MU-NLPC/Calc-aqua_rat huggingface dataset:
Sides of a rectangular park are in the ratio 3: 2 and its area is 3750 sq m, the cost of fencing it at 70 ps per meter is? Choose the correct choice from the following answers:
A) 287	B) 369	C) 175	D) 279	E) 361

Solution: 3x * 2x = 3750 => x = 25   2(75 + 50) = 250 m   250 * 0.70   = Rs.175   Answer:175
Answer: C
The average of five integers is 56, and none of these integers is greater than 100. If the average of three of the integers is 59, what is the least possible value of one of the other two integers? Choose the correct choice from the following answers.
A) 3
B) 15
C) 20
D) 21
E) 30

Solution: When it comes to averages, we know thataverage value = (sum of n values)/n   We can rewrite this into a useful formula:sum of n values = (average value)(n)   The average of five integers is 56   So, the sum of ALL 5 integers = (56)(5) =280   The average of three of the integers is 65   So, the sum of the 3 integers = (59)(3) =177   So, the sum of the 2 REMAINING integers =280-177= 
280-177 = 103
103   If the sum of the 2 REMAINING integers=103, and we want to minimize one value, we must MAXIMIZE the other value.   100 is the maximum value so let 1 integer = 100, which means the other must equal 3   3nswer: 3
Answer: A
The average (arithmetic mean) of seven numbers is 7. If 4 is subtracted from each of three of the numbers, what is the new average?
Choose the correct answer.
A) 4.2  B) 6.3  C) 5.2  D) 7.9  E) 8.3

Solution: Sum of 7 numbers = 7*7= 
7*7 = 49
49   If4 is subtracted from each of three of the numbers , we subtract  4*3= 
 4*3 = 12
12 from the total sum   Sum of 7 number after subtracting 4 from each of three of the numbers=49-12= 
49-12 = 37
37   New average= 37/7=5.2   Answer 5.2
Answer: C
If y = 30p, and p is prime, what is the greatest common factor of y and 14p, in terms of p?
Select the correct option
A) p
B) 2p
C) 5p
D) 7p
E) p^2

Solution: Y=30p   other number is 14p   then GCF(30p,14P)=2P; 2p is the correct answer
Answer: B
A train 600 m long can cross an electric pole in 20 sec and then find the speed of the train?	Select:
A) 72
B) 67
C) 108
D) 26
E) 27

Solution: Length = Speed * time   Speed = L/T   S = 600/20= 
600/20 = 30
30 M/Sec   Speed= 30*18/5 (To convert M/Sec in to Kmph multiply by 18/5)   Speed = 108 Kmph   Answer:108
Answer: C
Two trains are running in opposite directions with the same speed. If the length of each train is 60 metres and they cross each other in 12 seconds, then the speed of each train (in km/hr) is:	Select.
A) 8 km/hr.	B) 32 km/hr.	C) 34 km/hr.	D) 18 km/hr.	E) 12 km/hr.

Solution: Let the speed of each train be x m/sec.   Then, relative speed of the two trains = 2x m/sec.   So, 2x = (60 + 60)/12   2x = 10   x = 5.   Speed of each train = 5 m/sec = 5 x 18/5 km/hr = 18 km/hr.   answer :18 km/hr.
Answer: D
Excluding the stoppages, the speed of a bus is 48 km/hr and including the stoppages the speed of the bus is 12 km/hr. For how many minutes does the bus stop per hour?  Choose one
A) 45 min
B) 10 min
C) 12 min
D) 20 min
E) 18 min

Solution: Speed of the bus without stoppage=48 km/hr   Speed of the bus with stoppage=12 km/hr   Difference in speed=36 km/hr   so,the time taken in the stoppages = time taken to cover 36 km=(36/48)hr = 3/4 hr =45 min   45 minNSWER:45 min
Answer: A
rahul played weel in this season.his current batting averagge is 50.if he score 78 runs in today match.his batting average will become 54.how many matches had he played in this season.
Choose one
A) 8	B) 10	C) 9	D) 6	E) 5

Solution: 50x+78=54(x+1)   =>4x=24   =>x=6   ANSWER:6
Answer: D
Evaluate 2+22+222+2.22
Choices.
A) 269.72 B) 268.22 C) 248.21 D) 248.22 E) 268.21

