MU-NLPC/Calc-aqua_rat huggingface dataset:
If x = 1/q and y = (2/q) - 6, then for what value of q, x is equal to y ?
Choose the correct option:
A) 1/3  B) 1/6  C) 6  D) 3  E) 2

Solution: Explanation:   x = y <=> 1/q = (2/q) - 6 <=> 1/q = 6 <=> q = 1/6.   Answer: 1/6
Answer: B
Due to 10% decrease in the price of sugar and John can buy 7kg more sugar in Rs100 , then find the CP of sugar?
Choices.
A) s. 1(37/63)  B) s. 2(2/9)  C) s. 2(1/9)  D) s. 3(2/7)  E) s. 4(2/9)

Solution: Here r = 10 % ,x = 100 and A = 7 kg   Actual price of sugar = 10*100/((100-10 )*7) = Rs. 1(37/63)   s. 1(37/63)
Answer: A
The surface area of a sphere is same as the curved surface area of a right circular cylinder whose height and diameter are 16 cm each. The radius of the sphere is Choose the correct choice from the following answers:	A) 3 cm	B) 4 cm	C) 6 cm	D) 8 cm	E) None

Solution: Solution   4Î R2	= 2Î 8x16   â‡’ R2 = (8x16/2)   â‡’ 64   â‡’ R = 8 cm.   Answer 8 cm
Answer: D
70 + 5 * 12 / (180/3) = ? Pick
A) 23	B) 71	C) 27	D) 61	E) 81

Solution: Explanation:   70 + 5 * 12 / (180/3) = 70 + 5 * 12 / (60)   = 70 + (5 * 12)/60 = 70 + 1= 
70 + 1 = 71
71.   Answer:71
Answer: B
If Rahul finds that he is 12th from the right in a line of boys and 4th from the left, how many boys should be added to the line such that there are 28 boys in the line?
Choose the correct option.
A) 12  B) 14  C) 20  D) 13  E) 21

Solution: total no of boys=l+r-1=12+4-1= 
12+4-1 = 15
15   we required 28 boys so we have to add 13 to make it 28.   so 13 is answer   ANSWER:13
Answer: D
A bag contains 7 black and 8 white balls. If two balls are drawn simultaneously, what is the probability that both are of the same color is?	Choose the correct choice from the following answers.
A) 1/2	B) 1/3	C) 2/3	D) 3/5	E) 7/15

Solution: Drawing two balls of same color from seven black balls can be done in ⁷C₂ ways.   Similarly from eight white balls two can be drawn in ⁸C₂ ways.   P = ⁷C₂/¹⁵C₂ + ⁸C₂/¹⁵C₂ = 7/15   Answer is 7/15
Answer: E
S is the set of all fractions defined by the formula n/(n + 1), where n is a positive integer less than 20. What is the product D of all the fractions that are in S?	Choose the correct choice from the following answers:  A) 1) 1/20  B) 2) 1/21  C) 3) 1/2  D) 4) 19/40  E) 5) 19/20

Solution: 1/2 * 2/3 * 3/4 * ... 19/20   = 1/20   1) 1/20nswer - 1) 1/20
Answer: A
A watch was sold at a loss of 12%. If it was sold for Rs.140 more, there would have been a gain of 4%. What is the cost price?
Choose the correct choice from the following answers.
A) s.1000
B) s.875
C) s.1007
D) s.1006
E) s.1002

Solution: Explanation:   88%   104%   --------   16% ---- 140   100% ---- ? => Rs.875   Answer:s.875
Answer: B
In a sheep farm, the sheep give birth to lamps and the count of sheep increases by 20% every year. How many years it will take to get the count tripled?
Choose the correct option.
A) 2
B) 3
C) 4
D) 5
E) 6

Solution: 1 year: 100/4 = 20 : Total: 120   2nd year: 120/4= 
120/4 = 30
30: Total: 120+30= 
120+30 = 150
150   3rd year: 150/4= 38 approx: Total:  150+38= 
 150+38 = 188
188   4th year: 188/4= 
188/4 = 47
47: Total: 188+47= 
188+47 = 235
235   5th year : 235/4= 59 : total :   235+59= 
  235+59 = 294
294   6th year : 294/4= 74 : total :   294+74= 
  294+74 = 368
368   ;6 years;   ANSW6R: 6
Answer: E
A fair coin is tossed repeatedly. If heads appears on first 4 tosses what is the probability that tail appears on the next two tosses?  Choose the correct choice from the following choices:
A) 1/6  B) 1/5  C) 1/3  D) 1/4  E) 1/6

Solution: Explanation :   Like mentioned in the question, the coin is fair. So chance of appearing of head and tail on each toss is same and each toss is independent from the previous one. So the chance of appearing tail on the next two tosses is still 1/2 each.   1/2 * 1/2 = 1/4   Answer : 1/4
Answer: D
A, B, C together started a business. A invested Rs.6000 for 5 months B invested Rs.3600 for 6 months and C Rs.7500 for 3 months. If they get a total profit of Rs.7410. Find the share of B?	Choices: A) 2160 B) 3000 C) 3018 D) 3019 E) 3012

