MU-NLPC/Calc-aqua_rat huggingface dataset:
Pipe A fills a tank of capacity 850 liters at the rate of 40 liters a minute. Another pipe B fills the same tank at the rate of 30 liters a minute. A pipe at the bottom of the tank drains the tank at the rate of 20 liters a minute. If pipe A is kept open for a minute and then closed and pipe B is open for a minute and then closed and then pipe C is open for a minute and then closed and the cycle is repeated, when will the tank be full?
Choose the correct choice from the following.
A) 42 minutes B) 51 minutes C) 39 minutes D) 40 minutes 20 seconds E) None of these

Solution: In one cycle they fill 40+30-20= 
40+30-20 = 50
50 liters   850= 50*n => n = 17   here n = number of cycles.   total time = 17*3= 
17*3 = 51
51 as in one cycle there are 3 minutes.   thus 51 minutes   ANSWER:51 minutes
Answer: B
In a garden, there are yellow and green flowers which are straight and curved. If the probability of picking a green flower is 1/5 and picking a straight flower is 1/2, then what is the probability of picking a flower which is yellow and straight
Pick
A) 1/7  B) 1/8  C) 2/5  D) 3/4  E) 7/8

Solution: Good question.   So we have a garden where all the flowers have two properties: color (green or yellow) and shape (straight or curved).   We're told that 1/5 of the garden is green, so, since all the flowers must be either green or yellow, we know that 4/5 are yellow. We're also told there is an equal probability of straight or curved, 1/2.   We want to find out the probability of something being yellow and straight, Pr( Yellow and Straight ).   So if we recall, the probability of two unique events occurring simultaneously is the product of the two probabilities, Pr( A and B ) = P(A) * P(B). So we multiply the two probabilities, Pr(yellow)* Pr(straight) = 4/5 * 1/2 = 2/5, or 2/5.
Answer: C
You hold some gold in a vault as an investment. Over the past year the price of gold increases by 60%. In order to keep your gold in the vault, you must pay 10% of the total value of the gold per year. What percentage has the value of your holdings changed by over the past year. Answers
A) 45%
B) 46%
C) 50%
D) 55%
E) 44%

Solution: (100%+60%)*(100%-10%) = 160*0.90= 
160*0.90 = 144
144% an increase of 44%   Your gold holdings have increased in value by 44%.   The Answer is 44%
Answer: E
A man can row with a speed of 15 kmph in still water. If the stream flows at 5 kmph, then the speed in downstream is? Choose the correct choice from the following options:
A) 22
B) 27
C) 20
D) 99
E) 78

Solution: M = 15   S = 5   DS = 15 + 5= 
15 + 5 = 20
20   Answer: 20
Answer: C
A, B, C subscribe Rs. 50,000 for a business. A subscribes Rs. 4000 more than B and B Rs. 5000 more than C. Out of a total profit of Rs. 35,000, A receives: Select the correct option.
A) Rs. 8400	B) Rs. 11,900	C) Rs. 13,600	D) Rs. 14,700	E) Rs. 13700

Solution: Let C = x.   Then, B = x + 5000 and A = x + 5000 + 4000 = x + 9000.   So, x + x + 5000 + x + 9000 = 50000   3x = 36000   x = 12000   A : B : C = 21000 : 17000 : 12000 = 21 : 17 : 12.   A's share = Rs. (35000 x	21/50) = Rs. 14,700.   THE CORRECT ANSWER IS Rs. 14,700.
Answer: D
If the cost price of 50 articles is equal to the selling price of 40 articles, then the gain or loss percent is?
Choose the correct choice from the following:
A) 26%	B) 23%	C) 85%	D) 45%	E) 25%