Solution: 2+22+222+2.22= 
2+22+222+2.22 = 248.22
248.22   Option 248.22
Answer: D
In what time will a railway train 60 m long moving at the rate of 36 kmph pass a telegraph post on its way?
Choose one: A) 7 sec B) 8 sec C) 9 sec D) 6 sec E) 1 sec

Solution: T = 60/36 * 18/5= 
60/36 * 18/5 = 6
6 sec   Answer: 6 sec
Answer: D
S = { 1,5,3,7}
T = { 4,5,6,7 }
what is the probability that x chosen from S and y chosen from T will result x*y = even Select the correct option:
A) 1/3
B) 4/5
C) 2/3
D) 1/2
E) 1/6

Solution: p: the probability that x*y is even, then p=1-p(x*y is odd)   p(x*y odd)=p(x odd)*p(y odd)=4/4*2/4=2/4   And p=1-2/4=1/2   Option: 1/2
Answer: D
P and Q need 8 days to complete a work. Q and R need 12 days to complete the same work. But P, Q and R together can finish it in 6 days. How many days will be needed if P and R together do it?  Choose the correct option:
A) 4 B) 8 C) 12 D) 16 E) 18

Solution: Let work done by P in 1 day = p   work done by Q in 1 day =q   Work done by R in 1 day = r   p + q = 1/8 ---(1)   q + r= 1/12 ---(2)   p+ q+ r = 1/6 ---(3)   (3) – (2) => p = 1/6 - 1/12 = 1/12   (3) – (1) => r = 1/6 – 1/8 = 1/24   p + r = 1/12 + 1/24 = 3/24 = 1/8   => P and R will finish the work in 8 days   Answer is 8.
Answer: B
In how many different ways can the letters of the word 'APPLE' be arranged?	Select.
A) 10 ways B) 20 ways C) 30 ways D) 60 ways E) 40 ways

Solution: Totally there are 5 letters on the word APPLE. it contains 1A,2P,1L,1E.   The no of ways is 5!/2!=120/2= 
120/2 = 60
60 ways.   ANSWER:60 ways
Answer: D
A Man travelled a distance of 61 km in 9 hours. He travelled partly on foot at 4 km/hr and partly on
bicycle at 9 km/hr. What is the distance travelled on foot?  Pick: A) 16 km B) 14 km C) 12 km D) 10 km E) None of these

Solution: Explanation:   Let the time in which he travelled on foot = x hour   Time for travelling on bicycle = (9 - x) hr   Distance = Speed * Time, and Total distance = 61 km   So,   4x + 9(9-x) = 61   => 5x = 20   => x = 4   So distance traveled on foot = 4(4) = 16 km   16 kmnswer: Option 16 km
Answer: A
15, 31, 63, 127, 255, ?
Choices.
A) 543
B) 447
C) 972
D) 532
E) 511

Solution: 511   511   511ach number is double of the preceding one plus 1.
Answer: E
Sum of 3 consecutive even no.'s is 26 more than the 1st no. of the series. Find the middle no.?	Select
A) 9 B) 12 C) 15 D) 17 E) 19

Solution: Let the numbers be x, x+2 and x+4 then   x + x+2 + x+4 = x+26   3x + 6 = x + 26   2x = 20   \inline \therefore x = 10   \inline \therefore Middle number = x + 2 = 10+2= 
10+2 = 12
12   12
Answer: B
What is the area of a square field whose diagonal of length 24 m?
Choose the correct choice from the following:	A) 240 sq m	B) 250 sq m	C) 200 sq m	D) 400 sq m	E) 800 sq m

Solution: d2/2 = (24 * 24)/2 = 240   240 sq mNSWER:240 sq m
Answer: A
A man can row downstream at 18 kmph and upstream at 10 kmph. Find the speed of the man in still water and the speed of stream respectively?  Choose the correct option.
A) 14, 2
B) 16, 4
C) 14, 8
D) 14, 4
E) 14, 1

Solution: Let the speed of the man in still water and speed of stream be x kmph and y kmph respectively.   Given x + y = 18 --- (1)   and x - y = 10 --- (2)   From (1) & (2) 2x = 28 => x = 14,y = 4.   Answer: 14, 4
Answer: D
A metallic sphere of radius 12 cm is melted and drawn into a wire, whose radius of cross section is 16 cm. What is the length of the wire? Pick.
A) 6  B) 8  C) 5  D) 3  E) 9

