MU-NLPC/Calc-aqua_rat huggingface dataset:
The product of n+1 consecutive positive integers is always divisible by
Choose the correct option
A) n^2 -1	B) (n+1)!	C) 2n +1	D) n^2 + 1	E) n!

Solution: Plug in some vlues and check -   Product of first 2 number is 2*1   Product of first 3 number is 3*2*1   Product of first 4 number is 4*3*2*1   Product of first 5 number is 5*4*3*2*1   So, The product of first n natural numbers is always divisible by n! , answer will be ((n+1)!)
Answer: B
x% of y is increased by x%. What is the result in terms of x and y?	Choose the correct choice from the following answers
A) 100xy + x B) xy + x/100 C) 100xy + x/100 D) 100xy + xy/100 E) xy(x + 100)/10000

Solution: x% of y=xy/100   Increment is x% =xyx/100∗100   Total=xy/100+xyx/100∗100=xy(x+100)/10000   Answer = xy(x + 100)/10000
Answer: E
2 dice are tossed. What is the probability that the total score is a prime no. is?
Pick
A) 3/11
B) 5/12
C) 7/15
D) 3/13
E) 2/13

Solution: 5/12   5/12
Answer: B
If x, y, and z are positive integers and 2x = 3y = 4z, then the least possible value of x + y + z is	Pick one
A) 40
B) 50
C) 60
D) 70
E) 31

Solution: given 2x=3y=5z   x+y+z in terms of x   = x+(2x/3)+(2x/5) = 31x/15   now checking with each of the answers and see which value gives a minimum integer value.   A x = 15/31*40 , not an integer   B,C,D can be ruled out similarly.   31 is minimum value as x = 15*31/31= 
15*31/31 = 15
15   Answer is 31
Answer: E
Sum of the squares of three numbers is 99 and the sum of their products taken two at a time is 131. Find the sum? Choose the correct choice from the following answers:	A) 20	B) 25	C) 19	D) 28	E) 29

Solution: (a + b + c)2 = a2 + b2 + c2 + 2(ab +bc + ca) = 99 + 2* 131   a + b + c = √361 = 19   19
Answer: C
If Jake loses 8 pounds, he will weigh twice as much as his sister. Together they now weigh 290 pounds. What is Jake’s present weight, in pounds?	Answers.
A) 131
B) 135
C) 169
D) 196
E) 212

Solution: Lets say J is the weight of Jack and S is the wt of his sister.   If he loses 8 pounds, he s twice as heavy as his sister.   J-8=2*S   Also, together they weight 290 pounds   J+S=290   solvong the 2 equation ,we get J=196 pounds !   196
Answer: D
REDO’s manufacturing costs for sets of horseshoes include a $10,500 initial outlay, and $15per set. They can sell the sets $40. If profit is revenue from sales minus manufacturing costs, and the company producessells 500 sets of horseshoes, what was their profit?
Choose the correct answer
A) $2100	B) $2000	C) $2050	D) $2070	E) $2500

Solution: Total Manufacturing cost = 10500+500*15= 
10500+500*15 = 18_000
18000   Total Selling cost= 500*40= 
500*40 = 20_000
20000   Profit= 20000-18000= 
20000-18000 = 2_000
2000   Answer : $2000
Answer: B
A rectangular block has the dimensions 5x6x7 cm it is dropped into a cylindrical vessel of radius 6cm and height 10 cm. If the level of the fluid in the cylinder rises by 4 cm, What portion of the block is immersed in the fluid ?	Choices:
A) 22/7 x 24/35
B) 22/7 x 36 x 4
C) 22/7 x 36/5
D) 22/7 x 37/21
E) 22/7 x 32/21

Solution: Explanation:   Since level of water increased in cylinder by height 4.   This is because of the rectangular block .   Therefore , area of rectangular block immersed in water is = 22/7 x (6)^2 x 4   Thats why portion of block immersed in water is= (22/7 x 36 x 4) / total vol. of rectangle   = (22/7 x 36 x 4)/(7x5x6)   = 22/7 x 24/35.   22/7 x 24/35NSWER IS 22/7 x 24/35
Answer: A
A train 400 m long can cross an electric pole in 20 sec and then find the speed of the train?
Pick
A) 72 Kmph
B) 28 Kmph
C) 29 Kmph
D) 65 Kmph
E) 25 Kmph

