  10*10 = 100
100   Probability= 42/100 = 0.36   Answer:0.36
Answer: B
A certain number successively divided by 2, 5 and 7 leaves remainders 1, 2 and 3 respectively. When the same number is divided by 70, what is the remainder?	Choices: A) 33 B) 34 C) 35 D) 36 E) 37

Solution: 2) 105 (52 5) 52 (10 7) 10 (1   104 50 7   -------- -------- - -----   1 2 3   => 65   105/70 = 35 (Remainder)   ANSWER:35
Answer: C
John can finish a job in 30 days. If he worked for 15 days alone before he was joined by Kennedy to complete the job in 3 days, how many days will it take both of them to complete the entire job?  Choose the correct choice from the following options.
A) 4 B) 3 C) 5 D) 6.5 E) 6

Solution: 6xplanation:   John and Kennedy complete half work in 3 days   => they can complete whole work in 6 days   Answer: Option 6
Answer: E
SUMO,INC recently conducted a survey and found that 200,000 of its customers live in rural areas. if the number of it customers who live in urban areas is 200 percents grater than the numbers of customers who live in rural areas, how many of SUMO,INC customers live in urban areas ?
Pick one:
A) 200,000
B) 216,000
C) 360,000
D) 480,000
E) 600,000

Solution: Let's say that we have a starting value of X...   100% of X = X   100% MORE than X = X + X = 2X   200% MORE than X = X + 2X = 3X   300% MORE than X = X + 3X = 4X   Etc.   Here, we're told that 200,000 customers live in rural areas and the number who live in urban areas is 200% GREATER than the number who live in rural areas. That means that the number who are in urban areas is 3 times the number in rural areas...   3(200,000) = 600,000   Final Answer:600,000
Answer: E
A bag contains an equal number of one rupee, 50 paise and 25 paise coins respectively. If the total value is 175, how many coins of each type are there? Answers:
A) 20 coins  B) 30 coins  C) 50 coins  D) 100 coins  E) None of these

Solution: Let number of each type of coin = x. Then,   1 × x + .50 × x + .25x = 175   ⇒ 1.75x = 175 ⇒ x = 100 coins   Answer 100 coins
Answer: D
A train moves fast a telegraph post and a bridge 264 m long in 8 sec and 20 sec respectively. What is the speed of the train? Choose the correct option.
A) 89.2 km/hr	B) 79.9 km/hr	C) 99.2 km/hr	D) 79.2 km/hr	E) 72.2 km/hr

Solution: Let the length of the train be x m and its speed be y m/sec.   Then, x/y = 8 => x = 8y   (x + 264)/20 = y   y = 22   Speed = 22 m/sec = 22 * 18/5= 
22 * 18/5 = 396/5 = around 79.2
79.2 km/hr.   Answer: 79.2 km/hr
Answer: D
In a certain town, the ratio of NY Yankees fans to NY Mets fans is 2:1, and the ratio of NY Mets fans to Boston Red Sox fans is 3:7. If there are 320 baseball fans in the town, each of whom is a fan of exactly one of those three teams, how many NY Mets fans are there in this town? Select:	A) 48	B) 52	C) 56	D) 60	E) 64

Solution: The ratio of Yankees:Mets:Red Sox = 6:3:7   The Mets fans are 3/16 of the population.   (3/16)*320= 
(3/16)*320 = 60
60   The answer is 60.
Answer: D
There is 60% increase in an amount in 6years at SI. What will be the CI of Rs. 14,000 after 3 years at the same rate?  Choose the correct choice from the following answers:
A) 2372  B) 4634  C) 4542  D) 2343  E) 3972

Solution: Let P = Rs. 100. Then, S.I. Rs. 60 and T = 6 years.   R = 100 x 60 = 10% p.a.   100 x 6   Now, P = Rs. 14000. T = 3 years and R = 10% p.a.   C.I.   = Rs. 14000 x 1 +	10 3	- 1   100   = Rs. 14000 x	331   1000   = 4634.   4634
Answer: B
If the simple interest on a certain amount in at 4% rate 5 years amounted to Rs.2400 less than the principal. What was the principal?	Choices.
A) 1500
B) 2500
C) 2507
D) 3000
E) 11500

