MU-NLPC/Calc-aqua_rat huggingface dataset:
A box contains 2 white balls, 3 black ball and 4 red balls. In how many ways can 3 balls be drawn from the box, if at least one black ball is to be included in the draw?	Select:
A) 32
B) 48
C) 64
D) 96
E) 54

Solution: We may have ( 1 black and 2 non black) or (2 black and 1 non black)or(3 black)   =3c1 x 6c2 + 3c2 x 6c1 +3c3   =64   ANSWER 64 64
Answer: C
A shopkeeper sells 20% of his stock at 20% profit ans sells the remaining at a loss of 10%. He incurred an overall loss of Rs. 400. Find the total worth of the stock?	Options
A) 15500
B) 16000
C) 15000
D) 17000
E) 20000

Solution: Let the total worth of the stock be Rs. x.   The SP of 20% of the stock = 1/5 * x * 6/5 = 11x/50   The SP of 80% of the stock = 4/5 * x * 0.90 = 19x/25 = 36x/50   Total SP = 12x/50 + 36x/50 = 48x/50   Overall loss = x - 48x/50 = 2x/50   2x/50 = 600 => x = 15000   Answer:15000
Answer: C
If it would take one machine 10 minutes to fill a large production order and another machine 18 minutes to fill the same order, how many minutes would it take both machines working together, at their respective rates, to fill the order? Choose the correct choice from the following
A) 4 1/60  B) 5  C) 5 5/11  D) 6 3/7  E) 11

Solution: Since , Machine 1-M1 take 10 mins to fill the order   The work done by M1 in a min = 1/10   Machine 2- M2 take 18 mins to fill the same order   and work done by M2 in a min = 1/18   Total work done by M1 and M2 in a min = 1/10 + 1/18 = 14/90 = 7/45   Time needed for M1 and M2 to complete the order = 45/7 = 6 3/7   Answer 6 3/7
Answer: D
If the price of an item is decreased by 40% and then increased by 20%, the net effect on the price of the item is Answers:  A) A decrease of 99%  B) No change  C) A decrease of 1%  D) A increase of 1%  E) A decrease of 28%

Solution: initially assume 100 rupees   40% discount in 100 gives price of 60 rupees   then 20% raise in 60 is only 12 rupees.   therefore total price =72 rupees.   hence 28% is the loss   ANSWA decrease of 28%R:A decrease of 28%
Answer: E
If g,h,i,j represents the result gotten when the figure 8236.186 is rounded off to the nearest thousand, hundred ten and one, which of the following statements is correct?  Choose the most appropriate option:
A) h<gh<j<i
B) g<g<h<i
C) g<h<j<i
D) i<h<j<g
E) g<i<j<h

Solution: 8236.186..   Nearest thousand 8000..g   Nearest hundred 8200..h   Nearest ten 8300..i   Nearest one 8296..j   g<h<j<i   The correct option is g<h<j<i
Answer: C
what is the 50th term of term of the series 1,3,6,10,15,21? Answers:  A) 1265  B) 1270  C) 1275  D) 1280  E) 1285

Solution: The series is like 1,1+2,1+2+3,1+2+3+4,....   so 50th term wil be 1+2+3+4+....50   sum of n natural numbers =n*(n+1)/2 where n is 50   answer wil be   25*51= 
  25*51 = 1_275
1275   ANSWER:1275
Answer: C
A certain clock marks every hour by striking a number of times equal to the hour, and the time require for a stroke is exactly equal to the time interval between strokes. At 6:00 the time lapse between the beginning of the first stoke and the end of the last stroke is 22 seconds. At 9:00, how many seconds elapse between the beginning of the first stroke and the end of the last stroke?	Pick:
A) 36 B) 35 C) 34 D) 38 E) 40