Solution: Given that, cost price of 50 article is equal to selling price of 40 articles.   Let cost price of one article = Rs. 1   Selling price of 40 articles = Rs. 50   But Cost price of 40 articles = Rs. 40   Therefore, the trader made profit.\Percentage of profit   = 10/40 * 100= 
10/40 * 100 = 25
25%   Answer: 25%
Answer: E
If the sum of two positive integers is 22 and the difference of their squares is 44, what is the product of the two integers?	Choose the most appropriate option.
A) 108	B) 119	C) 120	D) 135	E) 143

Solution: Let the 2 positive numbers x and y   x+ y = 22 -- 1   x^2 - y^2 = 44   => (x+y)(x-y)=44 -- 2   Using equation 1 in 2 , we get   => x-y = 2 -- 3   Solving equation 1 and 3 , we get   x= 12   y= 10   Product = 12*10= 
12*10 = 120
120   Answer 120
Answer: C
A train running at the speed of 60 km/hr crosses a pole in 18 seconds. Find the length of the train.	Choose the correct choice from the following choices:
A) 150	B) 278	C) 179	D) 300	E) 191

Solution: :   Speed = 60*(5/18) m/sec = 50/3 m/sec   Length of Train (300istance) = Speed * Time     (50/3) * 18= 
  (50/3) * 18 = 300
300 meter   Answer:300
Answer: D
In a party every person shakes hands with every other person. If there are 105 hands shakes, find the number of person in the party. Choose the correct option:
A) 14 B) 12 C) 13 D) 15 E) 16

Solution: Let n be the number of persons in the party. Number of hands shake = 105; Total number of hands shake is given by nC2.   Now, according to the question,   nC2 = 105;   Or, n!/[2!*(n-2)!] = 105;   Or, n*(n-1)/2 = 105;   Or, n2-n = 210;   Or, n2-n-210 = 0;   Or, n = 15, -14;   But, we cannot take negative value of n.   So, n = 15 i.e. number of persons in the party = 15.   Option 15
Answer: D
Krishan and Nandan jointly started a business. Krishan invested three times as Nandan did and invested his money for double time as compared to Nandan. Nandan earned Rs. 4000. If the gain is proportional to the money invested and the time for which the money is invested then the total gain was?  Choose one:
A) 28,077	B) 28,019	C) 28,019	D) 28,000	E) 28,001

Solution: 3:1   2:1   ------   6:1   1 ----- 4000   7 ----- ? => Rs.28,000.Answer: 28,000
Answer: D
Of the diplomats who attended a summit conference: 20 spoke French, 32 did not speak Hindi and 20% of the diplomats spoke neither French nor Hindi. If 10% of the diplomats spoke both French and Hindi, then how many diplomats attended the conference?
Choices
A) 70  B) 96  C) 108  D) 120  E) 150

Solution: 2X2 matrix will be the easiest way to calculate this.   Text in black: given statements   Text in red: calculated values   Thus 120=120 is the correct answer
Answer: D
if 6 coins are tossed simultaneously what is the probability of getting atleast four heads	Pick.
A) 11/32 B) 12/32 C) 13/32 D) 15/32 E) 19/32

Solution: n(S)= 2^6= 64   n(E)= 6C4 + 6C5 + 6C6 = 15+6+1= 
15+6+1 = 22
22   p(E)= n(E)/n(S)= 22/64= 11/32   11/32NSWER:11/32
Answer: A
The average of temperatures at noontime from Monday to Friday is 40; the lowest one is 30, what is the possible maximum range of the temperatures?
Pick.
A) 20	B) 25	C) 50	D) 45	E) 75

Solution: Average=40, Sum of temperatures=40*5= 
40*5 = 200
200   As the min temperature is 30, max would be   200-4*30= 
  200-4*30 = 80
80 --> The range=80(max)-30(min)=50   Answer: 50
Answer: C
List L: ABC, BCA, CAB
In list L above, there are 5 positive integers, where each of A, B, and C is a different nonzero digit. Which of the following is the sum of all the positive integers that MUST be factors of the sum of the integers in list L? Choose the correct choice from the following answers.
A) 47	B) 114	C) 152	D) 161	E) 488

