MU-NLPC/Calc-aqua_rat huggingface dataset:
John went to the Hospital at the speed of 60 km per hour while returning for his home he covered the half of the distance at the speed of 10 per hour, but suddenly he realized that he was getting late so he increased the speed and reached the home by covering rest 1/2 of the distance at the speed of 30km per hour. The average speed of the John in the whole length of journey is?
Choose the correct choice from the following choices:
A) 20 km/hr	B) 22 km/hr	C) 24 km/hr	D) 26 km/hr	E) 30 km/hr

Solution: Let distance between his home and hospital =   d   d km   Total distance travelled   =   d   +   d   =   2   d   =d+d=2d km   Total time taken   =   d   60   +   (   d   2   )   10   +   (   d   2   )   30   =d60+(d2)10+(d2)30   =   d   60   +   d   20   +   d   60   =   5   d   60   =   d   12   =d60+d20+d60=5d60=d12 hr   Average speed in the whole journey   =   2   d   (   d   12   )   =   2   d   ×   12   d   =   24   =2d(d12)=2d×12d=24 km/hr   24 km/hr
Answer: C
If Rs.7500 are borrowed at C.I at the rate of 4% per annum, then after 2 years the amount to be paid is? Choose one
A) 22887
B) 2778
C) 2797
D) 8112
E) 1712

Solution: Explanation:   A = 7500(26/25)2 = 8112   Answer:8112
Answer: D
Martha has the unique talent of being able to guess other people’s height and weight. For every four people that Martha meets, she consistently guesses the people’s correct height three times, and for every six people that she meets, she consistently guesses the people’s correct weight four times. If Martha meets three people and her success rate remains constant, what is the probability that Martha correctly guesses a person’s weight and height at least once? Select
A) 8/27 B) 7/8 C) 49/81 D) 98/125 E) 125/144

Solution: Probability that she guesses the height correctly P(h)=3/4   Probability that she guesses the weight correctlyP(w)=4/6   Probability that she guesses both weight and height correctly(P(h)*P(w))=3/4 * 4/6= 12/24   Now the Q asks about the probability of this happening atleast once.   We calculate it by finding the probability of not being able to guess in any of the three occasions.   Probability of not being able to guess any no. of times =1-12/24=12/24=1/2   For all three occasions P(A)=1/2 * 1/2 * 1/2=1/8   Probability of the event happening atleast once=1- P(A)=1-1/8=7/8   Ans should be 7/8
Answer: B
Express a speed of 46 kmph in meters per second?	Choose the correct choice from the following options:
A) 10.78 mps B) 12.78 mps C) 97.78 mps D) 17.78 mps E) 18.78 mps

Solution: 46 * 5/18   = 12.78 mps   Answer: 12.78 mps
Answer: B
From a pack of 52 cards, 1 card is drawn at random. Find the probability of a face card drawn.	Choose the correct option: A) 4/13 B) 1/52 C) 1/4 D) 1/3 E) None of these

Solution: Explanation:   Total number of cases = 52   Total face cards = 16 [favourable cases]   So probability = 16/52 = 4/13   Option 4/13
Answer: A
David bought a 1-year, $5,000 certificate of deposit that paid interest at an annual rate of 10 percent compounded semiannually. What was the total amount of interest paid on this certificate at maturity?	Choose the correct choice from the following choices:
A) $310
B) $425
C) $450
D) $300
E) $312.50

Solution: 10 percent compounded semiannually --> 5% in 6 moths.   For the first 6 moths interest was 5% of $5,000, so $250;   For the next 6 moths interest was 5% of $5,250, so $262.50   Total interest for 1 year was $250+$262.50=$312.50   Answer : $312.50
Answer: E
If f(f(n)) + f(n) = 2n+3, f(0) = 1 then f(2014) = ? Choose the most appropriate option.
A) 2015  B) 2088  C) 270  D) 1881  E) 1781

