MU-NLPC/Calc-aqua_rat huggingface dataset:
J and M were each paid x dollars in advance to do a certain job together. J worked on the job for 12 hours and M worked for 4 hours less than J. If M gave J y dollars of her payment so that they would have received the same hourly wage, what was the dollar amount, in terms of y, that J was paid in advance?	Choices.
A) a)4y	B) b)5y	C) c)6y	D) d)8y	E) e)9y

Solution: J and M were both paid x dollars   If M gave Y dollars from her X to J then at the end   J will have X+Y dollars   M will have X- Y dollars   Now since the hourly wages have to be same then   Hourly wage of J = (X+Y) / 12 (Since J worked for 12 hrs)   Hourly wage of M = (X-y) /8 (Since M worked 4 hrs less than J)   Equating both   (X+Y)/12=(X-Y)/8   on simplifying X=5y   Answer b)5y
Answer: B
Find the simple interest on Rs. 70,400 at 16 2/3% per annum for 9 months.	Answers:
A) s.8500  B) s.8000  C) s.7500  D) s.8800  E) s.6500

Solution: P = Rs.70400,R = 50/3% p.a and T = 9/12 years = 3/4years.   S.I. = (P*R*T)/100 = Rs.(70,400*(50/3)*(3/4)*(1/100))   = Rs.8800   Answer is s.8800.
Answer: D
The C.P of 15 books is equal to the S.P of 18 books. Find his gain% or loss%? Choose the correct choice from the following options
A) 16 2/3% loss
B) 66 2/3% loss
C) 56 2/3% loss
D) 26 2/3% loss
E) 96 2/3% loss

Solution: Explanation:   15 CP = 18 SP   18 --- 3 CP loss   100 --- ? => 16 2/3% loss   16 2/3% lossnswer: 16 2/3% loss
Answer: A
City A to city B, David drove for 1 hour at 60 mph and for 3 hours at 90 mph. What was the average speed for the whole trip? Choices.
A) 82.5	B) 57.5	C) 58.2	D) 59	E) 62

Solution: The total distance is 1×60+3×90=330   And the total time is 4 hours. Hence,   82.5verage Speed=(Total Distance/Total Time)=330/4= 
330/4 = 165/2 = around 82.5
82.5   82.5nswer : 82.5
Answer: A
The banker's discount on Rs. 1600 at 15% per annum is the same as true discount on Rs. 1680 for the same time and at the same rate. The time is: Select:  A) 3 months  B) 4 months  C) 5 months  D) 6 months  E) 7 months

Solution: S.I. on Rs. 1600 = T.D. on Rs. 1680.   Rs. 1600 is the P.W. of Rs. 1680, i.e., Rs. 80 is on Rs. 1600 at 15%.   Time = (100x80)/(1600x15)= 1/3 year = 4 months   answer : 4 months
Answer: B
The H.C.F of two numbers is 8. Which one of the following can never be their L.C.M?	Options:
A) 8
B) 12
C) 60
D) 72
E) None

Solution: Solution   H.C.F of two numbers divides their L.C.M exactly.   Clearly, 8 is not a factor of 60.   Answer 60
Answer: C
A 1200 m long train crosses a tree in 80 sec, how much time will I take to pass a platform 1000 m long?  Select
A) 288
B) 146.66
C) 188
D) 180
E) 12

Solution: L = S*T   S= 1200/80= 
1200/80 = 15
15 m/Sec.   Total length (D)= 2200 m   T = D/S   T = 2200/15   T = 146.66Sec   Answer:146.66
Answer: B
A loan has a variable interest rate that fluctuates between 8% and 10% of the base payment per month. If base payments remain at $350 each month and an additional monthly surcharge of 1% is added to the combined (base + interest), what would be the greatest possible payment due in any given month?	Choose the most appropriate option.
A) $385.35
B) $386.80
C) $387.50
D) $388.35
E) $388.85