Solution: at 6'o clock, there would be 6 strikes. First strike, then a short interval, the second strike, then a short interval and so on till the 6th strike. So there would be in all 5 intervals between 6 strikes. Similarly, between 9 strikes, there would be 8 intervals.   According to the question, the time spent in the strike and the interval is same.   At 6'o clock, the 6 strikes and the 5 intervals together take 22 sec so each strike and each interval takes 2 secs.   At 12'o clock, the 9 strikes and 8 intervals will take 2*(9+8)= 
2*(9+8) = 34
34 secs   34
Answer: C
Given that 268 * 74 = 19832, find the values of 2.68 * 0.74.	Choose the correct choice.
A) 1.9328
B) 1.9832
C) 1.9823
D) 1.9382
E) None of them

Solution: Sum of decimal places = (2 + 2)= 
(2 + 2) = 4
4   2.68 * 0.74= 1.9832.   Answer is 1.9832.
Answer: B
The average weight of 7 person's increases by 3.5 kg when a new person comes in place of one of them weighing 75 kg. What might be the weight of the new person?
Pick one.
A) 74 kg	B) 78.5 kg	C) 99.5 kg	D) Data inadequate	E) None of these

Solution: Total weight increased = (7 x 3.5) kg = 24.5 kg.   Weight of new person = (75 + 24.5)= 
(75 + 24.5) = 99.5
99.5 kg.   Answer: Option 99.5 kg
Answer: C
Peter invested a certain sum of money in a simple interest bond whose value grew to $100 at the end of 2 years and further to $200 at the end of another 4 years. What was the rate of interest in which he invested his sum?  Choices.
A) 50% B) 25% C) 10% D) 30% E) 18%

Solution: Explanatory Answer   Initial amount invested = $ X   Amount at the end of year 2 = $ 100   Amount at the end of year 6 (another 4 years) = $ 200   Therefore, the interest earned for the 4 year period between the 2rd year and 6th year = $200 - $100 = $100   As the simple interest earned for a period of 4 years is $ 100, interest earned per year 200 -  100= 
200 -  100 = 100
$100   As the simple interest earned for a period of 4 years is $ 100, interest earned per year= $25.   Therefore, interest earned for 2 years = 2 * 25= 
2 * 25 = 50
$ 50.   Hence, initial amount invested X= Amount after 2years - interest for 2 years   = 100 - 50= 
100 - 50 = 50
$ 50.   Rate of interest= (interest per year/principal)*100 = 25/50*100= 
25/50*100 = 50
50%   correct choice is 50%
Answer: A
In how many different ways can the letters of the word 'SINGING' be arranged in such a way that the vowels always come together?
Choose the correct choice from the following choices:	A) A)360	B) B)480	C) C)720	D) D)5040	E) of these

Solution: The word 'SINGING' has 7 different letters.   When the vowels II are always together, they can be supposed to form one letter.   Then, we have to arrange the letters SNGNG (II).   Now, 6 (5 + 1 = 6) letters can be arranged in 6! = 720 ways.   The vowels (II) can be arranged among themselves in 1! = 1 way.   Required number of ways = (720 x 1) = 720.   ANSWER:720
Answer: C
In a dairy farm, 26 cows eat 26 bags of husk in 26 days. In how many days one cow will eat one bag of husk?
Choose the correct choice from the following answers: A) 1 B) 40 C) 20 D) 26 E) 30

Solution: Explanation :   One bag of husk = 26 cows per day   ⇒ 26 × 1 × 26 = 1 × 26 × x   For one cow = 26 days   Answer : 26
Answer: D
A certain university will select 1 of 6 candidates eligible to fill a position in the mathematics department and 2 of 10 candidates eligible to fill 2 identical positions in the computer science department. If none of the candidates is eligible for a position in both departments, how many different sets of 3 candidates are there to fill the 3 positions?
Choose the correct choice from the following answers.
A) 42  B) 270  C) 140  D) 165  E) 315