Solution: Volume of the wire (in Cylindrical shape) is equal to the volume of the sphere.   π(16)2 * h = (4/3)π (12)3 => h   = 9 cm   Answer:9
Answer: E
A train 140 m long passes a man,running at 6 kmph in the direction opposite to that of the train,in 6 seconds.The speed of the train is Answers:  A) 54 kmph  B) 60 kmph  C) 66 kmph  D) 72 kmph  E) 78 kmph

Solution: speed of train relative to man: 140/6 * 18/5 km/hr   = 84 km/hr   let speed of train= x   therefore x+6 = 84   x= 84-6= 
84-6 = 78
78 km/hr   ANSW78 kmphR:78 kmph
Answer: E
A and B began business with Rs.3000 and Rs.4000 after 8 months, A withdraws Rs.1000 and B advances Rs.1000 more. At the end of the year, their profits amounted to Rs.756 find the share of A.  Choose the correct choice from the following.
A) 240	B) 388	C) 288	D) 277	E) 122

Solution: Explanation:   (3*8 + 2*4):(4*8 + 5*4)   8:13   8/21 * 756= 
8/21 * 756 = 288
288   Answer: 288
Answer: C
In the standard formulation of a flavored drink the ratio by volume of flavoring to corn syrup to water is 1 : 12 : 30. In the sport formulation, the ratio of flavoring to corn syrup is three times as great as in the standard formulation, and the ratio of flavoring to water is half that of the standard formulation. If a large bottle of the sport formulation contains 6 ounces of corn syrup, how many ounces of water does it contain? Choices:
A) 15
B) 30
C) 45
D) 60
E) 90

Solution: Standard:   Fl: Corn S: Water = 1:12:30   Sport:   Fl: Corn S: Water = 3:12:180   This simplifies to 1:4:60   If the large bottle has a capacity of x ounces, then   4x / 65 = 6.   So, x = 195 / 2 ounces.   Water = (60 / 65) * (195 / 2) = 60 * 3 / 4 = 90 ounces.   Ans 90
Answer: E
If a, b, and c are consecutive even positive integers, which of the following could be equal to a + b + c ?
Choose the correct choice
A) 141
B) 200
C) 412
D) 391
E) 612

Solution: The key to answering this question quickly is to realize that a+b+c is a multiple of BOTH 2 and 3. With that information, you can quickly eliminate answer choices. If you don't recognize those two Number Properties though, then you can still get to the correct answer (but it will require a bit more work).   We're told that a, b and c are CONSECUTIVE EVEN INTEGERS, so we could write them algebraically as...   A + (A+2) + (A+4) = 3A + 6   We know that 3A + 6 COULD equal one of those five answers; we just have to find it...   Could 3A + 6 = 141   3A = 135   A = 45   This is NOT an EVEN INTEGER, so 141 is NOT the answer   Could 3A + 6 = 200   3A = 194   A = 64.6666   This is NOT an EVEN INTEGER, so 200 is NOT the answer   Could 3A + 6 = 412   3A = 406   A = 135.3333   This is NOT an EVEN INTEGER, so 412 is NOT the answer   Could 3A + 6 = 612   3A = 606   A = 202   This IS an EVEN INTEGER! The numbers would be 202, 204 and 206. This IS the answer   Final Answer:   612
Answer: E
If |5x-10| = 100, then find the sum of the values of x? Choose the correct choice.
A) 1	B) -2	C) 3	D) -3	E) 4

Solution: |5x-10| = 100   5x-10 = 100 or 5x-10 = -100   5x = 110 or 5x = -90   x = 22 or x = -18   sum = 21-18= 
21-18 = 3
3   Answer is 3
Answer: C
What is the are of an equilateral triangle of side 16 cm?	Pick one.
A) 64√6
B) 64√9
C) 64√4
D) 64√3
E) 64√2