Solution: f (f(0)) + f(0) = 2(0) + 3 ⇒⇒ f(1) = 3-1= 
3-1 = 2
2, f(1)= 2   f(f(1)) + f(1) = 2(1) + 3 ⇒⇒ f(2)  ( (1)) +  (1)= 
 ( (1)) +  (1) = 2
2(1) + 3 ⇒⇒ f(2)= 5-2= 
5-2 = 3
3, f(2)= 3   f(f(2)) + f(2) = 2(2) + 3 ⇒⇒ f(3) = 7-3= 
7-3 = 4
4, f(3)= 4   ..............   f(2014) = 2015   2015ns: 2015
Answer: A
With # andeach representing different digits in the problem below, the difference between #and ## is 712. What is the value of?
#
-##
____
712  Select the correct option
A) 7
B) 8
C) 9
D) 10
E) 11

Solution: 100x   -(10x +x)   -----------   89 x= 712   x = 8   8
Answer: B
A man walking at a rate of 10km/hr crosses a bridge in 15 minutes. The length of the bridge is? Choose the correct choice from the following choices: A) 1521 B) 1492 C) 1667 D) 2500 E) 1112

Solution: Speed = 10*5/18 = 50/18 m/sec   2500istance covered in 15 minutes = 50/18 *15 *60= 
50/18 *15 *60 = 2_500
2500 m   Answer is 2500
Answer: D
A 300 meter long train crosses a platform in 48 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform?  Choose the most appropriate option.
A) 500 B) 289 C) 350 D) 882 E) 281

Solution: Speed = [300 / 18] m/sec = 50/3 m/sec.   Let the length of the platform be x meters.   Then, x + 300 / 48 = 50/3   3(x + 300) = 2400 è x = 500m.   500nswer: 500
Answer: A
A doctor prescribed 18 cubic centimeters of a certain drug to a patient whose body weight was 135 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?	Choose the correct choice from the following options
A) 8%	B) 9%	C) 11%	D) 12.5%	E) 14.8%

Solution: Typical dosage is Dose : weight :: 2: 15.   Now if weight is 135 (Multiplying factor is 9: (135/15)) then typical dosage would be 2 *9= 
2 *9 = 18
18cc.   Dosage= 18 cc. Dosage is greater by 2 cc.   % dosage is greater: (2 / 18)*100 = 11.11 %   11% is the answer.
Answer: C
If x is an integer such that 3 < x < 10, 5 < x < 18, 9 > x > –2, 8 > x > 0, and x + 1 < 9, then x is  Select the correct option:
A) 3	B) 5	C) 7	D) 9	E) 11

Solution: 3 < x < 10,   6 < x < 18,   -2 < x <9   0 < x < 8   x<8   From above: 6< x < 8 --> x = 7.   Answer: 7.
Answer: C
In an election between two candidates, the winner has a margin of 20% of the votes polled. If 1000 people change their mind and vote for the loser, the loser would have won by a margin of 20% of the votes polled. Find the total number of votes polled in the election?	Choose the most appropriate option
A) 10000	B) 5000	C) 15000	D) 20000	E) 6000

Solution: Winner - Looser   60% - 40%   If 1000 people change their mind and vote for the loser:   Winner - Looser   40% - 60%   Thus 1,000 people compose 20% of all voters, which means that the total number of votes is 5,000.   Answer: 5000
Answer: B
Find the area of trapezium whose parallel sides are 20 cm and 18 cm long, and the distance between them is 15 cm.
Choose the most appropriate option
A) 287 cm2  B) 785 cm2  C) 285 cm2  D) 785 cm2  E) 295 cm2

Solution: Explanation:   Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them) = 1/2 (20 + 18) * (15) = 285 cm2   Answer: Option 285 cm2
Answer: C
A summer camp has 150 children coming for the summer. Out of them, 60% have applied for the water sports programme and 80% have applied for rock climbing. How many campers have applied for both? Choose one.
A) 50  B) 60  C) 70  D) 80  E) 90

