MU-NLPC/Calc-aqua_rat huggingface dataset:
All the students of class are told to sit in circle shape. Here the boy at the 7 th position is exactly opposite to 27 th boy. Total number of boys in the class?	Choose the correct choice from the following answers:
A) 25	B) 40	C) 35	D) 30	E) 28

Solution: As half the circle shape consist of 27-7= 
27-7 = 20
20 boys,   So total number of boys in full circle=2*20= 
2*20 = 40
40   ANSWER: 40
Answer: B
The sum of ages of 5 kids born at the intervals of 3 years each is 50 years. Find the age of the youngest kid?  Pick:
A) 4 years
B) 5 years
C) 3 years
D) 6 yeasr
E) 7 years

Solution: consider x as age and   (x+3)(x+6)(x+9) and (x+12)   5x = 20   x= 4   4 yearsNSWER 4 years
Answer: A
A certain bus driver is paid a regular rate of $14 per hour for any number of hours that does not exceed 40 hours per week. For any overtime hours worked in excess of 40 hours per week, the bus driver is paid a rate that is 75% higher than his regular rate. If last week the bus driver earned $998 in total compensation, how many total hours did he work that week?	Choose the correct option.
A) 54  B) 51  C) 58  D) 55  E) 52

Solution: For 40 hrs = 40*14= 
40*14 = 560
560   Excess= 998-560= 
998-560 = 438
438   For extra hours=.75(14)=10.5+14= 
10.5+14 = 24.5
24.5   Number of extra hrs=438/24.5=17.8=18 approx.   Total hrs =40+18= 
40+18 = 58
58   Answer 58
Answer: C
A can do a piece of work in 4 days. B can do it in 10 days. With the assistance of C they completed the work in 2 days. Find in how many days can C alone do it?  Choose the correct answer
A) 22 days
B) 20/3 days
C) 67 days
D) 17/6 days
E) 18 days

Solution: C = 1/2 - 1/4 - 1/10 = 3/20   => 20/3 days   Answer:20/3 days
Answer: B
Tough and Tricky questions: Word Problems.
In a rare coin collection, one in six coins is gold, and all coins are either gold or silver. If 10 silver coins were to be subsequently traded for an additional 10 gold coins, the ratio of gold coins to silver coins would be 1 to 7. Based on this information, how many gold coins would there be in this collection after the proposed trade?
Choose the correct choice:
A) 50
B) 60
C) 180
D) 200
E) 350

Solution: The correct answer is 350.
Answer: E
Two dice are thrown together .What is the probability that the sum of the number on the two faces is divided by 4 or 6	Choose the correct choice from the following
A) 5/7 B) 7/18 C) 3/4 D) 8/9 E) 11/15

Solution: Clearly n(S)=6*6= 
6*6 = 36
36   Let E be the event that the sum of the numbers on the two faces is divided by 4 or 6.Then   E={(1,3),(1,5),(2,2),(2,4),(2,6),(3,1),(3,3),(3,5),(4,2),(4,4),(5,1),(5,3),(6,2),   (6,6)}   n(E)=14.   Hence p(e)=n(e)/n(s)=14/36=7/18   Ans: 7/18
Answer: B
The sum of 2 consecutive numbers is definitely:  Pick one:	A) Positive.	B) Divisible by 2.	C) Divisible by 3.	D) Divisible by 4.	E) Divisible by 5.