Solution: Length = Speed * time   Speed = L/T   S = 400/20= 
400/20 = 20
20 M/Sec   Speed= 20*18/5 (To convert M/Sec in to Kmph multiply by 18/5)   Speed = 72 Kmph   72 Kmphnswer:72 Kmph
Answer: A
The number 95 can be written as the sum of the squares of 4 different positive integers in two ways. Of the following, which can be the sum of these 4 integers  Options:
A) 9	B) 10	C) 15	D) 18	E) 20

Solution: The only possible sum for 4 different squares of an integer with total sum number is 95 are :   49 + 36 + 9 + 1= 
49 + 36 + 9 + 1 = 95
95 which are the square from numbers : 7, 6, 3, 1 (total sum number is 20)   or     81 + 9 + 4 + 1= 
  81 + 9 + 4 + 1 = 95
95 which are the square from numbers : 9, 3, 2, 1 (total sum number is 15)   hence the answer is (20)
Answer: E
In a mixture 60 liters, the ratio of milk and water 2 : 1. If the this ratio is to be 1 : 2, then the quantity of water to be further added is:  Choose the correct choice from the following answers:
A) 20 liters  B) 30 liters  C) 40 liters  D) 60 liters  E) 80 liters

Solution: Explanation :   Quantity of milk =60 x 2/3	litres = 40 liters.Quantity of water in it = (60- 40)= 
(60- 40) = 20
20 liters.New ratio= 1 : 2Let quantity of water to be added further be x liters.Then, milk : water =	40/(20 + x)Now,	40/(20+x) =1/220 + x = 80x = 60.Quantity of water to be added = 60 liters.   Answer : 60 liters
Answer: D
In how many no. between 10 and 30 exactly Two of the digits is 2?	Choose the correct choice from the following answers
A) 25  B) 1  C) 35  D) 45  E) 50

Solution: It's simple can be solved by elimination of answer choices.   Option A and C are too large, not possible. Even DE are large to have correct choice.   Ans : 1
Answer: B
The consumption of diesel per hour of a bus varies directly as square of its speed. When the bus is travelling at 60 kmph its consumption is 1 litre per hour. if each litre costs $30 and other expenses per hous is $ 20, then what would be the minimum expenditure required to cover a distance of 600 Km? Select.
A) 500  B) 450  C) 600  D) 650  E) 750

Solution: 60 kmph consumption is 1 lt/hr   so 600 km will take 10 hrs and the consumption is 10 lt for entire distance.   1 lt costs $30   so 10 lt costs $300   extra expenses for 1 hr - $20   10 hrs - $200   total expense - $300 + $200= $500   500nswer : 500
Answer: A
A man's regular pay is $3 per hour up to 40 hours. Overtime is twice the payment for regular time. If he was paid $192, how many hours overtime did he work?	Choose the correct choice from the following answers:
A) 8	B) 5	C) 9	D) 6	E) 12

Solution: At $3 per hour up to 40 hours, regular pay = $3 x 40 = $120 If total pay = $168, overtime pay = $192 - $120 = $72 Overtime rate (twice regular) 192 -  120= 
192 -  120 = 72
$72 Overtime rate (twice regular)= 2 x $3 = $6 per hour => number of overtime hours = $72/$6 = 12   Ans is 1272/ 6= 
72/ 6 = 12
12   Ans is 12
Answer: E
Peter invests a sum of money and gets back an amount of $ 800 in 3 years . David invests an equal amount of money and gets an amount of $854 in 4 years. If both amounts were invested at the same rate (simple interest ) What was the sum of money invested ?
Choose the correct option.
A) 653
B) 664
C) 698
D) 744
E) 700

Solution: Since both Peter and David invested the same amount of money at the same rate, they would earn same interest per year.   David invested for one year more than Peter and hence he got interest amount for one more year.   Interest earned per year = 653mount received by David - 653mount received by Peter = 854 - 800= 
854 - 800 = 54
54   Interest earned for 3 years= 54*3= 
54*3 = 162
162   653mount invested= 815 - 162= 
815 - 162 = 653
653   653nswer: 653
Answer: A
Ron, Harry and Blake's age is in ratio 2:5:8. Find their ages if the sum of their age is 60 years. Choose the correct choice from the following answers
A) 4 , 16 and 40  B) 5, 20 and 35  C) 8, 20 and 32  D) 11, 23 and 27  E) 10, 20 and 30