Solution: Let's try to sum the 3 given numbers taking their place values into account:   (100A + 10B + C) + (100B + 10C + A) + (100C + 10A + B)   = 100(A + B + C) + 10(A + B + C) + (A + B + C)   = 111*(A + B + C)   We know 111 = 37 * 3 so the sum will certainly have 1, 3, 37 and 111 as factors. 1 + 3 + 37 + 111 = 152   Note: How do we know that (A + B + C) will not give us a factor that we get every time? Try and take a few cases where A, B and C have different characteristics e.g. case 1: they are all odd, case 2: they are all even with no multiple of 3 etc. We want to see if there are cases where (A+B+C) has no common factors with other cases.   Let's say A, B and C are all odd. 1+3+5 = 9. Factors 3 and 3   A, B and C are all even. 2+4+8 = 14. Factors 2 and 7   Other factors will depend on values of A, B and C. Hence there is no other factor which we MUST get.   161
Answer: D
One copy machine can make 30 copies a minute, and a second copy machine makes 20 copies a minute. If the two copiers work together, how long would it take them to make 2,000 copies?  Choose the correct answer:
A) 20 minutes
B) 40 minutes
C) 45 minutes
D) 50 minutes
E) 55 minutes

Solution: Total work done by both machines in a minute = 30 + 20= 
30 + 20 = 50
50 copies   Total number of copies required= 2000   Time = 2000/50= 
2000/50 = 40
40 mins   Answer 40 minutes
Answer: B
if log 2 = 0.30103, the number of digits in 2128 is
.	Choose the correct choice from the following answers:
A) 38
B) 39
C) 40
D) 41
E) 56

Solution: log(2128) = 128log(2) = 128 × 0.30103 ≈ 38.4   ie, its characteristic = 38   Hence, number of digits in 2128 = 38+1= 
38+1 = 39
39   Answer: Option 39
Answer: B
The ratio of the present age of two brothers is 1:2 and 5 years back, the ratio was 1:3. What will be the ratio of their ages after 5 years? Choose the correct choice from the following options.
A) 3:9 B) 3:0 C) 3:5 D) 3:2 E) 3:1

Solution: Let the present ages of the two brothers be x and 2x years respectively.   Then, (x - 5)/(2x - 5) = 1/3   3(x - 5) = (2x - 5) => x = 10   Required ratio = (x + 5) : (2x + 5) = 15 : 25 = 3:5   Answer: 3:5
Answer: C
There are 5,280 feet in 1 mile and 11 inches in one foot. How many inches are in a mile?  Pick one: A) 5,280 - 12 B) 5,280/12 C) 12(5,280) D) 11(5,280) E) 12/5,280

Solution: 1 feet = 11 inches   1 mile = 5280 feet   1 mile = 5280*11 inches   Ans: 11(5,280)
Answer: D
How many ways can 4 prizes be given away to 3 boys, if each boy is eligible for all the prizes? Choose the correct option:  A) 256  B) 24  C) 12  D) None of these  E) Cannot be determined

Solution: Solution:   Let the 3 boys be B1, B2, B3 and 4 prizes be P1, P2, P3 and P4.   Now B1 is eligible to receive any of the 4 available prizes (so 4 ways).   B2 will receive prize from rest 3 available prizes(so 3 ways).   B3 will receive his prize from the rest 2 prizes available(so 2 ways).   So total ways would be: 4*3*2*1= 
4*3*2*1 = 24
24 Ways.   Hence, the 4 prizes can be distributed in 24 ways.   Answer 24
Answer: B
A reduction of 40% in the price of bananas would enable a man to obtain 60 more for Rs.40, what is reduced price per dozen?
Choose the correct option
A) 1.2 B) 2.2 C) 3.2 D) 4.2 E) 5