Solution: If 1st term is x:   x+(x+1)=2x+1--->Positive   If 2nd term is x:   (x-1)+x=2x-1 --->Positive   Positive.
Answer: A
A and B put in Rs.200 and Rs.400 respectively into a business. A reinvests into the business his share of the first year's profit of Rs.210 where as B does not. In what ratio should they divide the second year's profit?  Choose the correct choice from the following choices:
A) 39:40 B) 39:49 C) 39:42 D) 39:47 E) 17:20

Solution: 17:20xplanation:   1:2   A = 2/3*210= 
2/3*210 = 140
140   340: 400   17:20   Answer:17:20
Answer: E
At 6′o a clock ticks 6 times. The time between first and last ticks is 45 seconds. How long does it tick at 12′o clock  Pick one:
A) 47
B) 76
C) 28
D) 66
E) 99

Solution: Explanation:   For ticking 6 times, there are 5 intervals.   Each interval has time duration of   45/5= 
  45/5 = 9
9 secs   At 12 o'clock, there are 11 intervals,   So total time for 11 intervals= 11 × 9 = 99 secs.   Answer: 99
Answer: E
Bruno and Sacha are running in the same direction around a stadium. Sacha runs at a constant speed of 8 meters per second, and Bruno runs at a constant speed of 5 meters per second. At a certain point Sacha overtakes Bruno. If one minute afterward, Sacha stops and waits for Bruno to reach him, then how many seconds does he have to wait?  Answers
A) 12 B) 24 C) 36 D) 60 E) 72

Solution: the difference of the speed is 3m per second so in one minute Sacha will be 180 m ahead of Bruno..   Bruno will cover this in  180/5= 
 180/5 = 36
36 secs..   36
Answer: C
A person lent a certain sum of money at 5% per annum at simple interest and in 8 years the interest amounted to $360 less than the sum lent. What was the sum lent?
Choose the correct choice.
A) 540
B) 560
C) 580
D) 600
E) 680

Solution: P - 360 = (P*5*8)/100   P = 600   The answer is 600.
Answer: D
At exactly what time past 6:00 will the minute and hour hands of an accurate working clock be precisely perpendicular to each other for the first time? Choose one:
A) 20 13/21 minutes past 7:00
B) 20 13/17 minutes past 7:00
C) 21 3/23 minutes past 7:00
D) 21 9/11 minutes past 6:00
E) 22 4/9 minutes past 7:00

Solution: A1 = hour angle   A2 = minute angle   A1-A2 = 90   Assume the minutes = M   A1 = (6*60+M)/12*60 )*360   A2 = M*360/60   Solving all three equation , results in the answer 21 9/11 minutes past 6:00
Answer: D
Ajay spends 45% of his monthly income on household items, 25% of his monthly income on buying cloths, 7.5% of his monthly income on medicines and saves the remaining amount which is Rs. 9000. Find his monthly income.	Choose the correct answer:
A) Rs. 40000  B) Rs. 36000  C) Rs. 50000  D) Rs. 45000  E) None of these

Solution: Let the monthly income of Ajay be Rs. x   Savings of Ajay = x - (45 + 25 + 7.5)/100 * x = 22.5/100 x   22.5/100 x = 9000   x = 40000.   Rs. 40000NSWER:Rs. 40000
Answer: A
Of 30 candidates for a job, 14 had at least 4 years of exper, 18 had degrees, and 3 had less than 4 years exper and did not have a degree, how many candidates had at least 4 years exper and a degree?	Select:	A) a)14	B) b)13	C) c)9	D) d)7	E) e)5

Solution: Answer is E. Here is how:   The quickest way is to setup a matrix and work through the given values in the question.   For all such problems, set up a matrix with number of columns and rows corresponding to the divisions mentioned in the question stem.   Degrees and e)5xperience   > 4 yrs e)5xp< 4 yrs e)5xpTotal   Degree5Required Value1318Given   No Degree9312   Total14Given1630Given answer is e)5
Answer: E
Out of first 30 natural numbers, one number is selected at random. The probability that it is either an even number or a prime number is ? Choices: A) 6/30 B) 2/30 C) 4/90 D) 24/30 E) 24/60

Solution: n(S) = 30   n(Even no) = 15 = n(E)   n(Prime no) = 10 = n(P)   P(EᴜP)   = 15/30 + 10/30 - 1/30   = 24/30   Answer:24/30
Answer: D
In a class, 20% of the students were absent for an exam. 30% failed by 20 marks and 10% just passed. Find the average score of the class if the remaining students scored an average of 65 marks and the cut off for passing the exam is 40. Options.
A) 36 B) 302 C) 272 D) 292 E) 271