Solution: Let the age of Ron, Harry and Blake be 2x, 5x and 8x.   2x + 5x + 8x = 60   15x = 60   x = 4   The ages are 8, 20 and 32.   Answer : 8, 20 and 32
Answer: C
Life expectancy is defined by the formula 2SB/G, where S = shoe size, B = average monthly electric bill in dollars, and G = GMAT score. If Melvin's GMAT score is twice his monthly electric bill, and his life expectancy is 40, what is his shoe size?	Choose one: A) 25 B) 30 C) 35 D) 40 E) 50

Solution: Solution -   Given that, G = 2B and Life expectancy(L) = 40   L=2SB/G -> 40 = 2SB/2B --> S=40.   ANS 40
Answer: D
Brent went on a hike to Leeland Lake. On his way up the trail he travelled at 2 Km/h. On his way down the trail he travelled at twice the speed and therefore his way back took three hours less. What is the distance (in Km) of the trail?  Choose the correct choice from the following options:
A) 6 Km. B) 8 Km. C) 450. D) 500. E) 600.

Solution: Distance is same   S1t1=s2t2   40t= 50 (t-1)   t=5   distance= speed *time    40*5= 
 40*5 = 200
200   8 Km. is the answer
Answer: B
A and B can do a work in 12 days, B and C in 30 days and C and A in 36 days. In how many days will the work be completed, if all three of them work together?	Options.
A) 124/13 days.
B) 241/13 days.
C) 180/13 days.
D) 155/13 days.
E) 150/13 days.

Solution: C   180/13 days.   One day work of A and B = 1/12   One day work of B and 180/13 days. = 1/30   One day work of 180/13 days. and A = 1/36   2(A + B + 180/13 days.) = 1/12 + 1/30 + 1/36   2(A + B + 180/13 days.) = 13/90   (A + B + 180/13 days.) = 13/180   Number of days required = 180/13 days.
Answer: C
In a function they are distributing noble prize. In how many ways can 3 prizes be distributed among 4 boys when No boy gets more than one prize? Choose the correct choice from the following:
A) 18 B) 20 C) 22 D) 24 E) 27

Solution: Sol. In this case, repetitions are not allowed. So, the first prize can be given in 4 ways. The second in 3 ways and the third in 2 ways. But fundamental principle, (4 x 3 x 2) ways = 24 ways   4: Or 4p = — 4:- 4X3X2X1- 24 ways   24
Answer: D
Last year Department Store X had a sales total for December that was 5 times the average (arithmetic mean) of the monthly sales totals for January through November. The sales total for December was what fraction of the sales total for the year?
Choose the correct choice from the following choices:
A) 1/4 B) 4/15 C) 1/3 D) 5/16 E) 4/5

Solution: Let avg for 11 mos. = 10   Therefore, 5/16ec = 50   Year total = 11*10 + 50= 
11*10 + 50 = 160
160   Answer= 50/160 = 5/16 = 5/16
Answer: D
In a bouquet of flowers, all but two are roses, all but two are tulips, and all but two are daisies. How many flowers are in the bouquet? Pick:
A) 1  B) 2  C) 3  D) 4  E) 5

Solution: 3   3   There are 3 flowers (1 rose, 1 tulip, and 1 daisy).
Answer: C
Anthony and Michael sit on the six-member board of directors for company w. If the board is to be split up into 2 three-person subcommittees, what percent of all the possible subcommittees that include Michael also include Anthony?  Choose the most appropriate option: A) 20% B) 30% C) 40% D) 50% E) 60%

Solution: Soln: Let the commitees be I and II   Assuming that Anthony and Michael w go into commitee I, there is just one more place left to be filled in that commitee and it can be taken by any of the 4 remaining people. Thus 4 ways.   Since the Anthony and Michael can also go into commitee II, we get 4 ways for that commitee also.   So in total = 8 ways   Now total number of ways of choosing 3 from 6 people is   = 640%3   = 6 * 5 * 4/3!   = 20 ways   Therefore Probability is = (8 /20) * 100= 
(8 /20) * 100 = 40
40%
Answer: C
Two employees X and Y are paid a total of Rs. 570 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week? Choose the correct answer:  A) s.259  B) s.289  C) s.299  D) s.300  E) s.389