Solution: P - 2400 = (P*5*4)/100   P = 3000   Answer: 3000
Answer: D
Flat 40% discount. a girl buys jacket for 480. what is the marked price?
Select.
A) 600  B) 700  C) 800  D) 850  E) 900

Solution: 40% discount.. means buy on 60% Marked price.   then 480 is 60% of the marked price   480/60= 
480/60 = 8
8   8 is 1% of marked price   then  8*100= 
 8*100 = 800
800   ANSWER:800
Answer: C
50 men took a dip in a water tank 40 m long and 20 m broad on a religious day. If the average displacement of water by a man is 3m3 , then the rise in the water level in the tank will be: Answers
A) 20 cm
B) 25 cm
C) 35 cm
D) 18.75 cm
E) None of these

Solution: Explanation:   Total volume of water displaced =(3 x 50) m3 = 150 m3   Rise in water level = 150/40Ã—20= 0.1875m = 18.75cm   Answer: 18.75 cm
Answer: D
In an examination amar got 8% less than the pass mark and mohan got 20% more than the pass mark. If the difference between the percentage of their mark is 14, then what is the pass percentage
Pick one:
A) 40%	B) 50%	C) 60%	D) cannot be determined.	E) None of these

Solution: Let P be the pass percentage, then   Amar got 0.92 P% and mohan got 1.2 p%   Given that, 1.2 P – 0.92 p = 14   P =14/0.28= 
14/0.28 = 50
50%   ANSWER:50%
Answer: B
If 8 goldsmiths, working 9 hours a day, can make 20 ornaments in 24 days, how many ornaments will 18 goldsmiths make in 36 days, each working 8 hours a day?	Choose the correct option:
A) 126  B) 60  C) 92  D) 138  E) 140

Solution: Explanation :   (Goldsmiths 8: 18) : (His/Day 9:8 ) : (Days 24 : 36) : : 20 : x   8 * 9 * 24*x =18 * 8 * 36 * 20 or x = 60   Answer : 60
Answer: B
Susan, John, Daisy, Tim, Matt, Jane and Kim need to be seated in 7 identical chairs in straight line so that Susan is seated always left to Tim. How many such arrangements are possible ? Choose the correct choice from the following.
A) 36  B) 120  C) 800  D) 2400  E) 2520

Solution: Total # of arrangement of 7 people is 7!.   In half of the cases Susan will be seated left to Tim and in half of the cases Susan will be seated right to Tim (why should one seating arrangement have more ways to occur than another?).   So, # of arrangements to satisfy the given condition is 7!/2=2520.   Answer: 2520.
Answer: E
The successive discounts 20% and 15% are equal to a single discount of?	Choose one: A) 12% B) 45% C) 32% D) 98% E) 78%

Solution: C   Let the CP of an article be Rs. 100   Given that successive discounts are 20% and 15%.   SP = 85% of 80% of 100 = (85/100)(80/100)(100)   => SP = Rs. 68   32%learly, single discount is 32%.
Answer: C
A can do a piece of work in 80 days and B in 100 days. They work together for 20 days and then B goes away.In how many days will A finish the remaining work?
Select:
A) 33 days	B) 44 days	C) 55 days	D) 42 days	E) 32 days

Solution: Explanation:   In this type of questions we first get the finishing of work in 1 minute for both pipes then we will add them to get the result, as:   Part finished by A in 1 day= 1/80   Part finished by B in 1 day = 1/100   Part finished by (A+B) in 1 day = 1/80 + 1/100   = 9/400   So (A+B)'s 20 days work =20*9/400=9/20 Remaining work =1-9/20=11/20. Number days to finish the remaining work by A =80*11/20= 
80*11/20 = 44
44 days.   Option 44 days
Answer: B
The average of first five prime numbers greater than 17 is?  Select
A) 32.2  B) 32.98  C) 32.3  D) 32.8  E) 27.8