Solution: The total number of campers coming for the summer is n = 150.   The number of campers who have applied for the water sports activities is 60% of it, thus   n (A)=60/100×150=6×15=90   The number of campers who have applied for rock climbing is 80%, thus   n (B)=80/100×150=8×15=120.   In order to calculate the number of campers who have applied for both programs we can use the following equation:   n (AnB)=n (A)+n (B) -n =90+120-150=50=60.   So, 60 campers have applied for both water sports and rock climbing.   ANSWER: 60
Answer: B
Three workers have a productivity ratio of 3 to 5 to 6. All three workers are working on a job for 4 hours. At the beginning of the 5th hour, the slowest worker takes a break. The slowest worker comes back to work at the beginning of the 8th hour and begins working again. The job is done in ten hours. What was the ratio of the work performed by the fastest worker as compared to the slowest?	Pick:
A) 12 to 1	B) 6 to 1	C) 5 to 1	D) 20 to 7	E) 1 to 5

Solution: The fastest worker who does 6 units of job worked for all 10 hours, so he did   6*10= 
  6*10 = 60
60 units of job;   The slowest worker who does 3 unit of job worked for only   4+3= 
  4+3 = 7
7 hours (first 4 hours and last 3 hours), so he did   3*7= 
  3*7 = 21
21   The ratio thus is 60 to 21, or 20 to 7.   Answer: 20 to 7.
Answer: D
Convert the 9/36 m/s into kilometers per hour? Choose one
A) 0.9 kmph B) 9.9 kmph C) 1.3 kmph D) 1.2 kmph E) 5.7 kmph

Solution: 9/36 m/s = 9/36 * 18/5 = 9/10= 
9/10 = 9/10 = around 0.9
0.9 kmph.   0.9 kmphnswer: 0.9 kmph
Answer: A
The speed of a boat in upstream is 60 kmph and the speed of the boat downstream is 110 kmph. Find the speed of the boat in still water and the speed of the stream? Choose the correct choice from the following options:	A) 10	B) 25	C) 77	D) 55	E) 22

Solution: Speed of the boat in still water = (60+110)/2= 
(60+110)/2 = 85
85 kmph. Speed of the stream= (110-60)/2= 
(110-60)/2 = 25
25 kmph.   Answer: 25
Answer: B
The average height of 35 boys in a class was calculated as 182cm. It has later found that the height of one of the boys in the class was wrongly written as 166 cm whereas his actual height was 106 cm. Find the actual average height of the boys in the class (Round off your answer to two decimal places?  Select the correct option:
A) 187.89 cm B) 180.29 cm C) 123.98 cm D) 149.98 cm E) 146.89 cm

Solution: Calculated average height of 35 boys = 182 cm.   Wrong total height of 35 boys = 182 * 35 cm. This was as a result of an actual height of 106 cm being wrongly written as 166 cm. Correct total height of 35 boys = 182 cm - (166 cm - 106 cm)/35   = 182 cm - (166 cm - 106 cm)/35 = 182 cm - 60 /35 cm   = 182 cm - 1.71 cm = 180.29 cm.   Answer: 180.29 cm
Answer: B
John has 75 pencils, he distribute 20 pencils to his friends in his class. Then how many pencils are remaining to him?
Pick:
A) 10	B) 67	C) 32	D) 44	E) 55

Solution: 75-20= 
75-20 = 55
55. Answer is 55
Answer: E
Read the following three equations:
5 ~ 4 ~ 3 ~ 9 = 4215
6 ~ 9 ~ 2 ~ 6 = 3816
4 ~ 7 ~ 3 ~ 3 = 1122
Now based on the rule that has been used, solve the following equation:
7 ~ 2 ~ 7 ~ 4 = ____
Select.
A) 3538
B) 2418
C) 2873
D) 3258
E) 4268

