MU-NLPC/Calc-aqua_rat huggingface dataset:
Machine M, N, O working simultaneously Machine M can produce x units in 3/4 of the time it takes machine N to produce the same amount of units. Machine N can produce x units in 2/5 the time it takes machine O to produce that amount of units. If all three machines are working simultaneously, what fraction of the total output is produced by machine N? Choose the correct choice from the following choices.
A) 1/2
B) 5/11
C) 4/13
D) 8/29
E) 6/33

Solution: Now ultimately the speed of every machine is given with respect to Mach O.   So lets assume the speed of O, say 12 hrs to make x units (assuming 6 because we can see we will need to divide by 3 and 4   Mach O makes x units in 12 hrs   So, Mach N = 2/5 of O = 2/5*12= 
2/5*12 = 24/5 = around 4.8
4.8 hrs to make x units   and Mach M= 3/4 of N = 3/4*4.8 = 6 hrs to make x units   No they are running simultaneously. Lets see how much each mach makes in 1 hr   Mach O = x/12 units   Mach N = 5x/24 units   Mach M = x/6 units   In 1 hr, together they make - x/12+5x/24+x/6 = 11/24   So what ratio of this has Mach N made?   (5x/24) / (11/24) = 5/11   Ans:5/11=5/11
Answer: B
How many words can be formed from the letters of the word ‘DIRECTOR’ So that the vowels are always together?
Answers:
A) 1524	B) 7845	C) 2160	D) 2541	E) 5631

Solution: In the given word, we treat the vowels IEO as one letter.   Thus, we have DRCTR (IEO).   This group has 6 letters of which R occurs 2 times and others are different.   Number of ways of arranging these letters = 6!/2! = 360.   Now 3 vowels can be arranged among themselves in 3! = 6 ways.   Required number of ways = (360x6) = 2160.   Ans: 2160
Answer: C
A box contains 2 red, 3 black and 4 blue balls. 3 balls are randomly drawn from the box. If two balls are found to be different, what is the probability that the third ball is blue? Select the correct option.
A) 8/3  B) 9/3  C) 5/3  D) 2/3  E) 1/3

Solution: there are 6 ways to draw a blue ball at third attempt if first two balls are different. they are   1)RED BLACK BLUE   2)RED BLUE BLUE   3)BLACK RED BLUE   4)BLACK BLUE BLUE   5)BLUE RED BLUE   6)BLUE BLACK BLUE   Probability of 1st way is (2/9)*(3/8)*(4/7)   as at first attempt we got red which are two in number out of 9 and in second we got black which are 3 in number out of 8 (as first ball is removed)and in 3rd attempt we got blue which are 4 in number out of 7 balls left.   similarly probability of other ways is as follows   (2/9)*(4/8)*(3/7)   (3/9)*(2/8)*(4/7)   (3/9) *(4/8)*(3/7)   (4/9)*(2/8)*(3/7)   (4/9)*(3/8)*(3/7)   total probability of getting a blue ball is sum of all above ways so p=(2/9)*(3/8)*(4/7)+(2/9)*(4/8)*(3/7)+(3/9)*(2/8)*(4/7)+(3/9) *(4/8)*(3/7)+(4/9)*(2/8)*(3/7)+(4/9)*(3/8)*(3/7)=1/3   so probability of ball to be blue is 1/3   Answer 1/3
Answer: E
Ramu bought an old car for Rs. 42000. He spent Rs. 13000 on repairs and sold it for Rs. 60900. What is his profit percent?  Select.
A) 10.7%  B) 19%  C) 18%  D) 14%  E) 16%

Solution: Total CP = Rs. 42000 + Rs. 13000   = Rs. 55000 and SP   = Rs. 60900   Profit(%) = (60900 - 55000)/55000 * 100   = 10.7%   10.7%nswer: 10.7%
Answer: A
The length of the bridge, which a train 110 metres long and travelling at 45 km/hr can cross in 30 seconds, is? Options:	A) 255	B) 265	C) 245	D) 277	E) 211