Solution: 1 of 6 will be chosen for the math   2 of 10 will be chosen for the computer   None of the 3 chosen people can be in more than one departments.   We can choose any of the 6 candidates for the math dep., which gives as 6 selections.   We can choose 2 of the 10 candidates for the computer dep., which gives us 2 selections and 8 rejections.   So, the way to find how many different selections of 2 candidates we can have for the computer dep., we do:   10! /2!*8!= (9*10) / 2 = 90 / 2= 
90 / 2 = 45
45.   We are multiplying our individual selections:  6*45= 
 6*45 = 270
270   In the bolded part, we don't have to multiply all of the numbers, as those in 8! are included in 10!, so we simplify instead.   Ans 270
Answer: B
In a certain company, a third of the workers do not have a retirement plan. 50% of the workers who do not have a retirement plan are women, and 40% of the workers who do have a retirement plan are men. If 120 of the workers of that company are men, how many of the workers are women?	Pick.
A) 80	B) 95	C) 105	D) 156	E) 210

Solution: Set up equation:   x = total number of workers   120 = 0,4 * 2/3 * x + 0,5 * 1/3 * x   120 = 13/30 x   x = 276   276 - 120= 
276 - 120 = 156
156   Answer 156
Answer: D
The visitors of a modern art museum who watched a certain Picasso painting were asked to fill in a short questionnaire indicating whether they had enjoyed looking at the picture and whether they felt they had understood it. According to the results of the survey, all 130 visitors who did not enjoy the painting also did not feel they had understood the painting, and the number of visitors who enjoyed the painting was equal to the number of visitors who felt they had understood the painting. If 3/4 of the visitors who answered the questionnaire both enjoyed the painting and felt they had understood the painting, then how many visitors answered the questionnaire?  Choose the correct choice from the following:
A) 90
B) 120
C) 160
D) 360
E) 520

Solution: If we exclude those cases and take the question at face value, then it seems straightforward.   Group #1 = (didn't like, didn't understand) = 130   Group #2 = (like understood) = 3/4   (1/4)N = 130   N = 520   Answer =(520)
Answer: E
Peter and Tom shared the driving on a certain trip. If Peter and Tom both drove for the same amount of time, but Peter only drove 3/5 of the total distance, what was the ratio of Peter's average speed to Tom's average speed?	Choose the correct choice from the following:
A) 1:5	B) 3:2	C) 1:2	D) 3:5	E) 2:3

Solution: The answer is suppose to be B. 3:2. It's from the GMATPrep   Answer:option 3:2
Answer: B
P,Q and R together earn Rs.1620 in 9 days. P and R can earn Rs.600 in 5 days. Q and R in 7 days can earn Rs.910. How much amount does R can earn per day?  Choose the correct choice from the following answers.
A) Rs.40	B) Rs.70	C) Rs.90	D) Rs.100	E) Rs.120

Solution: Explanation :   Amount Earned by P,Q and R in 1 day = 1620/9= 
1620/9 = 180
180 ---(1)   Amount Earned by P and R in 1 day= 600/5= 
600/5 = 120
120	---(2)   Amount Earned by Q and R in 1 day= 910/7= 
910/7 = 130
130	---(3)   (2)+(3)-(1)=> Amount Earned by P , Q and 2R in 1 day   - Amount Earned by P,Q and R in 1 day = 120+130-180= 
120+130-180 = 70
70=>Amount Earned by R in 1 day = 70   Answer : Option Rs.70
Answer: B
By selling a house for Rs.45000, it was found that 1/8 of the outlay was gained, what ought the selling to price to have been in order to have lost 5 p.c? Options:
A) 28788
B) 38000
C) 27992
D) 28872
E) 29982

Solution: CP + CP/8 = 45000   CP = 40000   SP = 40000*(95/100)= 
40000*(95/100) = 38_000
38000   Answer: 38000
Answer: B
if length of a room is three times of its breadth and its area is 12 sq.m.what is perimeter of room?
Choose the correct answer
A) 14 m	B) 18 m	C) 24 m	D) 16 m	E) none of the above