Solution: 60*5:36*6:75*3   100: 72: 75   72/247 * 7410= 
72/247 * 7410 = 2_160
2160   2160nswer: 2160
Answer: A
Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 5 seconds. What is the length of the fast train?	Choices: A) 23 m B) 23	2/9 m C) 27	7/9m D) 29 m E) 28 m

Solution: Explanation:   Relative speed = (40 - 20) km/hr =	(	20 x	5/18	)	m/sec =	(	50/9	)	m/sec.   Therefore Length of faster train =	(	50/9	x 5	)	m =	250/9	m = 27	7/9	m.   ANSWER IS 27	7/9m
Answer: C
If integers e and b are distinct factors of 30, which of the following CANNOT be a factor of 30?
I. eb + b^2
II. (e + b)^2
III. e + b Choose the correct choice from the following choices
A) I only	B) II only	C) III only	D) I and II only	E) I, II, and III

Solution: Factors of 30 are: 1, 2, 3, 5, 6, 10, 15, and 30.   I. eb + b^2 --> if e=1 and b=2 then eb + b^2=6, which is a factor of 30. OK;   II. (e + b)^2 --> (e + b)^2 is a perfect square, no perfect square (but 1) is a factor of 30. DISCARD;   III. e + b --> if e=1 and b=2 then e + b=3, which is a factor of 30. OK.   Answer: II only.
Answer: B
Two buses and a van were employed to transport a class of students on a field trip. 4/5 of the class boarded the first bus. 2/3 of the remaining students boarded the second bus, and the rest of the students boarded the van. When the second bus broke down, 1/2 of the students on the second bus boarded the first bus. What fraction of the class was on board the first bus?	Select the correct option:  A) a) 1/2  B) b) 26/30  C) c) 11/15  D) d) 23/30  E) e) 4/5

Solution: This is a pure ratio question (we aren't given any numbers for anything), so you can just choose any starting number you like, and use it to solve the problem. The best number to pick is almost always the product of all the denominators of your fractions, so here we could start with 30 students. Then we have:   • 4/5 of these, or 24 students, board the first bus   • there are 6 students left. 2/3 of these, or 4 students, board the second bus   • this bus breaks down, and 1/2 of the 4 students, or 2 students, board the first bus   • the first bus now contains 26 out of the original 30 students, so the answer is 26/30   Answer b) 26/30
Answer: B
20 % of 2 is equal to Choose one:
A) 0.2
B) 0.4
C) 0.6
D) 0.7
E) 0.9

Solution: 20 % of 2 = (20 / 100) * 2= 
(20 / 100) * 2 = 2/5 = around 0.4
0.4   Answer: Option 0.4
Answer: B
A certain quantity of 40% solution is replaced with 25% solution such that the new concentration is 35%. What is the fraction of the solution that was replaced?  Choose the correct answer: A) 1/4 B) 1/3 C) 1/2 D) 2/3 E) 3/4

Solution: Original quantity = A   Substituted quantity = 1/3   Then:   (A*0.4 + 0.25*1/3 тАУ 0.4*1/3 ) / A = 0.35   0.4 + (1/3/A)*(-0.15)=0.35   1/3/A=-0.05/-0.15=1/3   ANSWER:1/3
Answer: B
A train 220 m long passed a pole in 22 sec. How long will it take to pass a platform 550 m long?  Answers.
A) 77
B) 82
C) 43
D) 67
E) 29

Solution: Speed = 220/22= 
220/22 = 10
10 m/sec.   Required time= (220 + 550)/10= 
(220 + 550)/10 = 77
77 sec.   77nswer: 77
Answer: A
There are 2 groups named brown and red. They can n't marry in the same group. If the husband or wife dies then the person will revert to their own group. If a person is married then the husband will have to change his group to his wife's group. Children will own the mother's group. If man is red then his mother's brother belong to which group if he is married	Choose the correct choice from the following.
A) 138 B) 287 C) 207 D) 2768 E) 112

Solution: If a man is Red, his mother must be red, his mothers brother also red but after marriage, he gets converted to Brown.   Answer:287
Answer: B
X does 80% of a work in 20 days. He then calls in Y and they together finish the remaining work in 3 days. How long Y alone would take to do the whole work?
Choose the correct choice from the following answers
A) 37 1/2 B) 35 C) 36 D) 25 E) 34