Solution: The maximum interest in one month is 10%*$350=$35.   The combined payment (base plus interest) is $350 + $35 = $385.   The greatest possible payment is: 1.01*$385  350 +  35= 
  350 +  35 = 385
$385.   The greatest possible payment is: 1.01*$385=$388.85.   The answer is $388.85.
Answer: E
12 buckets of water fill a tank when the capacity of each tank is 13.5 litres. How many buckets will be needed to fill the same tank, if the capacity of each bucket is 9 litres? Pick:	A) 15 bukets	B) 17 bukets	C) 18 bukets	D) 19 bukets	E) None of these

Solution: Explanation:   Capacity of the tank = (12*13.5)= 
(12*13.5) = 162
162 litres   Capacity of each bucket= 9 litres.   So we can get answer by dividing total capacity of tank by total capacity of bucket.   Number of buckets needed = (162/9)= 
(162/9) = 18
18 buckets   Option 18 bukets
Answer: C
There are two inlets and one outlet to a cistern. One of the inlets takes 7/2 hours to fill up the cistern and the other inlet takes twice as much time to fill up the same cistern. Both of the inlets are turned on at 8:30 AM with the cistern completely empty, and at 10:30AM, the outlet is turned on and it takes 1 more hour to fill the cistern completely. How much time does the outlet working alone takes to empty the cistern when the cistern is full?  Choose the correct choice from the following
A) 2 hours
B) 2.5 hours
C) 3 hours
D) 3.5 hours
E) 4 hours

Solution: The combined inflow rate of the two inlets is 2/7 + 1/7 = 3/7 cistern/hour. Thus, working together, it takes 7/3 hours (time is reciprocal of rate) to fill the cistern.   From 8:30 AM to 10:30 AM, so in 2 hours, the inlet pipes will fill (time)*(rate) = 2*3/7 = 6/7 th of the cistern .   Then the outlet is turned on and the remaining 1/7 th of the cistern is filled in 1 hour.   Letting x to be the rate of the outlet, we would have: 3/7 - x = 1/7 --> x = 2/7 cistern/hour, which means that it takes 7/2 hours the outlet working alone to empty the cistern.   Answer: 3.5 hours.
Answer: D
There are a lot of houses such that the numbers of their doorplates are odd numbers and the first number of the doorplates is 545, the last number of the doorplates is 715. How many houses are there? Answers.
A) 86 B) 71 C) 81 D) 91 E) 101

Solution: So it starts from 545 and goes like 547, 549,...... 715. and both first and last number are inclusive. Since every other number is odd, it's just 1/2 of the numbers and since it starts with an odd and ends with an odd inclusive add one to the result.   i.e., ([715-545][/2]+1 = 86   86ns 86
Answer: A
Set S is the prime integers between 0 and 50. If three numbers are chosen randomly from set S, what is the probability that the sum of these three numbers is odd?
Options:
A) 15/56 B) 3/8 C) 15/28 D) 4/5 E) 3/4

Solution: Total number of combinations=15C3=455................(1)   Total number of combinations including 2 and two other numbers=14C2=91......................(2)   Therefore the difference ie. (1)-(2) is the set of 3 primes without 2=(455-91)= 
(455-91) = 364
364   So, probability=364/455=4/5   4/5
Answer: D
A working mom wakes up every day at 7 am and goes to sleep at 11 pm. She works 8 hours a day. Spends 2 hours working out at the gym. She spends 1.5 hours cooking dinner and doing dishes. She spends .5 of an hour giving her daughter a bath. She spends 1 hour helping with homework and getting her daughter ready for bed. She spends another. 5 of an hour packing lunches for the family for the next day. She spends .5 of an hour cleaning the house and 2 hours taking a shower and reading or watching t.v. before she goes to sleep. What percent of her day does she spend at work?  Pick: A) 60 B) 50 C) 70 D) 55 E) 40