Solution: let breadth=x m. and length = 3x m.   x*3x=12,x^2=4,x=2.   length=6m,breadth = 2 m.   perimeter=2*(6+2)= 
2*(6+2) = 16
16 m   answer 16 m
Answer: D
The curved surface of a sphere is 64 π cm2. Find its radius?	Answers
A) 8  B) 3  C) 4  D) 9  E) 7

Solution: Explanation:   4 πr2 = 64 => r = 4   Answer: Option 4
Answer: C
A train passes a station platform in 35 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? Choose one.
A) 225
B) 279
C) 240
D) 288
E) 231

Solution: Speed = [54 * 5/18] m/sec = 15 m/sec.   Length of the train = (15 * 20)= 
(15 * 20) = 300
300 m.   Let the length of the platform be x meters.   Then, x + 300 / 35= 15   x + 300 = 525   x = 225 m. 225nswer:225
Answer: A
A school’s annual budget for the purchase of student computers increased by 32% this year over last year. If the price of student computers increased by 20% this year, then the number of computers it can purchase this year is what percent greater than the number of computers it purchased last year?	Choose the correct option
A) 15% B) 5% C) 10% D) 12% E) 6%

Solution: Lats year: budget = $100, price = $1 --> the number of computers purchased = 100/1= 
100/1 = 100
100;   This year: budget= $132, price = $1.2 --> the number of computers purchased = 132/1.2= 
132/1.2 = 110
110.   Increase in the number of computers purchased= 10%.   Answer: 10%
Answer: C
A can give B 60 meters start and C 200 meters start in a kilometer race. How much start can B give C in a kilometer race?	Choose the correct choice from the following choices
A) 148.94
B) 148.13
C) 148.22
D) 111.0
E) 111.12

Solution: A runs 1000 m while B runs 940 m and C runs 800 m.   The number of meters that C runs when B runs 1000 m,   = (1000 * 800)/940   = 851.06 m.   B can give C = 1000 - 851.06= 
1000 - 851.06 = 148.94
148.94m.   148.94nswer:148.94
Answer: A
The respective ages of father and his son are 47 and 16 years. In how many years will the father be twice as old as his son ?	Choose the correct choice from the following choices:  A) 19 years  B) 9 years  C) 10 years  D) 15 years  E) 12 years

Solution: Suppose x years later the father will be twice as old as his son.   x + 47 = 2 (x + 16)   x = 47 - 32= 
47 - 32 = 15
15 years   answer : 15 years
Answer: D
In how many ways a committee consisting of 3 men and 2 women can be formed from 4 men and 3 women?
Choose the correct choice from the following answers
A) 10	B) 15	C) 20	D) 18	E) 21

Solution: Required number of ways = 4C3*3C2 = 4*3= 
4*3 = 12
12   10nswer is 10
Answer: A
What is the greatest positive integer x such that 7^x is a factor of 343^10?  Choose one: A) 5 B) 9 C) 10 D) 20 E) 30

Solution: 343^10 = (7^3)^10 = 7^30   ANSW30R:30
Answer: E
The average age of 8 men increases by 2 years when two women are included in place of two men of ages 20 and 24 years. Find the average age of the women?	Choose the correct option:
A) 5  B) 10  C) 50  D) 40  E) 30

Solution: 20 + 24 + 8 * 2= 
20 + 24 + 8 * 2 = 60
60/2= 
60/2 = 30
30   Answer: 30
Answer: E
The speed of a boat in still water is 70kmph and the speed of the current is 20kmph. Find the speed downstream and upstream?  Choose the most appropriate option
A) 80,47 kmph B) 80,80 kmph C) 80,42 kmph D) 90,50 kmph E) 83,40 kmph