Solution: Let the amount paid to X per week = x   and the amount paid to Y per week = y   Then x + y = 570   But x = 120% of y = 120y/100 = 12y/10   ∴12y/10 + y = 570   ⇒ y[12/10 + 1] = 570   ⇒ 22y/10 = 570   ⇒ 22y = 5700   ⇒ y = 5700/22 = Rs.259   s.259)
Answer: A
a, b, c and d are four consecutive numbers. If the sum of a and dis 109, what is the product of b and c?	Choose the correct choice from the following answers
A) 2652  B) 2578  C) 2970  D) 3354  E) 4234

Solution: 2970   2970   Here d = a + 3   a + a + 3 = 109   2a = 106   a = 53   So, numbers are 53, 54, 55 and 56   ∴ b × c= 54 × 55 = 2970
Answer: C
3 persons are standing at the middle of edges of a Triangle.All the 3 persons starts moving at same time with same speed in random direction
What is the probability of meeting atleast 2 persons?
Options.
A) 1/4 B) 2/4 C) 3/4 D) 5/4 E) 6/4

Solution: no of times that they dont meet is 2   so they meet in 6 ways   so required probability is=6/8=3/4   ANSWER:3/4
Answer: C
David obtained 36, 35, 42, 57 and 55 marks (out of 100) in English, Mathematics,Physics, Chemistry and Biology What are his average marks ? Choose one:
A) 75 B) 45 C) 87 D) 165 E) 11

Solution: Explanation:   Average = (36+ 35+ 42+ 57+ 55 )/ 5 = 225/5= 
225/5 = 45
45.   Answer:45
Answer: B
Vasya wrote down several consecutive integers. Which of the following could not be the percentage of odd numbers among them  Choose the correct choice:	A) 40	B) 45	C) 48	D) 55	E) 60

Solution: what you have to check is if the (answer given: 100-answer given) is either equal or two consecutive values..   reason for this is that there are only three possiblities of numbers of odd numbers in consecutive integers   1) equal to number of even numbers   2)one more than number of even numbers   3)one more than number of even numbers   (A) 40:60=2:3possible   (B) 45:55=9:11not possible   (C) 48:52=12:13possible   (55) 50:50=1:1possible   (E) 60:40=3:2possible   ans 55
Answer: D
An student identification code consists of a vowel followed by a 3-digit number greater than 200. Exactly 2 of the 3 digits in the code should be identical. How many different codes is it possible to form? Choose the correct choice from the following choices:
A) 211 B) 216 C) 1075 D) 1080 E) 2160

Solution: An student identification code will be of the type -,-,-,-   first digit can be selected from any of the 5 vowels in 5C1 ways   now for the remaining three digit lets consider the following two cases   case 1: when the number is greater than 200 but less than 300   number will be of the type 2,_,_. now suppose repeating number is same as first digit number i.e. 2. and the third number is one of the remaining 9 numbers (we are rejecting 2 here, because it will result in 222, which is not acceptable as per the given condition). thus these two number can arrange themselves in two blank spaces in 2! ways. hence total number of numbers in which repeating digit is same as the first digit = 1.9.2! =18   now, suppose that repeating number is different than first digit. thus possible case in this case are 8 as listed below:   211   233   244   255   266   277   288   299   here again we have rejected 200( because number must be greater than 200) and 222 ( exactly two repeating digits are allowed)   thus total possible cases are 18 + 8= 
18 + 8 = 26
26   case 2: number ranging from 300 to 999   here for first digit we have 7 cases (3,4,5,6,7,8,9)   now if the repeating number is same as the first number then we will have 18 cases ( same reasoning as mentioned in the previous case)   if the repeating number is different than first digit number then we will have 9 cases ( because here number ending with two zeros are allowed)   hence total number of ways= 7(18+9) = 189   thus different number of codes = 5(189+26) = 1075   hence 1075
Answer: C
A man's speed with the current is 15 km/hr and the speed of the current is 2.5 km/hr The man's speed against the current is
Choose the correct choice from the following answers:
A) 8.5 km/hr  B) 9 km/hr  C) 10 km/hr  D) 12.5 km/hr  E) None

Solution: Solution   Man's rate in still water	= (15 - 2.5) km/hr   = 12.5 km/hr.   Man's rate against the current	= (12.5 - 2.5) km/hr   = 10 km/hr.   Answer 10 km/hr
Answer: C
A man ate 100 bananas in five days, each day eating 6 more than the previous day. How many bananas did he eat on the first day? Choices
A) 6  B) 7  C) 8  D) 9  E) 10