Solution: 8+2+1.5+.5+1+.5+.5+2= 
8+2+1.5+.5+1+.5+.5+2 = 16
16= total number of hours   8/16=.05=50 percemt   The Answer is 50
Answer: B
How many integer values W are there for x such that 1 < 3x + 5 < 17?
Pick one
A) Two B) Three C) Four D) Five E) Six

Solution: 1 < 3x + 5 < 17   => -4 < 3x < 12   => -4/3 < x < 4   x can take integer values W -1,0 , 1 , 2 , 3   Answer Five
Answer: D
P and Q can complete a work in 15 days and 10 days respectively. They started the work together and then Q left after 2 days. P alone completed the remaining work. The work was finished in --- days. Pick one:
A) 12	B) 16	C) 20	D) 24	E) 28

Solution: Explanation :   Work done by P in 1 day = 1/15   Work done by Q in 1 day = 1/10   Work done by P and Q in 1 day = 1/15 + 1/10 = 1/6   Work done by P and Q in 2 days = 2 × (1/6) = 1/3   Remaining work = 1 – 1/3 = 2/3   Time taken by P to complete the remaining work 2/3 = (2/3) / (1/15)= 
(2/3) / (1/15) = 10
10 days   Total time taken= 2 + 10= 
2 + 10 = 12
12 days   12nswer : Option 12
Answer: A
If n ≠ 0, which of the following must be greater than n?
I. 2n
II. n^2
III. 2 - n  Choose the correct option:
A) I only  B) II only  C) I and II only  D) II and III only  E) None

Solution: n ≠ 0 => n = negative or n = positive   if n = negative:   2n < n (n = -1 then 2n = -2 => -2 < -1)   n^2 > n (n =-1 then n^2 = 1 => n^2 > n)   2 - n > n (n = -1 then 2--1 = 2+1= 
2+1 = 3
3=> 2-n > n)   but if n = positive:   n^2 > n (n = 2 then n^2 = 4 => n^2 > n) => II   2 - n < n(n =2 then 2-2= 
2-2 = 0
0)=> only II   =>answer is II only
Answer: B
How many boxes do you need if you have to pack 240 pairs ornamental bangles into boxes that each hold 2 dozens of bangles? Options:
A) 40
B) 35
C) 20
D) 25
E) 30

Solution: C   20   240 pairs of bangles = 480 bangles =40 dozens.   40 ÷ 2 = 20 boxes.
Answer: C
Find the sum of first 26 natural numbers
Choices.
A) 470 B) 468 C) 465 D) 351 E) 485

Solution: Explanation:   Sum of n natural numbers   =n(n+1)/2   =26(26+1)/2=26(27)/2=351   Answer: Option 351
Answer: D
What is the place value of 6 in the numeral 4634?	Choose the most appropriate option: A) 450 B) 500 C) 600 D) 800 E) 840

Solution: Option '600'    6 * 100= 
 6 * 100 = 600
600
Answer: C
A man swims downstream 48 km and upstream 32 km taking 8 hours each time; what is the speed of the current?
Answers.
A) 1
B) 2
C) 3
D) 4
E) 5

Solution: 48 --- 8 DS = 6   ? ---- 1   32 ---- 8 US = 4   ? ---- 1 S = ?   S = (6- 4)/2= 
(6- 4)/2 = 1
1   1nswer: 1
Answer: A
In a mixture 60 litres, the ratio of milk and water 2 : 1. If this ratio is to be 1 : 2, then the quanity of water to be further added is:
Choose the correct answer.
A) 20	B) 30	C) 40	D) 50	E) 60