Solution: 19 + 23 + 29 + 31 + 37= 
19 + 23 + 29 + 31 + 37 = 139
139/5= 
139/5 = 139/5 = around 27.8
27.8   Answer: 27.8
Answer: E
Shanti's school normally FINISHES AT 4 PM. her mom drives from home to pick her up, reaching the school exactly at 4 pm. one day, a half holiday is announced and the School finishes for the day at 1 pm. Rather than sitting and Waiting , Shanti decides to start walking towards home. Her mother meets her along the way and as a result they reach home an hour earlier than normal. what is the ratio of the Shanti's walking speed to her mother's driving Speed?  Answers
A) 1:2  B) 1:3  C) 1:4  D) 1:5  E) 1:6

Solution: together they save 1hr, i.e, in a one way trip, they would save half Hour each.   therefore, instead of meeting Shanti at 4pm in the school, her mother meets her at 3.30pm(half an hour earlier, to & fro will save 1 hour)   Therefore from the meeting point, to reach the school, the car would take .5 hrs   However, Shanti took 2.5 hrs(3.30-1) to reach the meeting point   Therefore, .5 Times Mom's speed = 2.5 Times Shanti's speed----->(distance=time x speed, since distance is same, equating the product of time and speed for both the cases)   therefore, ratio of the speeds is 1:5   ANSWER:1:5
Answer: D
A and B can together complete a piece of work in 4 days. If A can alone can complete the same work in 12 days, in how many days can B alone complete that work?  Pick one.
A) 6
B) 5
C) 4
D) 3
E) 2

Solution: (6+B)'s 1 day work = 1/4   6's 1 day work = 1/12   B's 1 day work = 1/6   6NSWER 6
Answer: A
Tim's garden is shaped like a square whose side is 28 meters. What's the length of the fence which surrounds the garden? Choices.
A) 110 meters	B) 111 meters	C) 112 meters	D) 113 meters	E) 114 meters

Solution: Solution:   All sides of the square are equal. The length of the fence is 4 times the side. P = 4 × 28 = 112 meters   Answer 112 meters
Answer: C
A train 700 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 min, then the length of the tunnel is?	Choose the correct choice from the following:
A) 288 m
B) 256 m
C) 600 m
D) 278 m
E) 287 m

Solution: Speed = 78 * 5/18 = 65/3 m/sec.   Time = 1 min = 60 sec.   Let the length of the train be x meters.   Then, (700 + x)/60   = 65/3   x = 600 m.   Answer:600 m
Answer: C
A lady bought five books namely A,B,C,D,E to distribute her 4 children. How many ways she can distribute books?  Choose the correct choice from the following options: A) 4^3 B) 4^4 C) 4^5 D) 4^6 E) 4^2

Solution: 4*4*4*4*4   4^5   ANSWER:4^5
Answer: C
A man performs 3/5 of the total journey by rail, 17/20 by bus and the remaining 6.5km on foot. His total journey is  Pick.
A) 65km B) 100km C) 120km D) 130km E) 140km

Solution: Explanation:   Let the journey be x km   Then, 3x/5 + 7x/20 +6.5 =x   12x +7x+130 =20x   X = 130km   Answer: Option 130km
Answer: D
If p^3 is divisible by 80, then the positive integer p must have at least how many distinct factors?  Choose the correct choice from the following choices:
A) 2
B) 3
C) 6
D) 8
E) 10

Solution: Let say p = 10, checking divisibility by 80   10∗10∗10/80=25/2   Numerator falling short of 2   So, lets say p = 20, again checking divisibility by 80   20∗20∗20/80=100   20 is the least value of p for which p3 can be completely divided by 80   There are 6 distinct factors of 20 >> 1, 2, 4, 5, 10, 20   Answer = 6
Answer: C
What is x if x + 2y = 10 and y = 1?  Options.
A) A)10  B) B)8  C) C)6  D) D)4  E) E)2

Solution: x = 10 - 2y   x = 10 - 2.= 
10 - 2. = 8
8   Answer : 8
Answer: B
When m is divided by 9, the remainder is 2. When m is divided by 13, the remainder is 7. If 1 < m < 300, what is the greatest possible value of m?	Choose one:
A) 20
B) 120
C) 137
D) 187
E) 254