Solution: Explanation:   Let total students be 100.   Hence, marks of 20 students is 0 as they were absent.   30 students scored 20 marks (as they failed by 20 marks)   10 students scored 40 marks (just passed)   40 students scored 65 marks (average of 65)   Therefore, average score of the class is: (0 + 600 + 400 + 2600)/100 = 3600/100= 
3600/100 = 36
36   36NSWER: 36
Answer: A
The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is:	Choose the correct choice from the following answers.
A) 200 m B) 225 m C) 245 m D) 250 m E) 350 m

Solution: Explanation:   Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (130 + x)/30 = 25/2 => 2(130 + x) = 750 => x = 245 m.   ANSWER IS 245 m
Answer: C
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? Choose the correct choice from the following choices:  A) 16  B) 12  C) 20  D) 25  E) 30

Solution: Since each desired number is divisible by 5,   so we much have 5 at the unit place.   The hundreds place   can now be filled by any of the remaining 4 digits .   so, there4 ways of filling it.   Required number of numbers = (1 * 5 * 4)= 
(1 * 5 * 4) = 20
20   Ans: 20
Answer: C
The labeled price of a table is Rs. 6,500. The shopkeeper sold it by giving 5% discount on the labeled price and earned a profit of 15%. What approximately is the cost price of the table? Choose the correct choice from the following options.
A) Rs. 5369
B) Rs. 6195
C) Rs. 6425
D) Rs. 7200
E) None of these

Solution: Explanation:   Labeled price = Rs. 6,500   By giving 5% discount on labeled price, the selling price is   = 95 / 100 * 6500 = Rs. 6175   By earning 15% profit on the selling of price Rs. 6175 the cost price is   = 100 / 115 * 6175 = Rs. 5369   Therefore, approximate cost is 5369   Rs. 5369NSWER Rs. 5369
Answer: A
An investor deposited $5,000 to open a new savings account that earned 4 percent annual interest, compounded quarterly. If there were no other transactions in the account, what was the amount of money in the account 6 months after the account was opened?	Pick one:
A) $5050.50
B) $5100.50
C) $5200.50
D) $5300.50
E) $5400.50

Solution: The amount in the account after 6 months is 1.01*1.01($5,000) = $5100.50   The answer is $5100.50.
Answer: B
What will be the fraction of 5% Choose the correct option.
A) 1/20
B) 1/50
C) 1/75
D) 1/25
E) None of these

Solution: Explanation:   5*1/100 = 1/20.   Option 1/20
Answer: A
A committee is to be formed by randomly choosing 4 people from 7 candidates. If Alice and Bob are candidates, what is the probability that Alice will be selected but Bob will not?
Answers:
A) 2/5  B) 2/7  C) 3/7  D) 3/35  E) 4/35

Solution: The total number of ways to form a committee is 7C4=35.   The number of committees which include Alice but not Bob is 5C3=10.   The probability that Alice is selected but Bob is not selected is 10/35=2/7.   The answer is 2/7.
Answer: B
Walking at 3/4 of her normal speed, a worker is 8 minutes later than usual in reaching her office. The usual time (in minutes) taken by her to cover the distance between her home and her office is
Choose the correct choice from the following choices: A) 20 B) 24 C) 28 D) 32 E) 36

Solution: Let V be her normal speed and let T be her normal time.   D = (3/4)V * (T+8)   Since the distance is the same we can equate this to a regular day which is D = V*T   V*T = (3/4)V * (T+8)   T/4 = 6   T=24   The answer is 24.
Answer: B
total 36 matches are conducted in Knockout match type. How many players will be participated in that tournament? Choose the correct answer
A) 35	B) 36	C) 21	D) 32	E) 26