Solution: Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (110 + x)/30 = 25/2 => 2(110 + x) = 750 => x = 265 m.   Answer:265
Answer: B
A shopkeeper loses 15%,if an article is sold for Rs. 102. What should be the selling price of the article to gain 20%? Choose the correct choice from the following.
A) Rs.148	B) Rs.144	C) Rs.120	D) Rs.129	E) Rs.126

Solution: Given that SP = Rs. 102 and loss = 15%   CP = [100(SP)]/(100 - l%) = (100 * 102)/85 = 20 * 6 = Rs. 120.   To get 20% profit, New SP = [(100 + p%)CP]/100 = (120 * 120)/100   = Rs.144   Answer:Rs.144
Answer: B
1907 x 1907 = ?
Answers:
A) A)3623216
B) B)3624216
C) C)3624316
D) D)3636649
E) E)3625216

Solution: 1907 x 1907 = (1907)2   = (1900 + 7)2   = (1900)2 + (7)2 + (2 x 1900 x 7)   = 3610000 + 49 + 26600.= 
3610000 + 49 + 26600. = 3_636_649
3636649.   3636649)
Answer: D
Given f(x) = 3x – 5, for what value of x does 2*[f(x)] – 19 = f(x – 4) ?
Choose the correct choice.
A) 2
B) 4
C) 6
D) 8
E) 10

Solution: 2(3x-5)-19 = 3(x-4) - 5   3x = 12   x = 4   The answer is 4.
Answer: B
3 person can fill tank in 25 min, a can fill in 30 min , b can fill in 35 min and c can empty the 5 gallon per min then what is the capacity of tank? Pick one
A) 208.26 gallons	B) 218.26 gallons	C) 228.26 gallons	D) 238.26 gallons	E) 248.26 gallons

Solution: A can fill the tank in 30 minutes   B can fill the same tank in 35 minutes   A B 228.26 gallons together fill the tank in 25 minutes   Equating we get,   1050/23*5 = 228.26 gallons   ANSWER:228.26 gallons
Answer: C
The edge of three cubes of metal is 3 dm, 4 dm and 5 dm. They are melted and formed into a single cube. Find the edge of the new cube?
Choose one:	A) 1	B) 9	C) 4	D) 6	E) 3

Solution: 33 + 43 + 53 = a3 => a   = 6   Answer: 6
Answer: D
A man gains 30% by selling an article for a certain price. If he sells it at double the price, the percentage of profit will be.  Choose the correct choice from the following options:
A) 130%
B) 140%
C) 150%
D) 260%
E) 170%

Solution: Explanation:   Let the C.P. = x,   Then S.P. = (130/100)x = 13x/10   New S.P. = 2(13x/10) = 26x/10   Profit = 26x/10 - x = 26x/10   Profit% = (Profit/C.P.) * 100   => (26x/10) * (1/x) * 100 = 260 %   Option 260%
Answer: D
A doctor prescribed 20 cubic centimeters of a certain drug to a patient whose body weight was 120 pounds. If the typical dosage is 2 cubic centimeters per 15 pounds of the body weight, by what percent was the prescribed dosage greater than the typical dosage?	Answers
A) 25%	B) 9%	C) 11%	D) 12.5%	E) 14.8%

Solution: Typical dosage per 15 pound of the body weight = 2 c.c   Typical dosage per 120 pound of the body weight = 2 *(120/15)   = 2 * 8= 
2 * 8 = 16
16 c.c   Dosage prescribed by doctor for 120 pound patient= 20 c.c   % prescribed dosage greater than the typical dosage = (20-16/16) *100%   =(2/16) *100%   = 25%   25%nswer 25%
Answer: A
The price of lunch for 15 people was $208.00, including a 15 percent gratuity for service. What was the average price per person, EXCLUDING the gratuity?
Options.
A) $11.73 B) $12.60 C) $13.80 D) $14.00 E) $15.87