Solution: 40*(40/100)= 
40*(40/100) = 16
16 --- 60   ? --- 12=> Rs.3.2   Answer: 3.2
Answer: C
A dishonest grocer professes to sell pure butter at cost price, but he mixes it with adulterated fat and thereby gains 30%. Find the percentage of adulterated fat in the mixture assuming that adulterated fat is freely available?	Options.
A) 15%  B) 25%  C) 33.33%  D) 40%  E) 35%

Solution: Say 100g pure butter costs $100   But; $100 is his 25% profit because he just used 80gram pure butter.   80g would have costed him $80 and he sold it for $100 by adding 20g of freely available fat. $100 is 1.30(85)   so;   total weight=100g   fat=20g   20%   15%
Answer: A
If a drawing has an outer circle of diameter 30 and an inner circle of diameter 24, then what fraction of outer circle's surface is not covered by the inner circle?	Select
A) 3/6 B) 8/24 C) 14/16 D) 9/25 E) 2/3

Solution: The questions asks us to find the surface which is not covered by the inner circle i.e., area of the surface not covered.   Where as circumference is the length along the edge of the circle,   2*pi*r implies the length of the curve   pi*r^2 implies area enclosed by that curve..hence Area of the circle is considered for this problem   Area of the inner circle=pi* r^2, where r=12   =>pi*144   Area of the outer circle=pi*225   Surface not covered by the inner circle=pi*225-pi*144=Pi*81   fraction of outer circle's surface is not covered by the inner circle= Pi*81/total area of the outer circle   =>Pi*81/Pi*225=9/25   Answer is 9/25
Answer: D
In a garden, there are yellow and green flowers which are straight and curved. If the probability of picking a green flower is 2/3 and picking a straight flower is 1/2, then what is the probability of picking a flower which is yellow and straight  Choose the correct answer
A) 1/6	B) 1/8	C) 1/4	D) 3/4	E) 7/8

Solution: Good question.   So we have a garden where all the flowers have two properties: color (green or yellow) and shape (straight or curved).   we're told that 2/3 of the garden is green, so, since all the flowers must be either green or yellow, we know that 1/3 are yellow. We're also told there is an equal probability of straight or curved, 1/2.   We want to find out the probability of something being yellow and straight, Pr( Yellow and Straight ).   So if we recall, the probability of two unique events occurring simultaneously is the product of the two probabilities, Pr( A and B ) = P(A) * P(B). So we multiply the two probabilities, Pr(yellow)* Pr(straight) = 1/3 * 1/2 = 1/6, or 1/6.
Answer: A
Simple interest on a sum at 5% per annum for 2 years is Rs.140. The C.I. on the same sum for the same period is?  Options:	A) 141.5	B) 142.5	C) 143.7	D) 144.6	E) 178.4

Solution: SI = 70 + 70   CI = 70 + 70 + 1.5= 
70 + 70 + 1.5 = 141.5
141.5   141.5nswer: 141.5
Answer: A
The average of 11 numbers is 10.9. If the average of first six is 10.5 and that of the last six is 11.4 the sixth number is?  Options:  A) 11.9  B) 11.2  C) 11.6  D) 11.5  E) 11.1

Solution: 1 to 11 = 11 * 10.9= 
11 * 10.9 = 119.9
119.9   1 to 6= 6 * 10.5= 
6 * 10.5 = 63
63   6 to 11= 6 * 11.4= 
6 * 11.4 = 68.4
68.4   63 + 68.4= 
63 + 68.4 = 131.4
131.4 – 119.9= 11.5   6th number = 11.5   Answer: 11.5
Answer: D
At what rate percent on simple interest will Rs.600 amount to Rs.950 in 5 years? Options:
A) 3.33%  B) 5.93%  C) 4.33%  D) 9.33%  E) 11.67%

Solution: 350 = (600*5*R)/100   R = 11.67%   ANSW11.67%R:11.67%
Answer: E
At a garage sale, all of the items were sold at different prices. If the price of a radio sold at the garage sale was both the 16th highest price and the 23rd lowest price among the prices of the items sold, how many items were sold at the garage sale?
Pick one:	A) 35	B) 36	C) 37	D) 38	E) 39