Solution: 13*9= 
13*9 = 117
117   Starting with   13+7= 
  13+7 = 20
20, this also has the form 9k+2.   The next possible number is  20 + 117= 
 20 + 117 = 137
137   The next possible number is  137 + 117= 
 137 + 117 = 254
254   The next possible number would be greater than 300.   The answer is 254.
Answer: E
. In a certain city, 60 percent of the registered voters are Democrats and the rest are Republicans. In a mayoral race, if 60 percent of the registered voters who are Democrats and 20 percent of the registered voters who are Republicans are expected to vote for Candidate A, what percent of the registered voters are expected to vote for Candidate A ?	Choose the correct choice from the following answers.
A) 50%
B) 53%
C) 44%
D) 55%
E) 57%

Solution: Registered voters = 100   D = 60   R = 40   60% of D ( 60) = 36   20% of R ( 40 ) = 8   Total voter% of registered voters = 44 / 100   44% Ans 44%
Answer: C
In N is a positive integer less than 200, and 14N/60 is an integer, then N has how many different positive prime factors R? Choose the correct choice from the following choices
A) 2	B) 3	C) 5	D) 6	E) 8

Solution: I like to put the numbers in prime factors so it is easier and faster to visualize.   14*n/60   If we write the factors of 14 --> 2, 7, and the factors of 60 --> 2, 2, 3, 5, we have   (2*7*n)/(2^2*3*5)   Simplifying   7*n/(2*3*5)   The only way the equation above has an integer value is if n has AT LEAST the factors 2, 3 and 5, so we can simplify again and we have the number 7.   The number could be 2*3*5, or 2*3*5*2, or 2*3*5*.....   However to be less than 200 we can not add any prime number.   2*3*5 = 120   If we added the next prime factor 7, we would have R=2*3*5*7 = 840   Thus, answer 3
Answer: B
The cube root of what integer power of 2 is closest to 50? Choose the correct choice:	A) 16	B) 17	C) 18	D) 19	E) 20

Solution: Integer powers of 2 = 2 , 2^2, 2^3, 2^4, 2^5, 2^6, 2^7 etc.   Let, Cube root of x is closest to 50   i.e. x is closest to cube of 50 = 50*50*50= 
50*50*50 = 125_000
125000   But x must be equivalent to an Integer power of 2   2^10= 1024   2^7 = 128   i.e. 2^17 = 128*1024 = 128000 (approx.)   i.e. 2^18 = 256*1024 = 256000 (approx.)   i.e. 2^16 = 64*1024 = 64000 (approx.)   i.e. 2^17 which is closest to 125000   i.e. Integer power of 2 must be 7   Answer: option 17
Answer: B
Simplify: (4 +3)+(8-3-1)  Choose one:	A) -11	B) –12	C) 11	D) 12	E) 10

Solution: Solution:   (4 +3)+(8-3-1)   =7+(8-3-1)   =7+8-3-1   =15-1   =11   Answer: (11)
Answer: C
A man has Rs. 480 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?  Choose the correct answer:
A) 90
B) 70
C) 50
D) 80
E) 60

Solution: Let number of notes of each denomination be x.   Then x + 5x + 10x = 480   16x = 480   x = 30.   Hence, total number of notes = 3x = 90.   90nswer is 90.
Answer: A
A pharmaceutical company received $3 million in royalties on the first $20 million in sales of and then $8 million in royalties on the next $108 million in sales. By approximately what percentage did the ratio of royalties to sales decrease from the first $20 million in sales to the next $108 million in sales?  Pick.
A) 8% B) 15% C) 46% D) 52% E) 56%

Solution: (8/108)/(3/20) = 30/54 = 49,3% it means that 8/108 represents only 49,3%. Therefore a decrease of 46%.   Answer 46%
Answer: C
A pipe can fill a cistern in 18 minutes whereas the cistern when fill can be emptied by a leak in 20 minutes. When both pipes are opened, find when the cistern will be full? Choices.
A) 17
B) 180
C) 70
D) 120
E) 12