Solution: Take the initial price before the gratuity is 100   The gratuity is calculated on the final price, so as we assumed the final bill before adding gratuity is 100 so gratuity is 15% of 100 is 15 so the total price of meals is 115 so the given amount i.e 208 is for 115 then we have to calculate for 100   for 115 208   for 100 x   so by cross multiplication we get 115x=100*208 => x=100*208/110 by simplifying we get x as 189 which is the price of lunch before gratuity so the gratuity is 19 so   as the question ask the average price person excluding gratuity is  189/15= 
 189/15 = 63/5 = around 12.6
12.6 so our answer is $12.60)
Answer: B
An adventuring party consists of 4 white mages, 6 warriors, and 4 archers. In how many ways can 3 white mages, 2 warriors and 2 archers be selected from the given group? Options.
A) 987 ways  B) 446 ways  C) 360 ways  D) 157 ways  E) 134 ways

Solution: The number of ways of selecting three white mages, two warriors and two archers is:   = ⁴C₃ * ⁶C₂ * ⁴C₂   = (4 * 3 * 2)/(3 * 2 * 1) * (6 * 5)/(2 * 1) * (4 * 3)/( 2 * 1)   = 4 * 15 * 6= 
4 * 15 * 6 = 360
360 ways.   Answer: 360 ways
Answer: C
Peter invests a sum of money and gets back an amount of $ 815 in 3 years . David invests an equal amount of money and gets an amount of $850 in 4 years. If both amounts were invested at the same rate (simple interest ) What was the sum of money invested ?
Choose the correct choice from the following.
A) 670  B) 664  C) 698  D) 744  E) 710

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 = Amount received by David - Amount received by Peter = 850 - 815= 
850 - 815 = 35
35   Interest earned for 3 years= 35*3= 
35*3 = 105
105   Amount invested= 815 - 105= 
815 - 105 = 710
710   Answer: 710
Answer: E
If x is equal to the sum of the integers from 60 to 80, inclusive, and y is the number of even integers from 60 to 80, inclusive, what is the value of x + y?	Choose the correct answer:
A) 1361
B) 1481
C) 1601
D) 1721
E) 1841

Solution: x = 60 + 61 +...+ 80 = 21(70) = 1470   y = 11   x+y = 1481   The answer is 1481.
Answer: B
A and B rent a pasture for 10 months. A put in 80 cows for 7 months. How many can B put in for the remaining 3 months, if he pays half as much again as A?
Choose the correct choice from the following:
A) 299
B) 277
C) 281
D) 280
E) 267

Solution: 80* 7: x* 3 = 1:1 1/2   560: 3x = 2: 3   x = 280   Answer: 280
Answer: D
If 2a – b = 3c, where a, b, and c are non-zero integers, which of the following could be the average (arithmetic mean) of a and b, if the average must itself be an integer?	Select the correct option:
A) -2  B) -1  C) 1  D) 10  E) 12

Solution: Let's say Average of a & b is c   a+b/2=c   a+b= 2c   2a-b=3c   a+b=2c   --------   3a = 5c   a=5c/3   we can plug in all answer choices for average - " c " and see which one gives us an integer as "a" is also an integer.   5(-2)/3 = -10/3   5(-1)/3 = -5/3   5(1)/3 = 5/3   5(10)/3 = 50/3   5(12)/3 = 60/3= 
60/3 = 20
20 ( Hence 12 is the correct answer)   ANSW12R:12
Answer: E
A group of n students can be divided into equal groups of 4 with 2 student left over or equal groups of 5 with 2 students left over. What is the sum of the two smallest possible values of n?	Choose one
A) 33 B) 46 C) 49 D) 64 E) 86

Solution: 4x+2 = 5y+2...........ie: 4x-5y = 0   x,y must be >1 and y is even ie ( 2,4,6,..etc)   if y = 2 thus x is fraction   if y = 4 thus x =5 n =22   if y = 6 thus x = not possible fraction   if y =8 thus x = 10 n =42   n= 22+42= 
22+42 = 64
64   64
Answer: D
What is the number which when multiplied by 13 is increased by 180?
Options:	A) 13	B) 15	C) 23	D) 35	E) 45