Solution: There were 15 items sold at a higher price than the radio and 22 items sold at a lower price than the radio. Including the radio, there were 15 + 22 + 1= 
15 + 22 + 1 = 38
38 items sold.   The answer is 38.
Answer: D
The length of the rectangular field is double its width. Inside the field there is square shaped pond 8m long. If the area of the pond is 1/72 of the area of the field. What is the length of the field?	Select the correct option
A) 73  B) 32  C) 34  D) 43  E) 96

Solution: 96xplanation:   A/72 = 8 * 8 => A = 8 * 8 * 72   x * 2x = 8 * 8 * 72   x = 48 => 2x = 96   Answer: Option 96
Answer: E
If x is the product of three consecutive positive integers, which of the following must be true?
I. x is an integer multiple of 4.
II. x is an integer multiple of 3
III. x is an integer multiple of 6
Choose the correct choice from the following choices
A) a) I only  B) b) II only  C) c) I and II only  D) d) I and III only  E) e)II and III only

Solution: The answer should be D i.e. X will be an integer and multiple of 3 and 6.   Let us take example n, n+1, n+2 as 3 three consecutive positive integers.   In a sequence of consecutive integers a number is multiple of 3 after every interval of 2 numbers i.e 3,4,5,6 Or 8,9,10,11,12   Hence in a product of 3 consecutive integers, the product is always divisible by 3.   Now, in a consecutive sequence every alternate is an even number, and when an even number is multiplied by 3 we will have 6 as one of the multiple also.   Now for a number to be a multiple of 4 we need at least 2 2's. this is only possible if the first number of three consecutive positive integers is an even number so that 3 is also even and we have 2 2's. But incase the sequence starts with odd we will have one 2 hence, the divisibility by 4 depends on the first number to be even   Answer e)II and III only
Answer: E
In a pond 100 fish were caught and examined for levels of mercury. Of this sample, 25 fish were found to have unhealthy levels of mercury. If we use this sample as an estimate, and we know the population of the pond to be 5,000 fish, what is the approximate number of fish in the pond that have healthy levels of mercury?	Options
A) 2,150 B) 750 C) 1,250 D) 3,750 E) 2,500

Solution: Let D = fish population of the pond = 5,000,   B = fish population of the sample = 100,   A = fish sample with healthy level of mercury = 100 - 25= 
100 - 25 = 75
75, and   C= fish population with healthy level of mercury, then:   Proportion: A/B = C/D   Proportion: 75/100 = C/5,000   C = 3,750. There are approximately 3,750 healthy fish in the pond.   Answer is 3,750
Answer: D
In a group of ducks and cows, the total number of legs are 12 more than twice the no. of heads. Find the total no.of buffaloes.  Select
A) 6	B) 8	C) 10	D) 4	E) 12

Solution: Let the number of buffaloes be x and the number of ducks be y   => 4x + 2y = 2 (x + y) + 12   => 2x = 12=> x = 6   6
Answer: A
A shop owner sells 40 Pencils and gains SP of 15 pencils. Find the gain %?
Choose one.
A) 55%	B) 40%	C) 50%	D) 60%	E) 78%

Solution: Gain=15 orangesTotal 40 orangesCP 40-15= 
40-15 = 25
25(15/25)*100=60%Ans 60%
Answer: D
Peter read C books last year, and Nikki read N books last year. If Peter read 35 more books than Nikki last year, which of the following reflects this relationship?	Choose the correct choice from the following
A) C > 35N  B) C < N − 35  C) C > N + 35  D) C = N − 35  E) C = N + 35