Solution: Area of an equilateral triangle = √3/4 S2   If S = 16, Area of triangle = √3/4 * 16 * 16 = 64√3 cm2;   Answer: 64√3
Answer: D
Four packages have an average weight of 11.5 pounds. What is the minimum possible weight of the heaviest package in pounds if the median is 10 pounds?  Choices: A) 11 B) 11.5 C) 13 D) 15 E) 16

Solution: Let us denote the weights of the packages in pounds by a, b, c, d naming from the lightest one to the heaviest one. The median is 10 pounds. Therefore (b + c) / 2 = 10.   b + c = 20   The average is 11.5 pounds. Therefore (a + b + c + d) / 4 = 11.5.   a + (b + c) + d = 46   a + 20 + d = 46   a + d = 26   The weight a must be no greater than 10, since 10 is the median. Therefore the minimum possible weight of the heaviest package is 26 – 10 = 16 pounds (all the other packages would weigh 10 pounds in this case).   Answer: 16
Answer: E
If log(2a - 3b) = log a - log b, then a =
Pick:
A) 3b2/2b -1
B) 3b/2b -1
C) b2/2b + 1
D) 3b2/2b + 1
E) None of these

Solution: 2a- 3b = a/b   =>2ab - 3b2 = a   =>3b2 = a(2b - 1)   Therefore, a = 3b2/2b -1.   3b2/2b -1NSWER:3b2/2b -1
Answer: A
A and B start a business with Rs.5000 and Rs.7000 respectively. Hoe should they share their profits at the end of one year? Choose one:  A) 3:5  B) 5:7  C) 3:9  D) 5:3  E) 3:2

Solution: They should share the profits in the ratio of their investments.   The ratio of the investments made by A and 5:7 =   5000 : 7000 => 5:7,Answer: 5:7
Answer: B
How many different three-digit multiples of 5 can be composed of digits 2, 3, 4, and 5 if none of the digits is repeated?
Choose the correct option
A) 3 B) 6 C) 10 D) 12 E) 18

Solution: Available: 2, 3, 4, 5   You need to make 3 digit numbers which are multiples of 5.   ___ ___ ___   For the number to be a multiple of 5, it must end with either 0 or 5. We only have 5 available so the number must end with 5.   ___ ___ 5   Now you select 2 numbers out of the leftover 3 numbers (2, 3 and 4) in 3C2 ways and arrange them in the 2 places in 2! ways which gives you 3C2*2! = 6   or you can say that you can select a number for the hundreds place in 3 ways and select a number for the tens place in 2 ways (since numbers cannot be repeated). So you can make the number in  3*2= 
 3*2 = 6
6 ways   ANS:6
Answer: B
Which of the following is the lowest positive integer that is divisible by 7, 8, 9, 10, and 11?
Choose the correct choice:
A) 27,720  B) 29,940  C) 31,960  D) 33,970  E) 35,890

Solution: The number needs to be divisible by 7, 2^3, 3^2, 2*5, and 11.   The lowest positive integer is 7 * 2^3 * 3^2 * 5 * 11 = 27,720   The answer is 27,720.
Answer: A
A sum of money lent out at S.I. amounts to a total of $420 after 2 years and to $595 after a further period of 5 years. What was the initial sum of money that was invested?  Choose the correct choice from the following answers
A) $310 B) $320 C) $330 D) $340 E) $350

Solution: S.I for 5 years = $595 - $420 = $175   The S.I. is $35/year   S.I. for 2 years 595 -  420= 
595 -  420 = 175
$175   The S.I. is $35/year   S.I. for 2 years= $70   Principal = $420 - $70 = $350   The answer is $350.420 -  70= 
420 -  70 = 350
$350   The answer is $350.
Answer: E
5/9 of the part of the population in a villagae are males.if 30 % of the males are married.the percentage of unmarried females in the total population is..  Choose the most appropriate option
A) 250/9% B) 150/9% C) 350/9% D) 450/9% E) 550/9%

Solution: Let total population = p   no. of males =5p/9   no. of females =(p-5p/9)=4p/9   married males = 30% of 5p/9=30*5p/100*9 =p/6   married females = p/6   unmarried females =(4p/9-p/6)=5p/18   %age of unmarried females in the total population = {(5p/18)/p}*100= 250/9%   250/9%NSWER:250/9%
Answer: A
A train leaves Mumabai at 9 am at a speed of 40 kmph. After one hour, another train leaves Mumbai in the same direction as that of the first train at a speed of 50 kmph. When and at what distance from Mumbai do the two trains meet?
Choose the correct choice from the following options
A) 338
B) 378
C) 200
D) 298
E) 122