Solution: 13 × 15 = 195   Answer: 15
Answer: B
Over a three-week period, the price of an ounce of gold increased by 10% in the first week, decreased by 20% in the following week, and increased by 10% in the third week. If the price of gold was G dollars per ounce at the beginning of the three weeks, what was the price at the end of the three weeks?
Select
A) 0.968G
B) 0.978G
C) 0.988G
D) 0.998G
E) 1.008G

Solution: 0.968Gfter 3 weeks, the price was 1.1*0.8*1.1*G=0.968G   The answer is 0.968G.
Answer: A
A man can do a piece of work in 5 days, but with the help of his son he can do it in 3 days. In what
time can the son do it alone ?  Choose the correct choice from the following:	A) 712days	B) 612days	C) 512days	D) 412days	E) None of these

Solution: Explanation:   In this type of question, where we have one person work and together work done. Then we can easily   get the other person work just by subtracting them. 712dayss   Son's one day work =   (13−15)=(5−315)=215   So son will do whole work in 15/2 days   which is =   712days   712daysnswer: 712days
Answer: A
Solve the given two equations and find the inequality of X and Y. (a) 2x^2 + 11x + 14 = 0 and (b) 4y^2 + 12y +9 =0
Pick:
A) If x>y
B) If x>=y
C) If x<y
D) If x<=y
E) x=y or relationship cannot be established

Solution: Solution:-   X=-7/2 or -2   Y=-3/2   If x<y   If x<y)
Answer: C
Present ages of Sameer and Anand are in the ratio of 5 : 4 respectively. Eight years hence, the ratio of their ages will become 11 : 9 respectively. What is Anand's present age in years? Choose one.
A) Can't be determined B) 40 C) 27 D) 64 E) None of these

Solution: Explanation:   Let the present ages of Sameer and Anand be 5x years and 4x years respectively.   Then, (5x+8)/(4x+8)=11/9   ⇒ 45x + 72 = 44x + 88⇒ 9(5x + 8) = 11(4x + 8)   ⇒ 45x - 44x = 88 - 72= 
88 - 72 = 16
16.   Anand's present age= 4x = 64 years.   Answer: 64
Answer: D
An error 2% in excess is made while measuring the side of a square. The percentage of error in the calculated area of the square is:  Options:
A) 4.00%  B) 4.14%  C) 4.04%  D) 4.26%  E) 4.27%

Solution: 100 cm is read as 102 cm.   A1 = (100 x 100) cm2 and A2 (102 x 102) cm2.   (A2 - A1) = [(102)2 - (100)2]   = (102 + 100) x (102 - 100)   = 404 cm2.   Percentage error = 404	x 100	%	= 4.04%   100 x 100   4.04%
Answer: C
A man can row upstream at 25 kmph and downstream at 35 kmph, and then find the speed of the man in still water? Options:	A) 18 kmph	B) 20 kmph	C) 30 kmph	D) 19 kmph	E) 10 kmph

Solution: US = 25   DS = 35   M = (35 + 25)/2= 
(35 + 25)/2 = 30
30   Answer:30 kmph
Answer: C
The original price of a suit is $200. The price increased 30%, and after this increase, the store published a 30% off coupon for a one-day sale. Given that the consumers who used the coupon on sale day were getting 30% off the increased price, how much did these consumers pay for the suit?	Choose the correct choice from the following answers.
A) $182	B) $191	C) $200	D) $209	E) $219

Solution: Given the foregoing discussion, it may be obvious now the trap-mistake answer is (C). Even if you can’t remember the correct thing to do, at the very least, learn to spot the trap!   The multiplier for a 30% increases is 1 + 0.30= 
1 + 0.30 = 1.3
1.3, and the multiplier for a 30% decrease is 1 – 0.30= 0.70, so the combined change is 1.3*0.7= 
1.3*0.7 = 0.91
0.91, 91% percent of the original, or a 9% decreases. Now, multiply $  200*0.91= 
  200*0.91 = 182
$182. $182nswer= ($182).
Answer: A
Two trains are running in opposite directions with the same speed. If the length of each train is 240 m and they cross each other in 12 sec, then the speed of each train is?  Choose the correct choice from the following:
A) 72
B) 89
C) 36
D) 34
E) 23