Solution: Peter read C books last year, and Nikki read N books last year. If Peter read 35 more books than Nikki last year, which of the following reflects this relationship?   A. C > 35N   B. C < N − 35   C. C > N + 35   D. C = N − 35   E. C = N + 35   Since Peter read more books than Nikki we have C>N. Moreover since Peter reads 35 more books than Nikki easily we can have C=N+35.   So the answer is (C = N + 35).
Answer: E
How much did Rohit get as profit at the year-end in the business done by Nitin, Rohit and Kunal?
I.Kunal invested Rs. 8000 for nine months, his profit was times that of Rohit’s and his investment was four times that of Nitin.
II.Nitin and Rohit invested for one year in the proportion 1 : 2 respectively.
III.The three together got Rs. 1000 as profit at the year end.
Choose the correct choice from the following answers.
A) Only I and II
B) Only I and III
C) Question cannot be answered even with the information in all the three statements.
D) All I, II and III
E) None of these

Solution: Explanation:   I and II give:   K = Rs. (8000 x 9) for 1 month = Rs. 72000 for 1 month.   N = Rs. ( 1/4 x 8000 x12 ) for 1 month = Rs. 24000 for 1 month.   R = Rs. 48000 for 1 month.   K : N : R = 72000 : 24000 : 48000 = 3 : 1 : 2.   III gives, total profit = Rs. 1000.   Rohit’s share = Rs. (1000 x 2/6 )= Rs. 333 1/3   answer is (All I, II and III).
Answer: D
A man can row his boat with the stream at 6 km/h and against the stream in 4 km/h. The man's rate is?	Choose the correct choice from the following answers:
A) 1 kmph B) 5 kmph C) 8 kmph D) 3 kmph E) 4 kmph

Solution: DS = 6   US = 4   S = ?   S = (6 - 4)/2= 
(6 - 4)/2 = 1
1 kmph   1 kmphNSWER:1 kmph
Answer: A
How many different 6 letter combinations can be created from the letters A,B,C,D,E and F?
Select:
A) 216
B) 36
C) 46656
D) 1296
E) 7776

Solution: This is a case of number of arrangements possible with repetition.   Thus you have 6 options each for the 1st,2nd,3rd,4th,5th and 6th letter giving you a total of   6*6*6*6*6*6= 
  6*6*6*6*6*6 = 46_656
46656 number of possible combinations.   Answer : 46656
Answer: C
man is 21 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is: Pick
A) 14years  B) 26 years  C) 19 years  D) 18 years  E) 22 years

Solution: Let the son's present age be x years. Then, man's present age = (x + 20) years.   (x + 21) + 2 = 2(x + 2)   x + 23 = 2x + 4   x = 19.   answer :19 years
Answer: C
Salaries of Ravi and Sumit are in the ratio 2 : 3. If the salary of each is increased by Rs. 4000, the new ratio becomes 40 : 57. What is Sumit's salary? Pick one:
A) Rs. 17,000
B) Rs. 20,000
C) Rs. 25,500
D) Rs. 38,000
E) Rs. 35,000

Solution: Explanation:   Let the original salaries of Ravi and Sumit be Rs. 2x and Rs. 3x respectively.   Then,	2x + 4000/	3x + 4000=40/57   57(2x + 4000) = 40(3x + 4000)   6x = 68,000   3x = 34,000   Sumit's present salary = (3x + 4000) = Rs.(34000 + 4000) = Rs. 38,000.   ANSWER IS Rs. 38,000
Answer: D
A certain rectangular crate measures 12 feet by 16 feet by 18 feet. A cylindrical gas tank is to be made for shipment in the crate and will stand upright when the crate is placed on one of its six faces. What should the radius of the tank be if it is to be of the largest possible volume?
Options.
A) 4	B) 5	C) 6	D) 8	E) 10

Solution: For max volume of cylinder (pi*r^2*h) we need to max out r^2*h. We don't know what the dimensions of the crate refer to. . Therefore for max vol base should be 18x16 i.e. of radius   16/2= 
  16/2 = 8
8   8
Answer: D
The probability that event M will not occur is 0.8 and the probability that event R will not occur is 0.9. If events M and R cannot both occur, which of the following is the probability that either event M or event R will occur?	Choose the correct choice:
A) 1/5
B) 2/5
C) 3/10
D) 4/5
E) 12/25