Solution: Quantity of milk = (60 x 2/3) litres = 40 litres.   Quantity of water in it = (60- 40)= 
(60- 40) = 20
20 litres.   New ratio= 1 : 2   Let quantity of water to be added further be x litres.   Then, milk : water = (40/(20 + x))   Now, (40/(20 + x))= 1/2   = 20 + x = 80   = x = 60.   Therefore, Quantity of water to be added = 60 litres.   Answer is 60.
Answer: E
If it is assumed that 60 percent of those who receive a questionnaire by mail will respond and 300 responses are needed, what is the minimum number of questionnaires that should be mailed?
Choose the correct choice from the following answers:
A) 400
B) 420
C) 480
D) 500
E) 600

Solution: Minimum no of mail to be sent for getting 300 responses at 60%   = 300/0.6= 
300/0.6 = 500
500   Option 500
Answer: D
In a 1000 m race, A beats B by 50 m and B beats C by 100 m. In the same race, by how many meters does A beat C?	Select
A) 145  B) 772  C) 552  D) 288  E) 132

Solution: By the time A covers 1000 m, B covers  (1000 - 50)= 
 (1000 - 50) = 950
950 m.   By the time B covers 1000 m, C covers  (1000 - 100)= 
 (1000 - 100) = 900
900 m.   So, the ratio of speeds of A and C=   1000/950 * 1000/900 = 1000/855 So, by the time A covers 1000 m, C covers 855 m.   So in 1000 m race A beats C by 1000 - 855= 
1000 - 855 = 145
145 m.   145nswer145
Answer: A
Sum of two numbers prime to each other is 20 and their L.C.M. is 99. What are the numbers?  Choose the correct choice from the following answers.
A) 8 and 12 B) 14 and 6 C) 19 and 1 D) 11 and 9 E) 12 and 9

Solution: As two numbers are prime, only two options satisfy ie option C and D.   but option C will not make the product of numbers i.e 99   ANSWER:11 and 9
Answer: D
Of the 600 residents of Clermontville, 35% watch the television show Island Survival, 40% watch Lovelost Lawyers and 50% watch Medical Emergency. If all residents watch at least one of these three shows and 18% watch exactly 2 of these shows, then how many Clermontville residents C watch all of the shows? Choose the correct option.
A) 150 B) 108 C) 42 D) 21 E) -21

Solution: OA is D.   100= A+B+C-AB-AC-BC+ABC, which is the same as the following formula   100= A+B+C+(-AB-AC-BC+ABC+ABC+ABC)-2ABC.   The term between parantheses value 18% so the equation to resolve is   100=35+40+50-18-2ABC   therefore the value of ABC is 3.5% of 600,C is 21. 21 is the correct answer
Answer: D
n a fort, there are 1200 soldiers. If each soldier consumes 3 kg per day, the provisions available in the fort will last for 30 days. If some more soldiers join, the provisions available will last for 25 days given each soldier consumes 2.5 kg per day. Find the number of soldiers joining the fort in that case? Pick
A) 289	B) 528	C) 273	D) 279	E) 270

Solution: Assume x soldiers join the fort. 1200 soldiers have provision for 1200 (days for which provisions last them)(rate of consumption of each soldier)   = (1200)(30)(3) kg.   Also provisions available for (1200 + x) soldiers is (1200 + x)(25)(2.5) k   As the same provisions are available   => (1200)(30)(3) = (1200 + x)(25)(2.5)   x = [(1200)(30)(3)] / (25)(2.5) - 1200 => x = 528.   Answer: 528
Answer: B
A chemical supply company has 60 liters of a 35% HNO3 solution. How many liters of pure undiluted HNO3 must the chemists add so that the resultant solution is a 50% solution?  Choose one:  A) 18  B) 15  C) 20  D) 24  E) 30

Solution: 60 liters of a 35% HNO3 solution means HNO3 = 21 liters in 60 liters of the solution.   Now, let x be the pure HNO3 added.   18s per question,   21 + x = 50% of (60 + x)   or x =18 Hence, 18
Answer: A
Given that a “24-inch pizza” means circular pizza with a diameter of 12 inches, changing from an 8-inch pizza to a 24-inch pizza gives you approximately what percent increase in the total amount of pizza?
Choose one.
A) 330  B) 500  C) 670  D) 800  E) 125