Solution: 2418   The rule that is being followed here is   P ~ Q ~ R ~ S = [first digit of (P * S)] [last digit of (Q * R)] [first digit of (Q * R)] [last digit of (P * S)]   Using the same rule in the incomplete equation,   7 ~ 2 ~ 7 ~ 4 = [first digit of (7 * 4)] [last digit of (2 * 7)] [first digit of (2 * 7)] [last digit of (7 * 4)]   = 2418   Thus 2418 is the missing number.
Answer: B
The speed at which a man can row a boat in still water is 9.5 kmph. If he rows downstream, where the speed of current is 8.5 kmph, what time will he take to cover 45.5 metres?	Answers
A) 18 seconds	B) 8.4seconds	C) 5 seconds	D) 9.1 seconds	E) 9.5econds

Solution: Speed of the boat downstream = 9.5 +8.5= 
9.5 +8.5 = 18
18 kmph= 18 * 5/18= 
18 * 5/18 = 5
5 m/s   Hence time taken to cover 45.5 m= 45.5/5= 
45.5/5 = 9.1
9.1 seconds.   Answer:9.1 seconds
Answer: D
If x is 20 percent more than y and y is 30 percent less than z, then x is what percent of z?
Choose the correct choice
A) 500%  B) 250%  C) 500/3%  D) 84%  E) 60%

Solution: Z = 100 ; Y = 70 so X = 84   X as % of Z = 84/100 * 100= 
84/100 * 100 = 84
> 84%   Answer will be (84%)
Answer: D
Tommer spent six lucky days in Las Vegas. On his first day he won a net amount of only $20, but on each of the following days, the daily net amount he won grew by d dollars. If Tommer won a total net amount of $1620 during his stay in Las Vegas, how much did he win on the last day?  Select.
A) 330  B) 500  C) 520  D) 540  E) 620

Solution: I drew a diagram:   1 - $20   2 -   3 -   4 - $320   5 -   6 -   Total: $1,620   Between 1 and 6 are 5 days where he won $1,600. This means he averaged $320 per day (1600/5). You can put $320 by 4 because it's the middle number. Now you just find the two points betwenn $20 and $320 (320-20 = 300 / 3= 
300 / 3 = 100
100). So each day, he earned $100 more. This means on day 6, tommer earned$520. Answer choice 520.
Answer: C
Let f(x) = x^2 + bx + c. If f(1) = 0 and f(-7) = 0, then f(x) crosses the y-axis at what y-coordinate?
Choose the correct option:
A) -7  B) -1  C) 0  D) 1  E) 7

Solution: When x = 1 and when x = -7, the expression f(x) = x² + bx + c equals 0.   Then f(x) = (x-1)(x+7)   f(0) = -7   The answer is -7.
Answer: A
In 2000 there were 10000 women stockbrokers in the United States. By 2005 the number had increased to 20000. Approximately what was the percent increase?  Choose the most appropriate option:  A) 1%  B) 2%  C) 1.5%  D) 3%  E) 4%

Solution: The percent increase is (20000-10000)/10000=10000/10000= 
10000/10000 = 1
1%   So the approximate answer is 1%
Answer: A
At present the son's age is same as was his father's age at the time of his birth. If father's age is 48. Find the son's age after 4 years from now.	Choose the correct choice from the following options:
A) 30 years	B) 24 years	C) 28 years	D) 29 years	E) 38 years

Solution: Let x be the son's age   And y be the father's age   Then, y=48.   And, x=y-x   ==> 2x=y   ==> x=y/2   So, x=48/2= 
48/2 = 24
24.   Son's age after four years,   x+4= 24+4= 
24+4 = 28
28 years.   ANSWER:28 years
Answer: C
A train 220 m long is running with a speed of 60 km/hr. In what time will it pass a man who is running at 4 km/hr in the direction opposite to that in which the train is going?  Choices:
A) 5 B) 12 C) 7 D) 9 E) 5