Solution: p(m) =0.2   p(r) =0.1   p(m intersection r) = 0 (If events M and R cannot both occur)   p(m or r) = 0.2+0.1= 
0.2+0.1 = 0.3
0.3   3/10orrected !!   Answer 3/10
Answer: C
Shekhar started a business investing Rs.25,000 in 1999.In 2000,he invested an additional amount of Rs.10,000 and Rajeev joined him with an amount of Rs.35,000.In 2001,Shekhar invested another additional amount of Rs.10,000 and Jatin joined them with an amount of Rs.35,000.What will be Rajeev’s share in the profit of Rs.1,20,000 earned at the end of 3 years from the start of the business in 1999 ?  Pick one
A) Rs.40,000	B) Rs.50,000	C) Rs.70,000	D) Rs.75,000	E) None of these

Solution: Solution   Shekhar : Rajeev : Jatin   = (25000x12+35000x12+45000x12) :(35000x24) : (35000x12)   = 1260000 : 840000 : 420000 = 3 : 2 : 1.   ∴ Rajeev’s share = Rs.(12000x2/6) = Rs. 40,000. Rs.40,000nswer Rs.40,000
Answer: A
The slant height of a cone is 22 cm and radius of the base is 7cm, find the curved surface of the cone?
Choose the correct choice from the following choices: A) 426 B) 284 C) 483 D) 256 E) 428

Solution: π * 22 * 7   = 483   Answer:483
Answer: C
Set #1 = {A, B, C, D, E, F}
Set #2 = {K, L, M, N, O, P}
There are these two sets of letters, and you are going to pick exactly one letter from each set. What is the probability of picking at least one vowel? Answers
A) 1/6  B) 1/3  C) 1/2  D) 2/3  E) 4/9

Solution: So Not a vowel in Set-1 : 4/6   And not a vowel in Ser-2:5/6   Now,   4/6∗5/6=5/9   This is for not a vowel.   Then for at least one vowel will be = 1−5/9=4/9   Answer will be 4/9.
Answer: E
99,998^2 - 2^2 =  Choices:
A) 10^10 - 2
B) (10^5 – 2)^2
C) 10^4(10^5 – 2)
D) 10^5(10^4 – 2)
E) 10^5(10^5 – 4)

Solution: (99,998)^2 - (2)^2 = (100,000 -2)^2 - (1)^2 = (100,000)^2 - 2*2*100,000 + 2^2-2^2=(10^5)^2 - 4*(10^5) = 10^10 - 4*(10^5)=10^5(10^5 - 4) Answer 10^5(10^5 – 4)
Answer: E
If Leo gains 10 pounds, he will weigh 50% more than his sister Kendra. Currently their combined weight is 170 pounds. What is Leo's current weight? Choose the correct choice from the following answers.
A) 80 B) 86 C) 92 D) 98 E) 104

Solution: L+K = 170 and so K = 170-L   L+10 = 1.5K = 1.5(170-L)   2.5L = 245   L = 98   The answer is 98.
Answer: D
In a certain boys camp, 20% of the total boys are from school A and 30% of those study science. If there are 56 boys in the camp that are from school A but do not study science then what is the total number of boys in the camp? Choose the most appropriate option.
A) 70  B) 400  C) 150  D) 35  E) 350

Solution: Since 30% of the boys from school A study science, then 70% of the boys from school A do NOT study science and since 20% of the total number of boys are from school A, then 0.2*0.7= 
0.2*0.7 = 0.14
0.14, or 14% of the boys in the camp are from school A and do not study science.   We are told that this number equals to 56, so 0.14*{total}= 56 --> {total} = 400.   Answer: 400.
Answer: B