Solution: When the second train leaves Mumbai the first train covers 40 * 1= 
40 * 1 = 40
40 km   So, the distance between first train and second train is 40 km at 10.00am   Time taken by the trains to meet= Distance / relative speed = 40 / (50 -40)= 
40 / (50 -40) = 4
4 hours   So, the two trains meet at 2 p.m. The two trains meet 4 * 50= 
4 * 50 = 200
200 km away from Mumbai.   Answer: 200
Answer: C
A can complete a project in 30 days while B can complete same project in 30 days. If A and B start working together and A leaves the work 10 days before completion of project, then in how many days the project will be completed?
Pick one.
A) 18  B) 19  C) 20  D) 21  E) 22

Solution: A's 1day work=1/30;   B's 1day work=1/30;   (A+B) 1day work=(1/30+1/30)=1/15;   It is given that A leaves the work 10 days before completion of the project..   Thus,B alone does the remaining job in 10 days.   So,In 10 days ,B can do 1/3 w ..   Thus,(A+B) have worked (1-1/3)=2/3 w..   (A+B)can do 1/15 work in 1 day...   They did 2/3 w in 10 days.   Total days=(10+10)= 
(10+10) = 20
20   ANSWER:20
Answer: C
If a sum of money doubles itself in 5 years at simple interest, the ratepercent per annum is  Choose the correct option:	A) 12	B) 12.5	C) 20	D) 13.5	E) 14

Solution: Explanation:   Let sum = x then Simple Interest = x   Rate = (100 * x) / (x * 5) = 20   Option 20
Answer: C
Mr. Smitherly leaves Cedar Rapids at 8:00 a.m. and drives north on the highway at an average speed of 50 km per hour. Mr. Dinkle leaves Cedar Rapids at 8:30 a.m. and drives north on the same highway at an average speed of 55 km per hour. Mr. Dinkle will Choose the correct choice from the following answers.
A) overtake Mr. Smitherly at 10:30 a.m. B) overtake Mr. Smitherly at 11:30 a.m. C) overtake Mr. Smitherly at 1:30 p.m. D) be 30 miles behind at 9:35 a.m. E) never overtake Mr. Smitherly

Solution: After thirty minutes, Mr. Smitherly is ahead by 25 km.   Mr. Dinkle gains on Mr. Smitherly 5 km each hour.   5 hours after 8:30 a.m., Mr. Dinkle will catch Mr. Smitherly.   The answer is overtake Mr. Smitherly at 1:30 p.m..
Answer: C
A and B can do a piece of work in 12 days. With the help of C they finish the work in 3 days. C alone can do that piece of work in? Choose the correct option:
A) 40 days  B) 2 days  C) 4 days  D) 8 days  E) 40 days

Solution: 4 days   30 days   4 days = 1/3 – 1/12 = 1/4 => 4 days
Answer: C
A group of 10 representatives is to be selected out of 12 seniors and 10 juniors. In how many different ways can the group be selected, if it should have 5 seniors and 5 juniors?
Choose the most appropriate option:
A) 2C7 * 10C6
B) 2C7 * 17C5
C) 2C7 * 10C5
D) 2C9 * 10C5
E) 2C7 * 30C5

Solution: Here, five seniors out of 12 seniors can be selected in ¹²C₅ ways. Also, five juniors out of ten juniors can be selected 10C5 ways. Hence the total number of different ways of selection = ¹²2C7 * 10C5₅ * ¹⁰2C7 * 10C5₅ = ¹²2C7 * 10C5₇ * ¹⁰2C7 * 10C5₅   = 122C7 * 10C55 = 122C7 * 10C57   Answer:2C7 * 10C5
Answer: C
In a bag, there are 6 brown, 4 blue and 10 orange pens. One pen is picked up randomly. What is the probability that it is neither brown nor blue?
Choose the correct choice from the following options:
A) 1/4
B) 1/5
C) 1/3
D) 1/2
E) 3/4