Solution: 35 players   35NSWER:35
Answer: A
Tough and Tricky questions: Exponents.
If a and b are positive integers and x = 2^a and y = 3^b, which of the following is a possible units digit of xy?  Choices:
A) 4, 2, 8, 6
B) 4 and 2
C) 2 and 8 only
D) 6 and 4
E) 8 and 6

Solution: Only Units digit of X and Y contribute to the Units digit of XY.   Finding all values of X for positive values of a   When,   a=1; X=2   a=2; X=4   a=3; X=8   a=4; X=16   a=5; x=32........ Units digit repeat in a cycle of 2,4,8,6,2,4......   Similarly, Finding all values of Y for positive values of b   When,   b=1; Y=3   b=2; Y= 9   b=3; Y= 27   b=4; Y=81   b=5; Y=243....... Units digit repeat in cycle of 3,9,7,1,3,9....   So, possible value of Units digit of XY can be found by considering all possibilities of Units digit of X and Y   When X=2 and Y=3: Units digit of XY = 6   When X=2 and Y=9: Units digit of XY = 18   When X=2 and Y=7: Units digit of XY = 14   When X=2 and Y=1: Units digit of XY = 2   When X=4 and Y=3: Units digit of XY = 12   When X=4 and Y=9: Units digit of XY = 36   When X=4 and Y=7: Units digit of XY = 28   When X=4 and Y=1: Units digit of XY = 4   When X=8 and Y=3: Units digit of XY = 24   When X=8 and Y=9: Units digit of XY = 72   When X=8 and Y=7: Units digit of XY = 56   When X=8 and Y=1: Units digit of XY = 8   When X=6 and Y=3: Units digit of XY = 18   When X=6 and Y=9: Units digit of XY = 54   When X=6 and Y=7: Units digit of XY = 42   When X=6 and Y=1: Units digit of XY = 6   There are 4 possibilities for Units digit of XY i.e. 4, 2, 8 and 6   4, 2, 8, 6ns: 4, 2, 8, 6
Answer: A
Two stations A and B are 200 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet? Choose the correct choice from the following.
A) 9
B) 10
C) 11
D) 12
E) 8

Solution: Suppose they meet x hours after 7 a.m.   Distance covered by A in x hours = 20x km.   Distance covered by B in (x - 1) hours = 25(x - 1) km.   Therefore 20x + 25(x - 1) = 200   45x = 225   x = 5.   So, they meet at 12 a.m.   Answer: Option 12
Answer: D
Find the no.of ways of arranging the boy and 10 guests at a circular table so that the boy always sits in a particular seat?	Choose the correct choice
A) 3!
B) 10!
C) 7!
D) 9!
E) 11!

Solution: Ans.(B)   Sol. Total number of persons = 11 Host can sit in a particular seat in one way. Now, remaining positions are defined relative to the host. Hence, the remaining can sit in 10 places in 10P10 = 10! Ways ... The number of required arrangements = 10! x 1= 10! = 10! ways
Answer: B
Some consecutive natural numbers, starting with 1, are written on the board. Now, one of the numbers was erased and the average of the remaining numbers is 800/39. Find the number which was erased.  Choose the correct choice from the following answers.
A) 20
B) 87
C) 266
D) 288
E) 11

Solution: We know that average of n consecutive numbes average = n×(n+1)2n=(n+1)2n×(n+1)2n=(n+1)2   If the given n is sufficiently large, the average does not change much even though we exclude one or two numbers from it. So the approximate number of observations is almost double to the average (Remember: the average of consecutive numbers almost lies in the middle)   The approximate average is 800/39 = Approx 20. So the initial numbers may be nearer to 40.   In this question it is actually 40 as from the denominator of the new average 800/39. The initial numbers are 40.   Sum of 40 consecutive numbers = 40×(40+1)2=82040×(40+1)2=820   Sum of 39 numbers = average x numbenumber of observations = 80039×3980039×39 = 800   So the number excluded = 820 - 800= 
820 - 800 = 20
20   20nswer:20
Answer: A
Today Mary’s father is four times as old as Mary. Seven years ago, he was 7 times as old. How old is Mary today? Choose the most appropriate option: A) 11 B) 12 C) 13 D) 14 E) 15