Solution: Let the speed of each train be x m/sec.   Then, relative speed of the two trains = 2x m/sec.   So, 2x = (240 + 240)/12 => x = 20   Speed of each train = 20 m/sec.   = 20 * 18/5= 
20 * 18/5 = 72
72 km/hr.   72nswer: Option 72
Answer: A
What is the banker's discount if the true discount on a bill of Rs.540 is Rs.90 ?	Choose the correct choice from the following answers:
A) 108
B) 120
C) 102
D) 106
E) 105

Solution: Explanation:   Present Worth, PW = F - TD = 540 - 90 = Rs. 450   Simple Interest on the Present Worth = True Discount   Hence Simple Interest on 450 = 90 ------(Equation 1)   Simple Interest on the face value = Bankers Discount   => Simple Interest on 540 = Bankers Discount   From Equation 1, Simple Interest on 450 = 90   Hence, Simple Interest on 540 = 90/450×540=540 = Rs. 108   => Bankers Discount = Rs. 108   108nswer: Option 108
Answer: A
Each of the integers from 0 to 8, inclusive, is written on a separate slip of blank paper and the ten slips are dropped into hat. If the slips are then drawn one at a time without replacement, how many must be drawn to ensure that the numbers on two of the slips drawn will have a sum of 10? Pick one:
A) 8
B) 9
C) 7
D) 6
E) 5

Solution: You should consider the worst case scenario: if you pick numbers 0, 1, 2, 3, 4 and 5 then no two numbers out of these 6 add up to 10.   Now, the next, 7th number whatever it'll be (6,7, or 8) will guarantee that two number WILL add up to 10. So, 7 slips must be drawn to ensure that the numbers on two of the slips drawn will have a sum of 10   Answer: 7
Answer: C
The average weight of 10 men is increased by 1 ½ kg when one of the men who weighs 48 kg is replaced by a new man. What is the weight of the new man?
Choose the correct choice from the following choices: A) 80 kg B) 63 kg C) 70 kg D) 75 kg E) 85 kg

Solution: Since the average has increased by 1.5 kg, the weight of the man who stepped in must be equal to 48+10x1.5   48+15= 
48+15 = 63
63 Kg   Ans: '63 kg'
Answer: B
If an article is sold at 19% profit instead of 12% profit, then the profit would be Rs. 105 more. What is the cost price?  Choose the correct choice from the following answers
A) Rs. 1505
B) Rs. 1510
C) Rs. 1500
D) Rs. 1490
E) None of these

Solution: Let the cost price of an article be Rs. x.   (19% of x) - (12% of x) = 105   19x/100 - 12x/100 = 105 => 7x = 105 * 100   => x = 1500   Cost price = Rs. 1500   ANSWER:Rs. 1500
Answer: C
.005/?= .01 Select the correct option:
A) .5 B) .05 C) .005 D) .0005 E) None of them

Solution: Let .005/x = .01;   Then x = .005/.01= 
.005/.01 = 0.5
.5/1= 
.5/1 = 0.5
.5   .5nswer is .5
Answer: A
60% of x is greater than 1/3rd of x by 110.what is x?	Choose the correct option.
A) 100.5  B) 200.5  C) 300.5  D) 350.5  E) 412.5

Solution: 6x/10-x/3=110   4x/15=110   x=412.5   ANSW412.5R:412.5
Answer: E
The grade point average of one third of the classroom is 69; the grade point average of the rest is 60. What is the grade point average of the whole class?	Choose the correct choice from the following options.
A) 61.	B) 63.	C) 65	D) 67	E) It depends how many people are there in the class.