Solution: Speed downstream = 70 + 20= 
70 + 20 = 90
90 kmph   Speed upstream= 70 - 20= 
70 - 20 = 50
50 kmph.Answer:90,50 kmph
Answer: D
If x and y are non-zero integers, and 64x^4 – 4y^4 = 8x^2 + 2y^2, which of the following could be the value of x2 in terms of y?	Choices
A) 2y^2	B) 2y	C) 2y^2/8	D) 2y^2-1/8	E) 2y^2+1/8

Solution: 64x^4 – 4y^4 = 8x^2 + 2y^2   (8x^2 + 2y^2) (8x^2 - 2y^2) = 8x^2 + 2y^2   8x^2 - 2y^2 = 1   8x^2 = 2y^2+1   x^2 = 2y^2+1/8   Answer : 2y^2+1/8
Answer: E
Which of the following is satisfied with |x-4|+|x-3|<3?
Pick:
A) 1<x<5  B) 2<x<5  C) 4/3<x<10/3  D) 4/3<x<4  E) 3<x<4

Solution: --> If there is addition when there are 2 absolute values, you can just ignore the middle. That is, |x-4|+|x-3|<3 -> |x-4+x-3|<3 -> |2x-7|<3, -3<2x-7<3, 4<2x<10, 2<x<5->   Therefore, the answer is 2<x<5.</x<5->
Answer: B
After deducting a commission of 5%, a T.V. set costs $9595. Its market price is ?	Answers.
A) 10000
B) 10100
C) 21200
D) 21000
E) 11000

Solution: Let the marked price be x   then, x-5% of x = 9595   95% of x = 9595   x = 10100   Answer is 10100
Answer: B
A 1200 m long train crosses a tree in 120 sec, how much time will I take to pass a platform 700 m long?  Choose the correct choice:  A) 186 Sec  B) 190 Sec  C) 279 Sec  D) 978 Sec  E) 627 Sec

Solution: L = S*T   S= 1200/120= 
1200/120 = 10
10 m/Sec.   Total length (D)= 1900 m   T = D/S   T = 1900/10= 
1900/10 = 190
190 Sec   Answer:190 Sec
Answer: B
The length and breadth of a rectangle is increased by 10% and 30% respectively. What is the increase in the area? Choose one
A) 43.0	B) 44.0	C) 43.5	D) 45.0	E) 42.0

Solution: 100*100= 
100*100 = 10_000
10000   110*130= 
110*130 = 14_300
14300   ----------   4300   10000-------4300   100-------43.00   43.0nswer 43.0
Answer: A
A six-sided die is rolled once. What is the probability that the number rolled is an even number greater than 2?
Pick
A) 1/4	B) 2/4	C) 1/2	D) 1/3	E) 2/3

Solution: Out of the 6 possible numbers that may rolled, 3 are even: 2, 4 and 6 BUT only 4 and 6 are greater than 2. Hence the probability that the number rolled is an even number greater than 2 is given by   (number of even numbers greater than 2) / 6 = 2 / 6 = 1 / 3   correct answer 1/3
Answer: D
The average of 10 consecutive integers is 20. Then, 9 is deducted from the first consecutive number, 8 is deducted from the second, 7 is deducted form the third, and so on until the last number which remains unchanged. What is the new average?	Pick one: A) 14 B) 14.5 C) 15 D) 15.5 E) 16

Solution: The total subtracted is (9+8+...+1) = (9*10) / 2= 
(9*10) / 2 = 45
45   On average, each number will be reduced by   45/10= 
  45/10 = 9/2 = around 4.5
4.5   Therefore, the overall average will be reduced by 4.5   The answer is 15.5.
Answer: D
In a two-digit, if it is known that its unit's digit exceeds its ten's digit by 2 and that the product of the given number and the sum of its digits is equal to 144, then the number is:
Choose one:  A) 24  B) 26  C) 42  D) 46  E) 48