Solution: area of 8 inch pizza= 4*4*pi=16 pi   area of 24 inch pizza =12*12*pi=144 pi   128/16*100= 
128/16*100 = 800
800 increase   hence answer is 800
Answer: D
If c ≠ 1 and if dc/(d - c) = 1, what is the value of d in terms of c?
Choose the correct choice from the following answers:
A) (c-1)/c	B) c/(1-c)	C) c/(c + 1)	D) (c + 1)/c	E) (1 - c)/c

Solution: This question comes with a particular 'quirk' (one that you probably won't see on Test Day). The GMAT won't test you on the concept of undefined numbers (re: numbers divided by 0), so any time that this concept is a possibility, the question writers have to add a restriction that removes the option that a 0 could occur in the denominator.   Here, we're told that B CANNOT = 1, which is a bit strange because that restriction doesn't seem to impact the original equation much. In fact, it impacts JUST ONE of the answer choices - so you have to ask WHY that restriction is even there. It's actually because that one answer is the correct one.   Final Answer:   c/(1-c)
Answer: B
P can complete a work in 12 days working 8 hours a day.Q can complete the same work in 8 days working 10 hours a day. If both p and Q work together,working 8 hours a day,in how many days can they complete the work?  Select:
A) 60/11  B) 61/11  C) 71/11  D) 72/11  E) 70/11

Solution: Explanation:   P can complete the work in (12 * 8)= 
(12 * 8) = 96
96 hrs   Q can complete the work in  (8 * 10)= 
 (8 * 10) = 80
80 hrs   P's 1 hour work=1/96 and Q's 1 hour work= 1/80   (P+Q)'s 1 hour's work =(1/96 + 1/80)=11/480   so both P and Q will finish the work in 480/11hrs   Number of days of 8 hours each =(480/11 * 1/8)=60/11   60/11NSWER IS 60/11
Answer: A
Find the number of different 4-letter words with or without meaning that can be formed from the letters of the word " NUMBER"
Pick one:
A) 340
B) 360
C) 320
D) 420
E) 440

Solution: There are 6 letters in the word "NUMBER". So the number of 4-letter words 6P4 =360 Answer : 360
Answer: B
How many 3 digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9 which are divisible by 5 and none of the digits is repeated?
Answers.
A) 20	B) 16	C) 8	D) 24	E) 29

Solution: Explanation :   A number is divisible by 5 if the its last digit is a 0 or 5   We need to find out how many 3 digit numbers can be formed from the 6 digits (2,3,5,6,7,9)   which are divisible by 5.   Since the 3 digit number should be divisible by 5, we should take the digit 5   from the 6 digits(2,3,5,6,7,9) and fix it at the unit place.   There is only 1 way of doing this   1   Since the number 5 is placed at unit place, we have now five digits(2,3,6,7,9) remaining.   Any of these 5 digits can be placed at tens place   5 1   Since the digits 5 is placed at unit place and another one digits is placed at tens place,   we have now four digits remaining. Any of these 4 digits can be placed at hundreds place.   4 5 1   Required Number of three digit numbers = 4 x 5 x 1 = 20.. 20nswer : Option 20
Answer: A
In a certain animal shelter, the ratio of the number of dogs to the number of cats is 15 to 7. If 8 additional cats were to be taken in by the shelter, the ratio of the number of dogs to the number of cats would be 15 to 11. How many dogs are in the shelter?  Choose the correct choice
A) 15	B) 25	C) 30	D) 45	E) 60