Solution: let the number of bannanas in first day be x   for consecutive five days it will be like x,x+6,x+12,x+18,x+24   the sum of those are 100, 5x+60=100   so,x=8   ANSWER:8
Answer: C
A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is? Choose the correct choice from the following answers:	A) 288	B) 267	C) 190	D) 150	E) 123

Solution: Let the length of the train be x meters and its speed be y m/sec.   They, x / y = 15 => y = x/15   x + 100 / 25 = x / 15   x = 150 m.   Answer:150
Answer: D
The banker's discount on Rs. 1600 at 15% per year is the same as true discount on Rs. 1680 for the same time and at the same rate. The time is:
Choose the correct choice from the following: A) 3 months B) 4 months C) 6 months D) 8 months E) 7 months

Solution: Simple Interest on Rs. 1600 = T.D. on Rs. 1680.   Therefore Rs. 1600 is the P.W. of Rs. 1680, i.e., Rs. 80 is on Rs. 1600 at 15%.   Therefore, Time = (100 x 80 / 1600 x 15)	year   = 1/3 year = 4 months.   Correct answer is 4 months.
Answer: B
If a man running at the speed of x km/hr travels a distance of y km, which of the following cannot be equal to the distance traveled? Select:
A) x-y km	B) x/2 km	C) (x-y)/2 km	D) y-x km	E) y/x km

Solution: This question can be solved by TESTing VALUES, but there's a particular pattern that you have to recognize to make the workeasy.   We're not really limited by anything in this question, so X and Y can be anything. Under normal circumstances, I won't TEST the number 1 in PS questions (as it often leads to duplicate answers), but here it's a great option (since we're looking to eliminate 4 answers, multiple TESTs are going to be likely anyway).   We're given information on speed (X km/hour) and distance (Y km). We're asked which of the 5 answer choices CANNOT be the distance traveled.   IF....   X = 2 and Y = 1   Answers A (2-1 = 1) and B (2/2 = 1) are POSSIBLE. Eliminate A and B.   IF....   X = 3 and Y = 1   Answer C ([3-1]/2 = 1) is POSSIBLE. Eliminate C.   IF....   X = 1 and Y = 1   Answer E (1/1 = 1) is POSSIBLE. Eliminate E.   Final Answer:   y-x km
Answer: D
How many numbers can be formed by using digits 0 to 9, as the number should be divisible by 5 and it should be 4 digit one and no repitation is allowed on digits?	Options
A) 951 ways	B) 952 ways	C) 953 ways	D) 954 ways	E) 955 ways

Solution: For a number to be divisbly by 5 we have two choices 0 or 5   case 1 : when choice is 0   _ _ _ 0 first digt can be filled in 9ways , 2nd in 8 ways, 3rd in 7 ways so 9 * 8 *7= 
9 * 8 *7 = 504
504   case 2 : when choice is 5   _ _ _ 5 first digi can be in 8 ways (since 0 cannot come ) , 2nd in 8 ,3rd in 7 so  8*8*7= 
 8*8*7 = 448
448   so it can be in  504 + 448= 
 504 + 448 = 952
952 ways   ANSWER:952 ways
Answer: B
A candidate who gets 30% of the marks fails by 50 marks. But another candidate who gets 45% marks gets 25 marks more than necessary for passing. Find the number of marks for passing? Choose one:
A) 199 Marks B) 200 Marks C) 188 Marks D) 188 Marks E) 176 Marks

Solution: 30% ------------ 50   45% ------------ 25   ----------------------   15% ------------- 75   30% -------------- ?     150 + 50= 
  150 + 50 = 200
200 Marks   Answer:200 Marks
Answer: B
The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is? Answers:
A) 767 m
B) 467 m
C) 245 m
D) 567 m
E) 544 m

Solution: 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:245 m
Answer: C
A, B and C can do a piece of work in 24 days, 30 days and 40 days respectively. They began the work together but C left 4 days before the completion of the work. In how many days was the work completed?  Choose the correct choice: A) 12 days B) 16 days C) 18 days D) 11 days E) 38 days

Solution: One day work of A, B and C = 1/24 + 1/30 + 1/40 = 1/10 Work done by A and B together in the last 4 days = 4*(1/24 + 1/30) = 3/10   Remaining work = 7/10   The number of days required for this initial work = 7 days.   The total number of days required = 4 + 7= 
4 + 7 = 11
11 days.Answer: 11 days
Answer: D
The cost price of two types of tea are Rs. 180 per kg and Rs. 200 per kg respectively. On mixing them in the ratio 5:3, the mixture is sold at Rs. 210 per kg . In the whole transaction, the gain percent is Choose the correct choice from the following choices:	A) 10%	B) 11%	C) 12%	D) 13%	E) 14%