Solution: Let the ten's digit be x.   Then, unit's digit = x + 2.   Number = 10x + (x + 2) = 11x + 2.   Sum of digits = x + (x + 2) = 2x + 2.   (11x + 2)(2x + 2) + (  + 2)= 
+ (  + 2) = 2
2x + 2.   (11x + 2)(2x + 2)= 144   22x2 + 26x - 140 = 0   11x2 + 13x - 70 = 0   (x - 2)(11x + 35) = 0   x = 2.   Hence, required number = 11x + 2 = 24.   24nswer:24
Answer: A
A farmer spent $35 on feed for chickens and goats. He spent 40% money on chicken feed, which he bought at a 20% discount off the full price, and spent the rest on goat feed, which he bought at full price. If the farmer had paid full price for both the chicken feed and the goat feed, what amount would he have spent on the chicken feed and goat feed combined?
Choose the correct choice from the following answers:
A) $37.80
B) $38.50
C) $39.20
D) $39.50
E) $40.60

Solution: A farmer spent 40% money on chicken feed, so he spent 0.4*$35=$14 on chicken feed, thus he spent the remaining 35-14 0.4* 35= 
 0.4* 35 = 14
$14 on chicken feed, thus he spent the remaining   35-14= 
  35-14 = 21
$21 on goat feed.   Now, since he bought chicken feed at a 20% discount then the original price of it was x*0.8=$14 --> x=$17.5.   Therefore if the farmer had paid full price for both the chicken feed and the goat feed, then he would he have spent 17.5+21=$38.5.   Answer: $38.50.
Answer: B
What is the average of xx, 2x2x, and 66? Choose the correct choice from the following choices.
A) 2x+2 B) x+2x-2 C) x+2x+2 D) x+2 E) x+2x

Solution: By the definition of an average, we get:   x+2x+63=3x+63x+2x+63=3x+63   =3(x+2)3=x+2.=3(x+2)3=x+2.   Hence, the answer is x+2x+2 or   Option x+2x+2
Answer: C
A courier charges for packages to a certain destination are 65 cents for the first 250 grams and 10 cents for each additional 100 grams or part thereof. What could be the weight in grams of a package for which the charge is $2.15?	Choices:
A) 980  B) 1120  C) 1260  D) 1420  E) 1670

Solution: The charge is 65 cents for the first 250 grams.   This leaves a charge of $2.15 - $0.65 = $1.50   The charge for the next 1400 grams is $1.40 which leaves a charge of $0.10   The weight is somewhere between 1650 and 1750.   The answer is 1670. 2.15 -  0.65= 
 2.15 -  0.65 = 1.5
$1.50   The charge for the next 1400 grams is $1.40 which leaves a charge of $0.10   The weight is somewhere between 1650 and 1750.   The answer is 1670.
Answer: E
If 4 men can colour 48 m long cloth in 2 days, then 6 men can colour 72 m long cloth in Answers.
A) 1 day	B) 2 days	C) 3 days	D) 4 days	E) 5 days

Solution: The length of cloth painted by one man in one day = 48 / 4 × 2 = 6 m   No. of days required to paint 36 m cloth by 6 men = 72/ 6 × 6 = 2 day.   2 days
Answer: B
In a 400 member association consisting of men and women, exactly 20% of men and exactly 25 % women are homeowners. What is the least number of members who are homeowners?  Pick one:
A) 81  B) 147  C) 145  D) 143  E) 141

Solution: Solution simple   Out of 400 20% are male i.e 80 and 25% are female i.e 100 , so total homeowner is 180.   Now min number homeowner is 80 and max is 180 so question ask us to find least and 81 has least value among all option.   So ans is 81.   81nswer : 81
Answer: A
A can work four times as fast as B. Together they can finish a job in 10 days. In how many days can A complete the job alone?
Choose the correct choice from the following choices:
A) 11.5  B) 12.5  C) 13.5  D) 14.5  E) 15.5