Solution: Explanation :   Neither brown nor blue means the pen drawn is orange.   Total number of outcomes = (6+4+10)= 
(6+4+10) = 20
20.   Number of Favourable outcomes= 10 = Number of orange pens.   Hence, Probability of the event = 10/20 = 1/2.   Answer : 1/2
Answer: D
A and B are walking with 25 kmph and 30 kmph. A is walking towards east and B is towards south. They both started at 7:00 A.M at what time they are 130 metres apart.  Pick:
A) 130m B) 140m C) 150m D) 160m E) 170m

Solution: let after t sec they are 130m apart then   (25* 5/18 *t)^2 + (30* 5/18 *t)^2 = 130^2   => t * (5/18) * 5 * √ 61 = 130   => t = 12.98425 sec ~ 13 sec   so, at 7:00:13 AM they are 130m apart.   130mNSWER:130m
Answer: A
Thefactor countof an integer n greater than 1 is the number of distinct prime factors of n. For example, the factor count of 36 is 2, since 2 and 3 are the distinct prime factors of 36 = 2 x 2 x 3 x 3. For which of the following integers is the factor count greatest E? Select the correct option:  A) 60  B) 61  C) 62  D) 63  E) 64

Solution: 60 = 2*2*3*5 factor count =3   61= prime number   62 = 2*31 factor count=2   63=3*3*7 factor count=2   64=2*2*2*2*2*2 factor count=1=E   answer is 60.
Answer: A
Rs.1500 is divided into two parts such that if one part is invested at 6% and the other at 5% the whole annual interest from both the sum is Rs.82. How much was lent at 5%? Choose the correct choice from the following.
A) 899
B) 866
C) 878
D) 800
E) 877

Solution: (x*5*1)/100 + [(1500 - x)*6*1]/100 = 82   5x/100 + 90 – 6x/100 = 82   x/100 = 8   => x = 800   Answer:800
Answer: D
How many paying stones, each measuring 2 1/2 m * 2 m are required to pave a rectangular court yard 30 m long and 16 1/2 m board?
Pick one.
A) 41	B) 23	C) 56	D) 99	E) 87

Solution: Explanation:   30 * 33/2 = 5/2 * 2 * x => x = 99   Answer: 99
Answer: D
The sum of all the integers g such that -26 < g < 24 is Choose the correct choice from the following answers:  A) 0  B) -2  C) -25  D) -49  E) -51

Solution: Easy one -   -25, -24, -23,-22,...... -1,0, 1, 2...., 22, 23   Cancel everyhitng and we're left with - -25 and -24 g= -49.   -49 is the answer.
Answer: D
A can do a piece of work in 12 days. When he had worked for 2 days B joins him. If the complete work was finished in 8 days. In how many days B alone can finish the work?	Choose one:
A) 18
B) 99
C) 77
D) 62
E) 12

Solution: 8/12 + 6/x = 1   X = 18 days   18nswer:18
Answer: A
In a race of 1000 m, A can beat by 100 m, in a race of 800m, B can beat C by 100m. By how many meters will A beat C in a race of 600 m?  Select the correct option:  A) 57.5 m  B) 127.5 m  C) 150.7 m  D) 98.6 m  E) 95 m

Solution: When A runs 1000 m, B runs 900 m and when B runs 800 m, C runs 700 m.   When B runs 900 m, distance that C runs = (900 * 700)/800 = 6300/8= 
6300/8 = 1_575/2 = around 787.5
787.5 m.   In a race of 1000 m, A beats C by   (1000 - 787.5)= 
  (1000 - 787.5) = 212.5
212.5 m to C.   In a race of 600 m, the number of meters by which A beats C= (600 * 212.5)/1000= 
(600 * 212.5)/1000 = 127.5
127.5 m.   ANSWER:127.5 m
Answer: B
The areas of the two spheres are in the ratio 1: 4. The ratio of their volume is?	Select.
A) 1:4  B) 1:16  C) 1:8  D) 1:64  E) 2:3

Solution: 4πr12 : 4πr22 = 1 : 4   r1 : r2 = 1 : 2   4/3 πr13 : 4/3 πr23   r13 : r23 = 1 : 8   ANSWER:1:8
Answer: C
Let f(x) = x^2 + bx + c. If f(4) = 0 and f(-3) = 0, then b + c =
Choose one.
A) 18 B) 15 C) -13 D) -21 E) -24