Solution: Speed of train relative to man = 60 + 4= 
60 + 4 = 64
64 km/hr.= 64 * 5/18 = 160/9 m/sec.   Time taken to pass the men = 220 * 9/160 = 12 sec.Answer: 12
Answer: B
If 2x=4y=z, what is x-y, in terms of z?	Choose the correct choice from the following choices.
A) z/4	B) z/2	C) z	D) 2z	E) 4z

Solution: 2x=4y=z   i.e. x = z/2   and y = z/4   x-y = z/2 - z/4 = z/4   z/4nswer: Option z/4
Answer: A
The population of cities A and B is equal. The population of city A increases in two successive years by 20% and 15% respectively and that of city B increases successively by 20% and 10% respectively. If the difference in the population of two cities after 2 years is 768, then what was the total population of the two cities initially?	Pick one:
A) 12,800
B) 26,500
C) 24,600
D) 25,600
E) 27,600

Solution: Population of city A = Population of city B = A   M . F of A = 120/100*115/100 = 138/100   M . F of B = 120/100*110/100 =132/100   Population of A after 2 years = A*138/100   Population of B after 2 years = A*132/100   25,600ifference = A/100( 138 –132 ) = 768   A = 768*100/6= 
768*100/6 = 12_800
12800   Total initial population= 12800+12800 = 25,600   ANSWER:25,600
Answer: D
A man deposits $1000 in a bank at 2% per annum and $ 1500 in UTI at 7% per annum. Find the rate of interest for the whole sum.  Choices:
A) 5%
B) 8%
C) 3%
D) 7%
E) 1%

Solution: Following the above formula,we have the rate of interest for the whole sum   =(1000*2)+(1500*7)/1000+1500=12500/2500= 
12500/2500 = 5
5%.   5%nswer is 5%
Answer: A
Two sides of a triangle have length 6 and 8. Which of the following are possible areas of the triangle?
I. 4
II. 12
III. 24	Choose the correct choice
A) I, II, and III
B) I and II only
C) II and III only
D) I and III only
E) II only

Solution: Answer = A. I, II, and III   With dimensions of only 2 sides given (for a triangle), this becomes an open ended question   I, II, and IIIny area is possible out of the three
Answer: A
If goods be purchased for Rs.840 and one-fourth be sold at a loss of 20% at what gain percent should the remainder be sold so as to gain 20% on the whole transaction?
Select.
A) 33 1/9% B) 73 1/3% C) 33 1/3% D) 33 1/9% E) 39 1/3%

Solution: 1/4 33 1/3%P = 210 SP = 21*(80/100) = 168   SP = 840*(120/100)= 
840*(120/100) = 1_008
1008   1008 - 168= 
1008 - 168 = 840
840   3/4 SP= 630   Gain = 210   630 --- 210   100 --- ? => 33 1/3%   Answer:33 1/3%
Answer: C
Walking 7/6 of his usual rate, a boy reaches his school 4 min early. Find his usual time to reach the school?
Choose the correct choice from the following answers
A) 18 min  B) 19 min  C) 11 min  D) 28 min  E) 16 min

Solution: Speed Ratio = 1:7/6 = 6:7   Time Ratio = 7:6   1 -------- 7   4 --------- ? è 28 m   Answer: 28 min
Answer: D
If 15 lions can kill 15 deers in 15 minutes how long will it take 100 lions to kill 100 deers? Choose the correct choice from the following.
A) 1 minutes B) 15 minute C) 100 minutes D) 10000 minutes E) 1000 minutes

Solution: we can try the logic of time and work,our work is to kill the deers so 15(lions)*15(min)/15(deers)=100(lions)*x(min)/100(deers)hence answer is x=15   ANSWER:15 minute
Answer: B
The length of a rectangular floor is more thanits breadth by 200%. If Rs.324 is requiredto paint the floor at the rate of Rs.3/sq m, what would be the length of the floor? Pick one.
A) 12 B) 18 C) 20 D) 22 E) 24