Solution: This ratio question can be solved in a couple of different ways. Here's an Algebraic approach...   We're told that the ratio of the number of dogs to the number of cats is 15:7. We're then told that 8 more cats are added to this group and the ratio becomes 15:11. We're asked for the number of dogs.   Algebraically, since the number of dogs is a multiple of 15 and the number of cats is a multiple of 7, we can write this initial relationship as...   15X/7X   When we add the 18 cats and factor in the 'ending ratio', we have an equation....   15X/(7X+8) = 15/11   Here we have 1 variable and 1 equation, so we can solve for X....   (15X)(11) = (7X+8)(15)   (X)(11) = (7X+8)(1)   11X = 7X + 8   4X = 8   X = 2   With this X, we can figure out the initial number of dogs and cats...   Initial dogs = 15X = 15(2) = 30   Final Answer: 30
Answer: C
Before being simplified, the instructions for computing income tax in country R were to add 7 percent of one's annual income to the average(arithmetic mean) of 100 units of Country R's currency and 1 percent of one's annual income. Which of the following represents the simplified formula for computing the income tax, in country R's currency, for a person in that country whose annual income is I?	Answers:
A) 50 + I/200
B) 50 + 15I/100
C) 50+ I/40
D) 100+ I/50
E) 100+ 3I/100

Solution: Income of a person is I   7 percent of ones annual income = 7I/100   100 units of Country R's currency = 100   1 percent of one's annual income = I/100   Average of 100 units and 1 percent annual income = 50 + I/200   Sum of average and 7 percent = 7I/100 + 50 + I/200   = 50 + 15I/200   So answer is 50 + 15I/100.
Answer: B
10men and 10 women are there, they dance with each other, is there possibility that 2 men are dancing with same women and vice versa?  Select:
A) 22	B) 20	C) 13	D) 5	E) none

Solution: in question they gave "they dance with each other" , so there is no possibility that 2 men are dancing with same women...   ANSWnoneR:none
Answer: E
A can do a particular work in 6 days . B can do the same work in 8 days. A and B signed to do it for Rs. 3200. They completed the work in 3 days with the help of C. How much is to be paid to C?
Choose the correct choice from the following answers:
A) 100
B) 150
C) 200
D) 300
E) 400

Solution: Amount of work A can do in 1 day = 1/6   Amount of work B can do in 1 day = 1/8   Amount of work A + B can do in 1 day = 1/6 + 1/8 = 7/24   Amount of work A + B + C can do = 1/3   Amount of work C can do in 1 day = 1/3 - 7/24 = 1/24   work A can do in 1 day: work B can do in 1 day: work C can do in 1 day   = 1/6 : 1/8 : 1/24 = 4 : 3 : 1   Amount to be paid to C = 3200 × (1/8) = 400   Answer is 400.
Answer: E
What is the largest 4 digit number exactly divisible by 24?  Choose the correct choice:
A) 4676	B) 4678	C) 8888	D) 9504	E) 9984

Solution: Largest 4 digit number = 9999   9999 ÷ 24 = 416, remainder = 15   Hence largest 4 digit number exactly divisible by 24   = 9999 - 15= 
9999 - 15 = 9_984
9984   answer :9984
Answer: E
A starts business with Rs. 3500 and after 5 months, B joins with A as his partner. After a year, the profit is divided in the ratio 2 : 3. What is B's contribution in the capital?	Options.
A) Rs. 9228  B) Rs. 9129  C) Rs. 9120  D) Rs. 9000  E) Rs. 1922

Solution: Let B's capital be Rs. x.   {3500\12}/{7x}={2}/{3}   => x = 9000.   Answer: Rs. 9000
Answer: D
Darcy lives 1.5 miles from work. She can walk to work at a constant rate of 3 miles per hour, or she can ride the train to work at a constant rate of 20 miles per hour. If she rides the train, there is an additional x minutes spent walking to the nearest train station, waiting for the train, and walking from the final train station to her work. If it takes Darcy a total of 5 more minutes to commute to work by walking than it takes her to commute to work by riding the train, what is the value of x?  Choose the correct choice from the following choices.
A) 20.5 B) 15 C) 25.5 D) 30 E) 60