Solution: 1/18 - 1/20 = 1/180   180 minutes   Answer: 180
Answer: B
The ratio of local and international calls made by Amy this week is 5 to 2. If the ratio changes to 5 to 3 after Amy makes three more international calls, how many local calls did Amy make this week?
Choose the correct choice from the following:	A) 3	B) 5	C) 10	D) 15	E) 21

Solution: The ratio of local and international calls made by Amy this week is 5 to 2   let the current ratio be 5x/2x   the ratio changes to 5 to 3 after Amy makes three more international calls   5x/(2x+3)= 5/3   solving we get x=3   initial ratio 15:6 (5:2) final ratio 15:(6+3)= 15:9= 5:3   so total number of local calls=15   ANSWER:15
Answer: D
Two trains A and B start simultaneously in the opposite direction from two points P and Q and arrive at their destinations 16 and 9 hours respectively after their meeting each other. At what speed does the second train B travel if the first train travels at 120 km/h Choose the correct choice from the following choices.
A) 334	B) 160	C) 387	D) 278	E) 112

Solution: Answer: 160) 160 km/h
Answer: B
An alloy of zinc and copper contains the metals in the ratio 5 : 3. The quantity of zinc to be added to 16 kg of the alloy so that the ratio of the metal may be 3 : 1 is:  Choose the correct choice from the following choices:
A) 2
B) 4
C) 8
D) 3
E) 1

Solution: 5/8*16= 
5/8*16 = 10
10   3/8*16= 
3/8*16 = 6
6   (10+x)/6=3/1   =8   ANSWER:8
Answer: C
Find the area of a parallelogram with base 24 cm and height 16 cm.  Choose the correct choice from the following choices.
A) 277 cm2	B) 384 cm2	C) 670 cm2	D) 266 cm2	E) 265 cm2

Solution: Area of a parallelogram = base * height   = 24 * 16= 
24 * 16 = 384
384 cm2   Answer: 384 cm2
Answer: B
In the exam the average was found to be p mark. After deducting typographical error the average marks of 104 student reduced from 94 to 64 . Due to this the average came down by 16 marks. What was the number of students who took the exam?  Select.
A) 100	B) 120	C) 110	D) 195	E) 160

Solution: Explanation :   Number of student = (94-64) * 104/16= 
(94-64) * 104/16 = 195
195   Answer : 195
Answer: D
In how many different ways can pennies (1 cent), nickels (5 cents), dimes (10 cents), and quarters (25 cents) be combined for a total of $1.05 (105 cents), if at least two of each type of coin must be included?	Choose the correct choice from the following answers
A) 0 B) 9 C) 12 D) 15 E) 73

Solution: I. Case I = Four Quarters = this is impossible, because if we already have a dollar in quarters, then we cannot have any dimes. We can't have all four coins represented if we have four quarters.   II. Case II = Three Quarters (75 cents)   Two dimes and two nickels would bring us up to $1.05, and we wouldn't have any pennies.   III. Case III = Two Quarters (50 cents)   This allows for 2-4 dimes.   Subcase 1 = 2 Q, 4 D (90 cents)   (1 way) two nickels allows for 5 pennies   Subcase 2 = 2 Q, 3 D (80 cents)   (3 ways) we could have 2-4 nickels   Subcase 3 = 2 Q, 2 D (70 cents)   (5 ways) we could have 2-6 nickels   Case III allows for a total of 9 ways   There's no other case, because we have to have at least two quarters and two dimes. The total over the cases equals   Total = 0 + 0 + 9= 
0 + 0 + 9 = 9
9 ways.   OA=(9)
Answer: B
A, B, C are three consecutive positive integers (A>B>C). What is the value of the expression A +B +3C? Options.
A) 6A+7.	B) 5A+1.	C) 5A-1.	D) 6A-5.	E) 5A-7.