Solution: Let the number of students in class A be = X1 + X2 + ...... + A1 ( where A1 = remaining students )   Now the remaining avg of the students be A1 / T = 60   A1 = 60T ( we are not sure on the number of students , assuming it as T ).   A = X1 + X2 + ...... + A1 ( First set of students + remaining students).   One third of A students avg is 60.   A / 3 = 69   => A = 207.   Now X1 + X2 + ...... + A1 = 207.   X1 + X2 + ...... = 207 - 60T.   We are not sure about the number of students in the remaining class + whole class and without that we can't solve this.   Answer: It depends how many people are there in the class. is correct option.
Answer: E
Two trains are running at 40 kmph and 20 kmph respectively in the same direction.Fast train completely passes a man sitting in the slower train in 9 seconds.What is the length of the fast train?	Choose one:
A) 23 m B) 23 2/9 m C) 27m D) 46 m E) 50 m

Solution: relative speed=20kmph=50/9m/sec   length of the train=50/9*9= 
50/9*9 = 50
50 m   ANSW50 mR:50 m
Answer: E
The seats in an Engineering college for Computer science, electronics and civil are in the ratio of 5 : 7 :8. There is a proportion to increase these seats by 40%, 50% and 75% respectively. What will be the ratio of increased seats ?	Select the correct option:  A) 2 : 3 : 4  B) 6 : 7 : 8  C) 6 : 8 : 9  D) 6 : 8 : 7  E) none of these

Solution: Originally, let the number of seats for Computer science, electronics and civil are 5x : 7x : 8x respectively.   Number of increased seats are (140% of 5x), (150% of 7x) and (175% of 8x)   7x : 21x/2 : 14x = 14x : 21x : 28x = 2 : 3 : 4.   2 : 3 : 4NSWER:2 : 3 : 4
Answer: A
The average weight of 4 persons increases by 1.5 kg. If a person weighing 65 kg is replaced by a new person, what could be the weight of the new person?
Choose the correct choice from the following answers.
A) 71 kg
B) 77 kg
C) 76.5 kg
D) Data inadequate
E) None of these

Solution: total weight increases = 4 × 1.5 = 6 kg   so the weight of new person = 65 + 6= 
65 + 6 = 71
71 kg   71 kgnswer 71 kg
Answer: A
The numerator of a certain fraction is 8 less than the denominator. If 3 is added to the numerator and 3 is subtracted from the denominator, the fraction becomes 3/4. Find the original fraction?
Choose the correct choice.
A) 3/11	B) 4/11	C) 5/11	D) 6/13	E) 7/13

Solution: Explanation:   The denominator be P, the numerator will be (P - 8).   The fraction will be (P - 8)/P.   Adding 3 to the numerator and subtracting 3 from the denominator, (P - 8 + 3)/(P - 3) = 3/4.   (P - 5)/(P - 3) = 3/4   P = 20 - 9 => P = 11.   The fraction is: 3/11.   3/11)
Answer: A
Which of the following leads to the correct mathematical solution for the number of ways that the letters of the word RADAR could be arranged to create a five-letter code?  Answers: A) 5!/(2! x 2!) B) 6! − (3! + 2!) C) 6! − (3! × 2!) D) 6!/(3! + 2!) E) 6!/(3! × 2!)

Solution: Number of letters in word 'RADAR' = 5.   The letters 'A' and 'R' appear 2 times and 2 times respectively in the word 'RADAR'.   Therefore the mathematical solution for number of ways that the letters of the word R5!/(2! x 2!)D5!/(2! x 2!)R can be arranged to create five-letter code   = 5!/(2!*2!)   5!/(2! x 2!)nswer:5!/(2! x 2!)
Answer: A
The captain of a cricket team of 11 members is 26 years old and the wicket keeper is 2 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team?	Choose the correct choice from the following choices.
A) 23 years  B) 22 years  C) 25 years  D) 26 years  E) 27 years

Solution: EXPLANATION   Let the average age of the whole team by x years.   11x â€“ (26 + 28) = 9(x -1)   11x â€“ 9x = 45   2x = 45   x = 22.   So, average age of the team is 22 years.   Answer 22 years
Answer: B
In covering a distance of 30 km, A takes 2 hours more than B. If A doubles his speed, then he would take 1 hour less than B. A's speed is:  Choose the correct choice from the following choices:
A) 5 km/hr.  B) 3 km/hr.  C) 1 km/hr.  D) 7 km/hr.  E) 9 km/hr.