Solution: Let the length and the breadth of the floor be l m and b m respectively.   l = b + 200% of b = l + 2b = 3b   Area of the floor = 324/3= 
324/3 = 108
108 sq m   l b= 108 i.e., l * l/3 = 108   l2 = 324 => l = 18.   18
Answer: B
A military commander has to choose 3 soldiers out of a company of 6 for guarding the headquarters. How many different group combinations of 3 does he have to choose from?	Choose the correct choice from the following choices
A) 20 B) 15 C) 16 D) 27 E) 35

Solution: A military commander has to choose 3 soldiers out of a company of 7.   different group combinations of 3   He can do this in 6C3 ways   6*5*4/3*2*1= 20 ways   20NSWER:20
Answer: A
I. x2 + 11x + 30 = 0,
II. y2 + 15y + 56 = 0 to solve both the equations to find the values of x and y?	Choose the correct choice from the following answers:
A) If x < y	B) If x > y	C) If x ≤ y	D) If x ≥ y	E) If x = y or the relationship between x and y cannot be established.

Solution: I. x2 + 6x + 5x + 30 = 0   =>(x + 6)(x + 5) = 0 => x = -6, -5   II. y2 + 8y + 7y + 56 = 0   =>(y + 8)(y + 7) = 0 => y = -8, -7   => x > y   ANSWER:If x > y
Answer: B
A certain board game has a row of squares numbered 1 to 100. If a game piece is placed on a random square and then moved 3 consecutive spaces in a random direction, what is the probability the piece ends no more than 3 spaces from the square numbered 49?  Choose one: A) 10% B) 11% C) 12% D) 13% E) 7%

Solution: No more than 3 spaces from 49 means in the rangefrom 49-3= 
49-3 = 46
46 to  49+3= 
 49+3 = 52
52, inclusive. Total numbers in this range   52-46+1= 
  52-46+1 = 7
7, the probability favorable/total=7/100   Answer: 7%
Answer: E
A room contains 120 people, 15 percent of whom are women. A group of people, 30 percent of whom are women, leaves the room. Of the people remaining in the room, 10 percent are women. How many people left the room?	Select the correct option:
A) 10
B) 20
C) 30
D) 40
E) 50

Solution: Say group of x people left the room.   # of women in the room was 0.15*120= 
0.15*120 = 18
18;   # of women in the group that left 0.3x;   # of women in the room after the group left it is 0.1(120-x);   So, 18-0.3x= 0.1(120-x) --> x=30.   Answer: 30.
Answer: C
A crow leaves its nest, and flies back and forth from its nest to a nearby ditch to gather worms. The distance between the nest and the ditch is 250 meters. In one and a half hours, the crow manages to bring worms to its nest 15 times. What is the speed of the crow in kilometers per hour?
Options
A) 1 B) 3 C) 4 D) 5 E) 6

Solution: The distance between the nest and the ditch is 250 meters.   15 times mean = A crow leaves its nest, and flies back ( going and coming back) i.e. 2 times we get total 30 rounds.   So the distance is  30 * 250= 
 30 * 250 = 7_500
7500.   5= ST   7500/1.5 = T , I think we can take 7500 meters as 7.5 km, then only we get T = 5.( 1000 meters = 1 km)   5)
Answer: D
A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 42 years now, the son's age 8 years back was:  Choose the correct option:
A) 13 years. B) 14 years. C) 17 years. D) 16 years. E) 19 years.