Solution: 14ad's age = 4M   7*(M-7) = 4M-7   3M = 42   M = 14   The answer is 14.
Answer: D
What is the perimeter of a square with area 9p^2/25 ?	Select the correct option.
A) 3p/4 B) 3p^2/4 C) 3p D) 3p^2 E) 12p/5

Solution: Area of square, (side)^2 = (3p/5)^2   Therefore side of the square = 3p/5   Perimeter of square = 4*side = 4* (3p/5) = 12p/5   Answer is 12p/5.
Answer: E
Find the odd man out
253, 136, 352, 328, 631, 244 Choose the correct option:
A) 328 B) 136 C) 352 D) 631 E) 531

Solution: The sum all three digits comes to 10 except 328   328NSWER:328
Answer: A
What will be the ratio of simple interest earned by certain amount at the same rate of interest for 6 years and that for 3 years? Options
A) 1 : 3  B) 2 : 1  C) 1 : 2  D) 3 : 2  E) 1 : 4

Solution: Let the principal be P and rate of interest be R%.   Required ratio =   (P x R x 6)/100 DIVIDED BY	(P x R x 3)/100   =	6PR/3PR	=	6/3= 
6/3 = 2
2 : 1.   ANSWER : 2 : 1
Answer: B
What is the smallest number which, when increased by 7, is divisible by 8, 11, and 24?  Select the correct option:
A) 264
B) 257
C) 269
D) 270
E) 282

Solution: LCM(8,11,24)=24x11=264   So the least divisible number is 264, and the number we are looking for is   264-7= 
  264-7 = 257
257.   The answer is 257.
Answer: B
Which of the following must be non-negative number?  Choices
A) (a-0.9)(a-1)  B) (a+1)(a-1)  C) (a+0.9)(a+1)  D) (a-0.8)(a-0.8)  E) a(a+1)

Solution: 5-sec approach:   D. (a-0.8)(a-0.8) = (a-0.8)^2.   The square of a number is always non-negative.   Answer: (a-0.8)(a-0.8).
Answer: D
A dice is thrown. What is the probability that the number shown in the dice is divisible by 3?	Pick one
A) 5/5
B) 5/9
C) 5/1
D) 1/3
E) 5/2

Solution: Total number of outcomes possible when a die is rolled, n(S) = 6 (∵ 1 or 2 or 3 or 4 or 5 or 6)   E = Event that the number shown in the dice is divisible by 3 = {3, 6}   The probability = 2/6 = 1/3.   Answer: 1/3
Answer: D
If n = 8^11 – 1, what is the units digit of n?
Choices.
A) 3  B) 1  C) 0  D) 6  E) 4

Solution: 8 ^ 11 - 8 = 8 (8 ^ 10 - 1)   ==> 8 (2 ^ 30 - 1)   Last digit of 2 ^ 30 is 4 based on what explanation LiveStronger is saying. 2 ^ 30 - 1 yields   4 - 1= 
  4 - 1 = 3
3 as the unit digit. Now on multiply this with 1, we get unit digit as 3.   3nswer : 3
Answer: A
A sum of money deposited at C.I. amounts to Rs.2420 in 2 years and to Rs.2783 in 3 years. Find the rate percent?	Choose the correct choice from the following choices:
A) 15  B) 10  C) 28  D) 24  E) 82

Solution: Explanation:   2420 --- 363   100 --- ? => 15%   15nswer: Option 15
Answer: A
A student chose a number, multiplied it by 2, then subtracted 138 from the result and got 102. What was the number he chose?
Options.
A) 123  B) 267  C) 277  D) 267  E) 120