Solution: C   5 km/hr.   Let A's speed be X km/hr.   Then, 30/x - 30/2x = 3   6x = 30   x = 5 km/hr.
Answer: A
One half of a two digit number exceeds its one third by 8. What is the sum of the digits of the number?  Choose the correct choice
A) A)3 B) B)5 C) C)12 D) D)9 E) E)11

Solution: x/2 – x/3 = 8 => x =48   4 + 8= 
4 + 8 = 12
12   ANSWER:12
Answer: C
The ages of two persons differ by 16 years. If 5 years ago, the elder one be 5 times as old as the younger one, their present ages (in years) are respectively	Choose the correct option:
A) 20,20
B) 20,10
C) 25,9
D) 30,10
E) None of these

Solution: Explanation:   Let their ages be x and (x + 16) years.   5 (x - 5) = (x + 16 - 5) or 4x = 36 or x = 9.   Their present ages are 25 years and 9 years   Option 25,9
Answer: C
Patrick purchased 90 pencils and sold them at a loss equal to the selling price of 40 pencils. The cost of 90 pencils is how many times the selling price of 90 pencils?
Choose the correct option
A) 0.75  B) 0.8  C) 1  D) 1.2  E) 1.44

Solution: Say the cost price of 90 pencils was $90 ($1 per pencil) and the selling price of 1 pencil was p.   Selling at a loss: 90 - 90p = 40p --> p = 9/13.   (cost price)/(selling price) = 1/(9/13) = 13/9 = 1.44.   Answer: 1.44.
Answer: E
Mandy drove from point A to point B at 60 Km/h. On her way back she drove at 80 Km/h and therefore her way back lasted one hour less. What is the distance (in Km) between A and B?	Choose the correct option:
A) 140.	B) 200.	C) 240.	D) 300.	E) 600.

Solution: distance=speed*time   d1=s1t1   d2=s2t2   The distance from point A to point B is the same for each trip so,   d1=d2 and   t2=t1-1   thus,   s1t1=s2(t1-1)   60t1=80(t1-1)   t1=4   60*4= 
60*4 = 240
240   Answer: 240.
Answer: C
S is the infinite sequence S1 = 2, S2 = 22, S3 = 222,...Sk = Sk–1 + 2(10k–1). If p is the sum of the first 30 terms of S, what is the eighth digit of p, counting right to left from the units digit?	Choose the most appropriate option:
A) 1 B) 2 C) 4 D) 6 E) 9

Solution: C   Sum of unit digits of first 30 terms = 60   Sum of tens digits of first 30 terms = 58   Sum of thousands digits of first 30 terms = 56   and so on..   p1 = 0   p2 = (6+58) = 4   p3 = (6+56) = 2   p4 = (6+54) = 0   p5 = (6+52) = 8   p6 = (5+50) = 5   p7 = (5+48) = 3   p8 = (5+46) = 1   1NSWER : 1
Answer: A
In a certain apartment building, there are one-bedroom and two-bedroom apartments. The rental prices of the apartment depend on a number of factors, but on average, two-bedroom apartments have higher rental prices than do one-bedroom apartments. Let M be the average rental price for all apartments in the building. If M is $1,000 higher than the average rental price for all one-bedroom apartments, and if the average rental price for all two-bedroom apartments is $9,000 higher that M, then what percentage of apartments in the building are two-bedroom apartments? Answers.
A) 50% B) 40% C) 20% D) 30% E) 10%

Solution: Ratio of 2 Bedroom Apartment: 1 Bedroom Apartment = 1000 : 9000 -----> 1 : 9   Let total number of Apartments be X   No. of 2 Bedroom Apartment = (1 / 10) * X   percentage of apartments in the building are two-bedroom apartments ---->   (1/10) * 100 ---> 10%   Answer : 10%
Answer: E