Solution: Exp. Let 5kg of first kind of tea be mixed with 3 kg of second kind   C.P of 8 kg of tea = Rs. ( 180*5 + 200*3 ) = Rs. 1500   S.P of 8 kg of tea = Rs. (210 * 8) = Rs. 1680   Gain = Rs. ( 1680 – 1500 ) = Rs. 180   Gain% = ( 180/1500*100 )= 
( 180/1500*100 ) = 12
12%   ANSWER:12%
Answer: C
Seven children — A, B, C, D, E, F, and G — are going to sit in seven chairs in a row. Child A has to sit next to both BG, with these two children immediately adjacent to here on either side. The other four children can sit in any order in any of the remaining seats. How many possible configurations Y are there for the children?  Pick:
A) 240	B) 480	C) 720	D) 1440	E) 3600

Solution: MAGOOSHOFFICIAL SOLUTION:   First, we will consider the restricted elements — children ABG have to be in three seats in a row. How many “three in a row” seats are there in a row of seven seats?   X X X _ _ _ _   _ X X X _ _ _   _ _ X X X _ _   _ _ _ X X X _   _ _ _ _ X X X   There are five different “three in a row” locations for these three children. Now, for any given triplet of seats, we know A has to be in the middle, so the children could be seated B-A-G or G-A-B — just those two orders. This means the total number of configurations for these three children is 5*2= 
5*2 = 10
10.   Now, consider the non-restricted elements, the other four. Once ABG are seated, the remaining four children can be seated in any order among the remaining four seats — that’s a permutation of the 4 items —- 4P4= 4! = 24. For any single configuration of ABG, there are 24 ways that the other children could be seated in the remaining seats.   Finally, we’ll combine with the Fundamental Counting Principle. We have 10 ways for the first three, and 24 ways for the remaining four. That’s a total number of configurations Y of  24*10= 
 24*10 = 240
240.   240nswer= 240
Answer: A
A man is 24 years older than his son. In four years, his age will be twice the age of his son. The present age of the son is Choices:
A) 14 years  B) 18 years  C) 20 years  D) 22 years  E) None

Solution: Solution   Let the son's present age be x years .Then, man's present age	= (x+24)years.   Then	â€¹=â€º(x+24)+4= 2(x+4)   â€¹=â€ºx+28=2x+8   x= 20.   Answer 20 years
Answer: C
A bag contains 12 white and 18 black balls. 2balls are drawn in succession. What is the probability that first is white and second is black?  Choose the correct choice from the following options.
A) 23/113
B) 36/145
C) 21/117
D) 11/154
E) 21/115

Solution: The probability that first ball is white:   =12C130C1=12C130C1   =1230=1230   =25=25   Since, the ball is not replaced; hence the number of balls left in bag is 29.   Hence, the probability the second ball is black:   =18C129C1=18C129C1   =1829=1829   Required probability,   =(25)×(1829)=(25)×(1829)   =36/145   36/145
Answer: B
In a certain parking lot, 2% of the cars are towed for parking illegally. However 80% of the cars which are parked illegally are not towed. What percentage of cars in the parking lot are parked illegally?  Choose the correct choice from the following options.
A) 4%	B) 6%	C) 8%	D) 10%	E) 12%

Solution: Let x be the number of cars and let y be the number of cars parked illegally.   2%*x = 20%*y   y/x = 1/10 = 10%   The answer is 10%.
Answer: D
Look at this series: 5000,1000, 200, ... What number should come next? Select the correct option:	A) 17	B) 10	C) 15	D) 18	E) 40

Solution: E   40   This is a simple division series. 40ach number is divided by 5.
Answer: E
When a number is divided by 13, the remainder is 11. When the same number is divided by 17, then remainder is 9. What is the number ? Choose the correct choice.
A) 350 B) 349 C) 389 D) 369 E) 388

Solution: x = 13p + 11 and x = 17q + 9   13p + 11 = 17q + 9   17q - 13p = 2   q =	2 + 13p/17   The least value of p for which q =2 + 13p/17is a whole number is p = 26   x = (13 x 26 + 11)   = (338 + 11)= 
(338 + 11) = 349
349   Answer 349
Answer: B