Solution: Let the son's present age be x years. Then, (42 - x) = x   2x = 42.   x = 21   Son's age 8 years back (21- 8)= 
(21- 8) = 13
13 years.   13 years.NSWER :13 years.
Answer: A
A works twice as fast as B. If B can complete a work in 12 days independently, the number of days in which A and B can together finish the work in :
Choose one:
A) 4 days	B) 6 days	C) 8 days	D) 18 days	E) 28 days

Solution: Explanation:   Ratio of rates of working of A and B = 2 : 1.   So, ratio of times taken = 1 : 2.   B's 1 day's work =1/12   A's 1 day's work =	1/6 ; (2 times of B's work)   (A + B)'s 1 day's work = (1/6 +1/12)=3/12=1/4   So, A and B together can finish the work in 4 days.   4 daysNSWER IS 4 days
Answer: A
A motorist travel to a place 150 km away at an avearge speed of 50 km/hr and returns ar 30
km/hr.His average speed for the whole jouney in km/hr is  Choices:  A) 36.5 km/hr  B) 37.5 km/hr  C) 35.5 km/hr  D) 34.5 km/hr  E) None of these

Solution: Explanation:   Average speed will be   2xyx+ykm/hr   = \frac{2(50)(30)}{50+30} km/hr   = 37.5 km/hr   Answer: Option 37.5 km/hr
Answer: B
If a book has twelve thousand words, two long chapters, and four short chapters, how many words are in a short chapter if there are as many words in the four short chapters put together as in one long chapter? Choose the correct choice from the following:
A) Eleven thousand words
B) Five thousand words
C) Two thousand words
D) One thousand words
E) Six hundred words

Solution: D. A long chapter has 1/3 of the total words. A short chapter has 1/4 of 1/3 of the total words. 1/4 of 1/3 is 1/12. 1/12 of twelve thousand is one thousand, so the answer is One thousand words.
Answer: D
A set of five positive integers has an arithmetic mean of 150. A particular number among the five exceeds another by 100. The rest of the three numbers lie between these two numbers and are equal. How many different values can the largest number among the five take? Choose one:	A) 18	B) 19	C) 21	D) 42	E) 59

Solution: Lets say numbers are in this order: x < y = y = y < x+100. Question is, how many different values can x take.   x+3y+x+100 = 750   2x+3y = 650   We have condition x < y < x + 100 so lets use it   2x + 3y < 2x + 3*(x+100) = 5x + 300   2x + 3y > 2x + 3x = 5x   2x + 3y  2  + 3= 
 2  + 3 = 5
5x   2x + 3y= 650   So we got double inequality:   5x < 650 < 5x + 300 which turns into   350 < 5x < 650   70 < x < 130   x can take   130-70-1= 
  130-70-1 = 59
59 values   ANSW59R:59
Answer: E
In a supermarket the single-yolk and double-yolk eggs got mixed. If the total number of yolks was 15 more than the total number of eggs. Find the number of double-yolk eggs. Choose the correct choice from the following choices:
A) 8	B) 13	C) 15	D) 11	E) 5

Solution: Let the number of single-yolk eggs be X and the number of double-yolk eggs be Y. Then   => X+(2*Y)= 15+(X+Y)   =>2Y=15+Y   =>Y=15   Option 15
Answer: C
What is the smallest possible common multiple of three integers, all larger than 25?	Choose the correct choice from the following choices:
A) 27.  B) 26  C) 846.  D) 19,656.  E) 21,924.

Solution: The Least common positive multiple would be for the immediate least number(s) after 25 i.e 26.   Since nowhere is it stated that the three integers must be different, the integers could be 26,26 and 26... leading to least possible positive common multiple to be 26. Answer 26.
Answer: B
The ratio of boarders to day students at a school was originally 2 to 5. However, after a number of new boarders join the initial 120 boarders, the ratio changed to 1 to 2. If no boarders became day students and vice versa, and no students left the school, how many new boarders joined the school?	Pick
A) 30
B) 50
C) 70
D) 80
E) 90

Solution: Let x be the number of new boarders.   The ratio changed from 2:5 = 4:10 up to 1:2 = 5:10.   120 / (120+x) = 4/5   x = 30   The answer is 30.
Answer: A