Solution: The time it takes Darcy to walk to work is (1.5/3)*60= 
(1.5/3)*60 = 30
30 minutes   The time it takes Darcy to take the train is (1.5/20)*60 + x= 4.5 + x minutes   It takes 15 minutes longer to walk, so 30 = 4.5 + x + 5   x=20.5 minutes   20.5nswer: 20.5
Answer: A
36^6 is equal to which of the following? Choose the correct choice from the following choices:
A) 2,176,782,336 B) 2,176,782,330 C) 2,176,782,334 D) 2,176,782,338 E) 2,176,782,339

Solution: A is the correct answer. We do not really need to calculate it. The last digit for 36^6 will be 6. Hence 2,176,782,336 is the correct answer
Answer: A
Seven points lie on the circumference of a circle. What is the positive difference between the number of triangles and the number of quadrilaterals that can be created by connecting these points?  Choose the correct choice: A) 4 B) 5 C) 6 D) 0 E) 20

Solution: Number of triangles can be formed out of 6 points= 7C3=35   Number of quadrilaterals can be formed out of 6 points= 7C4=35   35-35= 
35-35 = 0
0.   Answer=0
Answer: D
Tom opened a shop investing Rs.30000. Jose joined him 2 months later, investing Rs.45000. They earned a profit of Rs.27000 after completion of one year. What will be Jose's share of profit?	Choose the correct choice from the following
A) 20000  B) 15000  C) 25000  D) 34000  E) 30000

Solution: SoL = ~s- So Anju’s share = [5/9] x 27000 = 15000   15000
Answer: B
If 3x+4y=60 and 6x-4y=12, what is the product of x and y?	Answers:
A) 80 B) 54 C) 54 D) 72 E) 12

Solution: Given 3x+4y=60 ---Eq 1   6x -4y =12 -- Eq 2   Sum both eqns we get 9X = 72 => X = 8   sum 6X in eq 2 => 48 - 4y = 12.   => Y = 9   Now XY = 8 * 9= 
8 * 9 = 72
72   Option 72 is correct answer.
Answer: D
If the sum of a number and its square is 272, What is the number? Choices:
A) 14
B) 16
C) 19
D) 21
E) None of these

Solution: Explanation:   Let the integer be x.   Then, x + x2 = 272   x2 + x - 272 = 0   (x + 17) (x – 16) = 0   x = 16   ANSWER: 16
Answer: B
The average monthly income of P and Q is Rs. 5050. The average monthly income of Q and R is Rs. 6250 and the average monthly income of P and R is Rs. 5200. The monthly income of P+Q+R is:
Select the correct option:
A) 16100 B) 15700 C) 17500 D) 16000 E) 16500

Solution: Explanation:   Let P, Q and R represent their respective monthly incomes. Then, we have:   P + Q = (5050 x 2) = 10100 .... (i)   Q + R = (6250 x 2) = 12500 .... (ii)   P + R = (5200 x 2) = 10400 .... (iii)   Adding (i), (ii) and (iii), we get: 2(P + Q + R) = 33000 or P + Q + R = 16500 .... (iv)   (P+Q+R)'s monthly income = Rs. 16500.   Answer:16500
Answer: E
Find the smallest number which should be multiplied with 36963 to make it a perfect square.
Pick one:
A) 4  B) 7  C) 4  D) 3  E) 6

Solution: 36963 = 111*111*3   Required smallest number = 3   3 is the smallest number which should be multiplied with 36963 to make it a perfect square.   ANSWER:3
Answer: D
When 18 is divided by the positive integer k, the remainder is 4, for how many different values of k is this true? Select
A) 1	B) 2	C) 4	D) 6	E) 8

Solution: When 18 is divided by k, remainder is 4 i.e. there are 4 balls leftover after grouping. so k must be greater than 4.   It also means that 14 is completely divisible by k.   Factors of 14 are 1, 2, 7, 14.   Out of these, k can be 7 and 14.   Answer (2)
Answer: B