Solution: f(x) = x^2 + bx + c. If f(4) = 0 and f(-3) = 0, then b + c =   f(4) = 0= 16+4b+c--- Taking 16 to the other side   -> 4b+c= -16   f(-3) = 0= 9-3b+c --- taking -3b+c to the other side   -> 3b-c=9   When we add these 2 equations, we get 7b= -7---> b= -1   And while substituting b= -1 we get c= -12.   b+c= -13--- Answer -13
Answer: C
If x is negative and y is positive, which of the following cannot be positive?	Options.
A) xy	B) -xy	C) x/-y	D) x^2/y	E) x^4/y

Solution: - * + = -   xy is not positive.   xynswer : xy
Answer: A
Find large number from below question The difference of two numbers is 1395. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder  Answers.
A) 1235  B) 1345  C) 1678  D) 1767  E) 1671

Solution: Let the smaller number be x. Then larger number = (x + 1395).   x + 1395 = 6x + 15   5x = 1380   x = 276   Large number = 276+1395= 
276+1395 = 1_671
1671   1671
Answer: E
There are 6561 balls out of them 1 is heavy. Find the min. no. of times the balls have to be weighedfor finding out the heavy ball.
Choose the correct choice from the following.
A) 4 B) 5 C) 6 D) 7 E) 8

Solution: 6561 if u notice is 3^8...n can be divided by 3(prime factor) only...we keep on dividing it into sets of 3 and in 1 weighing itself you can determine which set is heavy. Divide that set into further 3 lots...keep doing that..   6561   2187 2187 2187 1st weighing   729 729 729   243 243 243   81 81 81   27 27 27   9 9 9   3 3 3   1 1 1   ANswer is 8 attempts   ANSW8R:8
Answer: E
A boy goes to his school from his house at a speed of 3 km/hr and returns at a speed of 2 km/hr. If he takes 5 hours in going and coming. The distance between his house and school is?  Choose the correct choice from the following options:
A) 288
B) 268
C) 208
D) 860
E) 270

Solution: CP = SP + 1CP = SP - g   800 + x = 980 - 2x   3x = 180 => x = 60   CP = 800 + 60= 
800 + 60 = 860
860   Answer: 860
Answer: D
A train which has 250 m long, is running 40 kmph. In what time will it cross a person moving at 4 kmph in same direction ?  Select
A) 30 sec  B) 28 sec  C) 29 sec  D) 35 sec  E) 25 sec

Solution: Time taken to cross a moving person = length of train/ relative speed   Time taken = 250/((40-4) (5/18) = 250/ 36*(5/18) = 250/10= 
250/10 = 25
25 sec   Answer: 25 sec
Answer: E
If f(f(n)) + f(n) = 2n+3, f(0) = 1 then f(2015) = ? Choose one:
A) 2016
B) 2088
C) 270
D) 1881
E) 1781

Solution: f (f(0)) + f(0) = 2(0) + 3 ⇒⇒ f(1) = 3-1= 
3-1 = 2
2, f(1)= 2   f(f(1)) + f(1) = 2(1) + 3 ⇒⇒ f(2)  ( (1)) +  (1)= 
 ( (1)) +  (1) = 2
2(1) + 3 ⇒⇒ f(2)= 5-2= 
5-2 = 3
3, f(2)= 3   f(f(2)) + f(2) = 2(2) + 3 ⇒⇒ f(3) = 7-3= 
7-3 = 4
4, f(3)= 4   ..............   f(2015) = 2016   2016ns: 2016
Answer: A
The positive integers y and z leave remainders of 2 and 3, respectively, when divided by 6. y > z. What is the remainder when y– z is divided by 6?  Choose the correct answer:
A) 1	B) 2	C) 5	D) 3	E) 4

Solution: Let's test out some values of p and q that satisfy the given information.   y leaves are remainder of 2 when divided by 6   So, y 5OULD equal 8   z leaves are remainder of 3 when divided by 6   So, z 5OULD equal 3   What is the remainder when y – z is divided by 6?   So, y - z = 8 - 3= 
8 - 3 = 5
5, and when we divide 5 by 6, we get 0 with remainder 5   Answer: 5
Answer: C