Solution: Let xx be the number he chose, then   2⋅x−138=1022⋅x−138=102   2x=2402x=240   x=120   Answer:120
Answer: E
Sum of two numbers is 25. Two times of the first exceeds by 5 from the three times of the other. Then the numbers will be?  Choose the correct answer
A) A)5
B) B)9
C) C)11
D) D)13
E) E)15

Solution: Explanation:   x + y = 25   2x – 3y = 5   x = 16 y = 9   9)
Answer: B
Kiran had 85 currency notes in all , some of which were of Rs.100 denomination and the remaining of Rs.50 denomination the total amount of all these currency note was Rs.5000.how much amount did she have in the denomination of Rs.50?  Choices
A) 3500	B) 1500	C) 2500	D) 4500	E) None of them

Solution: Let the no of fifty rupee notes be x   Then,no of 100 rupee notes =(85-x)   50x+100(85-x)=5000   x+2(85-x)=100   x=70   so, required amount=Rs.(50*70)= Rs.3500   3500nswer is 3500.
Answer: A
Cost is expressed by the formula tb^4. If b is doubled, the new cost is what percent of the original cost? Select
A) 200  B) 600  C) 800  D) 1600  E) 50

Solution: Original Cost C1=t1*b1^4   New Cost C2=t2*b2^4....only b is doubled so t2=t1 and b2=2b1   C2=t2*(2b1)^4   =16(t1*b1^4)   =16C1   16 times C1=>1600% of C1   Ans 1600=1600
Answer: D
The function g(a) is defined for integers a such that if a is even, g(a) = a/2 and if a is odd, g(a) = a + 5. Given that g(g(g(g(g(a))))) = 19, how many possible values for a would satisfy this equation? Choose the correct answer
A) 1  B) 5  C) 7  D) 8  E) 11

Solution: Let me define terms:   in g(a) = R   a is argument, R is result, g() is function,   in g(g(g(g(g(a))))), g1 is inner most, g5 is outermost for identification.   From definition of function g, we can deduce that:   If Result is even then two possibilities for argument = 1 Even 1 Odd   If Result is odd then one possibility for argument = 1 Even   Since final result = 19 = Odd   Possibilities:   g1:1 Even   g2: 1*(Even,Odd ) =1 Even 1 Odd   g3: 1*(Even,Odd) + 1 Even =2 Even 1 Odd   g4: 2*(Even, Odd) + 1 Even =3 Even 2 Odd   g5: 3*(Even, Odd) + 2 Even =5 Even 3 Odd = Total 8   Ans 8 it is!
Answer: D
Sum of three numbers 275, If the first number be twice then second and third number be one third of the first, then the second number is
Choose the most appropriate option
A) A)70 B) B)71 C) C)72 D) D)73 E) E)75

Solution: 75xplanation:   Let the second number is x, then first is 2x, and third is 1/3(2x)   =>2x+x+2x/3=275   <=>11x/3=275   =>x=75   Answer: Option 75
Answer: E
125^n divides 325^325 Choose one
A) 216  B) 217  C) 218  D) 219  E) 220

Solution: 325^325=(13*25)^325 = (13^325)*(5^650)   125^n=5^(3n)   power of 5 in numerator should be greater then denominator   so 650>3n and hence   n=216   216NSWER:216
Answer: A
In 1 hour, a boat goes 6 km along the stream and 12 km against the stream. The speed of the boat in still water (in km/hr) is : Pick:
A) 3 km/hr.
B) 2 km/hr.
C) 6 km/hr.
D) 8 km/hr.
E) 9 km/hr.