Solution: B's rate is x and A's rate is 4x.   x + 4x = 1/10   x = 1/50   A's rate is 4x = 1/12.5   A can complete the job in 12.5 days.   The answer is 12.5.
Answer: B
On an order of 5 dozen boxes of a consumer product, a retailer receives an extra dozen free. This is equivalent to allowing him a discount of:
Choose the correct option:
A) 15%
B) 16 1/6%
C) 16 2/3%
D) 20%
E) 30%

Solution: Clearly, the retailer gets 1 dozen out of 6 dozens free.   Equivalent discount = 1/6 * 100 = 16 2/3%.   ANSWER:16 2/3%
Answer: C
An arithemetic sequence of numbers begins p, 2p + 1, 4p + 2... What is the 14th member of this sequence?  Choose the correct choice from the following options
A) A)37	B) B)40	C) + 13	D) D)53	E) + 13

Solution: Common difference of an arithmetic series is constant.   2p+2-p=4p+3-2p-2   p=1   1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34, 37   Ans:40
Answer: B
Tom found a box of 220 baseball cards. Being a thoughtful older brother, he wanted to save at least 50 percent of the cards for himself and split the remaining cards evenly among his 5 younger brothers. What is the lowest possible number of cards that Tom can save for himself that will also allow each of his 5 younger brothers to get an equal number of cards?  Pick
A) 110
B) 112
C) 116
D) 118
E) 122

Solution: This question can be easily solved by looking at the options.   Assuming number of cards to be x   We need to find the option for which (1/5)*(x/2) is an integer   Or x/10 is an integer.   Hence we need the lowest multiple of 10 from the given options.   Let us start from the lowest value:   Option A: 110. This is not a multiple of 10. Hence the correct answer.   Correct Option: 110
Answer: A
What percentage of numbers from 1 to 60 have 1 or 9 in the unit's digit? Options:  A) 12  B) 14.11  C) 18.33  D) 20  E) 21

Solution: Clearly, the numbers which have 1 or 9 in the unit's digit, have squares that end in the digit 1. Such numbers from 1 to 60 are 1, 9, 11, 19, 21, 29, 31, 39, 41, 49, 51, 59   Number of such number =11   ANSWER :18.33
Answer: C
The H.C.F. of two numbers is 5 and their L.C.M. is 150. If one of the numbers is 25, then the other is:	Select:
A) 30
B) 28
C) 24
D) 20
E) 35

Solution: Product of two nos = product of HCF and LCM   Let one number = x   => 25 * x = 5 * 150   x=5*150/25= 
5*150/25 = 30
30   30NSWER 30
Answer: A
The amount of an investment will double in approximately 70/ p years, where p is the percent interest, compounded annually. If Thelma invests $ 30,000 in a long-term CD that pays 5 percent interest, compounded annually, what will be the approximate total value of the investment when Thelma is ready to retire 42 years later?  Choose the correct option.
A) $ 240,000
B) $ 320,000
C) $ 360,000
D) $ 450,000
E) $ 540,000

Solution: The amount of an investment will double in approximately 70/ p years, where p is the percent interest, compounded annually. If Thelma invests $ 30,000 in a long-term CD that pays 5 percent interest, compounded annually, what will be the approximate total value of the investment when Thelma is ready to retire 42 years later?   The investment gets doubled in 70/p years. Therefore, the investment gets doubled in   70/5= 
  70/5 = 14
every 14 years. After 42 years, the investment will get doubled 42/14= 
42/14 = 3
3 times.   So the amount invested will get doubled thrice.   So, 30000 *2^3= 240000   Hence, the answer is $ 240,000.
Answer: A
x, y, a, and b are positive integers. When x is divided by y, the remainder is 6. When a is divided by b, the remainder is 12. Which of the following is NOT a possible value for y + b?
Pick one:  A) 24  B) 21  C) 18  D) 17  E) 15

Solution: Important note: remainder is ALWAYS less than divisor, thus y>6 and b>12 --> y+b>18.   Answer: 18.
Answer: C