Solution: B = A-1   C= A-2   Putting these values in A +B +3C we get 5A-7   5A-7. is the answer
Answer: E
Find the smallest number of five digits exactly divisible by 16,24,36 and 54.	Choose one:
A) 10368
B) 10638
C) 10836
D) 10846
E) None of them

Solution: Smallest number of five digits is 10000.   Required number must be divisible by L.C.M. of 16,24,36,54 i.e 432,   On dividing 10000 by 432,we get 64 as remainder.   Therefore, Required number = 10000 +( 432 – 64 ) = 10368.   10368nswer is 10368.
Answer: A
Foodmart customers regularly buy at least one of the following products: milk, chicken, or apples. 70% of shoppers buy milk, 50% buy chicken, and 35% buy apples. If 10% of the customers buy all 3 products, what percentage of Foodmart customers purchase exactly 2 of the products listed above?
Choose the correct choice from the following answers.
A)  5%	B)  10%	C)  15%	D)  35%	E)  30%

Solution: Total = n(A) + n(B) - n(Exactly 2 products) -2 (AnBnC) + Neither.   Neither is zero.   Hence 100 = 70 + 50 + 35 - n (Exactly 2 products) - 2*10   100 = 135 - n (Exactly 2 products) => n (Exactly 2 products) = 35.   Answer:  35%
Answer: D
What percent is 3 gm of 1 kg?	Answers.
A) 1.5 % B) 0.3 % C) 2.5 % D) 3.5 % E) 4 %

Solution: 1 kg = 1000 gm   3/1000 × 100 = 300/1000   =3/10= 
3/10 = 3/10 = around 0.3
0.3 %   0.3 %)
Answer: B
|-3| (|-15|-|5|)= ??
Source: Preparation Material MBA Center  Choose the correct choice from the following options:	A) 30	B) 35	C) 40	D) 75	E) 100

Solution: Absolute value will turn negatives into their positive 'equivalents', and will leave positives unchanged, so |-3| = 3, |-15| = 15, and |5| = 5. Getting rid of our absolute values we have:   |-3| (|-15|-|5|) = (3) (15 - 5) = 3*10= 
3*10 = 30
30
Answer: A
The incomes and expenditures of P, Q, R are in the ratio of 6 : 8 : 11 and 5 : 8 : 12 respectively. If P saves 1/4th of his income, what is the ratio of the savings of P, Q and R ? Choose the correct choice from the following choices.
A) 15 : 8 : 8	B) 15 : 8 : 6	C) 15 : 8 : 2	D) 15 : 8 : 3	E) 15 : 8 : 9

Solution: Explanation:   Let the incomes of P, Q, R be 6x, 8x, 11x and expenditure be 5y, 8y and 12y respectively.   Therefore, savings are : (6x – 5y), (8x – 8y) and (11x – 12y)   Now, 6x – 5y = 1/4(6x)   24x – 20y = 6x   18x = 20y   x/y = 20/18 = 10 / 9   Savings of P / Savings of Q = 6x – 5y / 8x – 8y   = [6(x/y) – 5] / [8(x/y) – 8]   = [(6 * 10/9) – 5] / [(8 * 10/9) – 8]   = 15/8   Savings of Q / Savings of R = 8x – 8y / 11x – 12y   = [8(x/y) – 8] / [11(x/y) – 12]   = (8 * 10/9) – 8 / (11* 10/9) – 12   = 8/2   Ratio of savings of P : Q : R = 15 : 8 : 2   ANSWER: 15 : 8 : 2
Answer: C
In a group of cows and hens, the number of legs are 30 more than twice the number of heads. The number of cows is
Choose the correct choice from the following
A) 15  B) 7  C) 10  D) 12  E) 14

Solution: Explanation:   Let the number of cows be x and the number of hens be y.   Then, 4x + 2y = 2 (x + y) + 30   4x + 2y = 2x + 2y + 30   2x = 30   x = 15   15nswer: 15
Answer: A
A can do a work in 6days. B can do in 12days. If both A&B are working together in how many days they can finish the work?	Choose the correct choice from the following choices:
A) 4	B) 5	C) 6	D) 10	E) 15

Solution: 1day work of 4 = 1/6   1day work of B = 1/12   1day work of 4&B = 1/6 + 1/12 = 1/4   4&B finish the work in 4days   4nswer is 4
Answer: A