Solution: Speed in still water = 1/2(6 + 12) km/hr   = 9 km/hr. ANSW9 km/hr.R :9 km/hr.
Answer: E
Machine P and Machine Q are each used to manufacture 110 sprockets. It takes Machine P 10 hours longer to produce 110 sprockets than Machine Q. Machine Q produces 10% more sprockets per hour than Machine A. How many sprockets per hour does Machine A produce?	Pick one.
A) 5
B) 15
C) 55
D) 95
E) 1

Solution: P makes x sprockets per hour.   Then Q makes 1.1x sprockets per hour.   10/x = 110/1.1x + 10   1.1(110) = 110 + 11x   11x = 11   x = 1   The answer is 1
Answer: E
If a two-digit positive integer has its digits reversed, the resulting integer differs from the original by 36. By how much do the two digits differ?  Choices
A) 3 B) 4 C) 5 D) 6 E) 7

Solution: Given that (10a + b) - (10b + a) = 36 --> 9a - 9b =36 --> a - b 36 --  9  - 9= 
36 --  9  - 9 = 36
36 --> a - b= 4.   Answer: 4.
Answer: B
If 3 workers collect 48 kg of cotton in 4 days, how many kg of cotton will 9 workers collect in 2 days?  Choose the correct option: A) 32 kg B) 25 kg C) 72 kg D) 88 kg E) 92 kg

Solution: 72 kg   72 kg   (3 * 4)/48 = (9 * 2)/ x   x = 72 kg
Answer: C
If 0.60: x : : 6 : 4, then x is equal to	Choose the correct answer.
A) 0.1 B) 0.4 C) 0.82 D) 0.8 E) None

Solution: Sol.   (x×6) = (0.60×4) ⇒ x = 2.4/6 = 0.40.   Answer 0.4
Answer: B
When a certain tree was first planted, it was 4 feet tall, and the height of the tree increased by a constant amount each year for the next 6 years. At the end of the 6th year, the tree was 1/7 taller than it was at the end of the 4th year. By how many feet did the height of the tree increase each year? Options:  A) 3/10  B) 2/5  C) 1/2  D) 2/3  E) 6/5

Solution: Say, the tree grows by x feet every year.   Then, 4 + 6x = (1+1/7)(4+4x)   or, x = 2/5   Answer 2/5
Answer: B
A teacher prepares a test. She gives 9 objective type questions out of which 4 have to be answered. Find the total ways in which they can be answered if the first 6 questions have 3 choices and the last 3 have 4 choices. Pick: A) 7255 B) 7632 C) 7192 D) 7100 E) 7144

Solution: Two cases.   First Case: 2 Questions - 3 Choices, 2 Questions - 4 Choices   6C2 * 3C2 ways to select the questions   3C1 * 3C1 * 4C1 * 4C1 ways to answer the questions   = 15 * 3 * 3 * 3 * 4 * 4= 
15 * 3 * 3 * 3 * 4 * 4 = 6_480
6480   Second Case: 1 Question - 3 Choices, 3 Questions - 4 Choices   6C1 * 3C3 ways to select the questions   3C1 * 4C1 * 4C1 * 4C1 ways to answer the questions= 6 * 1 * 3 * 4 * 4 * 4= 
6 * 1 * 3 * 4 * 4 * 4 = 1_152
1152   Total= 6480 + 1152= 
6480 + 1152 = 7_632
7632   7632
Answer: B
The population of a bacteria colony doubles every day. If it was started 10 days ago with 2 bacteria and each bacteria lives for 12 days, how large is the colony today?  Options.
A) 512
B) 768
C) 1024
D) 2048
E) 4096

Solution: 2^10(2) = 2^11 = 2048   The answer is 2048.
Answer: D
The difference of the squares of two consecutive even integers is divisible by which of the following integers ?
Choose the correct choice from the following options.
A) 2
B) 3
C) 4
D) 8
E) 10

Solution: Let the two consecutive even integers be 2n and (2n + 2). Then,   (2n + 2)2 = (2n + 2 + 2n)(2n + 2 - 2n)   = 2(4n + 2)   = 4(2n + 1), which is divisible by 4.   Option 4
Answer: C