Solution: Whole work is done by X in ( 20 x 5/4) = 25 days.   Now, ( 1 - 4 /5) i.e., 1/5	work is done by X and Y in 3 days.   Whole work will be done by X and Y in (3 x 5) = 15 days.   A's 1 day's work = 1 , (X + Y)'s 1 day's work = 1 .   25 15   Therefore Y's 1 day's work = ( 1/15	- 1 /25	) = 4/150 = 2/75   So, Y alone would do the work in 75/2	= 37 1/2 days.
Answer: A
Two men started from the same place walk at the rate of 10kmph and 12kmph respectively. What time will they take to be 10 km apart, if they walk in the same direction?
Choose the correct option
A) 5hours  B) 6hours  C) 8hours  D) 10hours  E) 12hours

Solution: To be 2km apart they take 1 hour   To be 10km apart they take = 1/2 * 10= 
1/2 * 10 = 5
5 hours   5hoursnswer is 5hours
Answer: A
In a college, the ratio of the number of boys to girls is 8 : 5. If there are 400 girls, the total number of students in the college is	Choose the correct option:
A) 1040	B) 920	C) 980	D) 720	E) 820

Solution: Explanation:   Let the boy are 8x and Girls are 5x   => 5x = 400   => x = 80   Total students = 8x+5x = 13x 8 +5= 
8 +5 = 13
13x= 13(80) = 1040   Option 1040
Answer: A
P can do a work in 48 days. Q can do the same work in 9 days and R can do the same in 12 days. Q and R start the work and leave after 3 days. P finishes the remaining work in --- days. Choose one: A) 7 B) 8 C) 9 D) 10 E) 20

Solution: Work done by P in 1 day = 1/24   Work done by Q in 1 day = 1/9   Work done by R in 1 day = 1/12   Work done by Q and R in 1 day = 1/9 + 1/12 = 7/36   Work done by Q and R in 3 days = 3Ã—7/36 = 7/12   Remaining work = 1 â€“ 7/12 = 5/12   Number of days in which P can finish the remaining work = (5/12) / (1/48)= 
(5/12) / (1/48) = 20
20   Option 20
Answer: E
A collector collects stamps from foreign countries. In June, she gave 20 percent of her stamps to her friend. In July, she gave 30 percent of her remaining stamps to another friend. If these were the only changes in the number of stamps in the stamp collection during those two months, what percent of her collection at the beginning of June did she give to away in June and July?	Choose the correct choice from the following answers:
A) 32%  B) 36%  C) 40%  D) 44%  E) 48%

Solution: Let x be the number of stamps in the original collection.   The percentage of the collection given away is:   0.2x + 0.3(0.8x) = 0.2x + 0.24x = 0.44x 0.2  + 0.24= 
0.2  + 0.24 = 0.44
0.44x= 44%   The answer is 44%.
Answer: D
What is the number?
I.
The sum of the two digits is 8. The ratio of the two digits is 1 : 3.
II.
The product of the two digit of a number is 12. The quotient of two digits is 3.  Choose the correct choice from the following answers:
A) I alone sufficient while II alone not sufficient to answer
B) II alone sufficient while I alone not sufficient to answer
C) Either I or II alone sufficient to answer
D) Both I and II are not sufficient to answer
E) Both I and II are necessary to answer

Solution: Let the tens and units digit be x and y respectively. Then,   I. x + y = 8 and	x/y	=	1/3   I gives, 4y = 24 y = 6.   So, x + 6 = 8 x = 2.   II. xy = 12 and	x/y	=	3/1   II gives, x^2 = 36 x = 6.   So, 3y = 6 y = 2.   Therefore, Either I or II alone sufficient to answer.   Option Either I or II alone sufficient to answer
Answer: C
A mixture of 70 litres of milk and water contains 10% water. How many litres of water should be added to the mixture so that the mixture contains 12 1/2% water? Select
A) 2 litres  B) 6 litres  C) 8 litres  D) 3 litres  E) 9 litres

Solution: Quantity of milk in the mixture = 90/100 (70) = 63 litres.   After adding water, milk would form 87 1/2% of the mixture.   Hence, if quantity of mixture after adding x liters of water, (87 1/2) / 100 x = 63 => x = 72   Hence 72 - 70= 
72 - 70 = 2
2 litres of water must be added.   2 litresnswer: 2 litres
Answer: A
if a man earns Rs20 on first day and spends Rs15 on second day ,and earns Rs20 on third day and spends Rs 15 on fourth day and goes on on which day he will be having Rs 60.	Choose the correct choice:
A) 40Rs B) 45Rs C) 50Rs D) 55Rs E) 60Rs

Solution: Earns Rs20 on first day and spends Rs15 on second day means,   End of day 2, he have 5Rs.   Therefore,   In 16days he have 40Rs     2 * 8= 
  2 * 8 = 16
16days   5rs* 8 = 40Rs   And On the 17th day again he earn Rs.20,   40 + 20  5  * 8= 
 5  * 8 = 40
40Rs   And On the 17th day again he earn Rs.20,   40 + 20= 
40 + 20 = 60
60Rs.   ANSW60RsR:60Rs
Answer: E
A part-time employee whose hourly wage was increased by 50 percent decided to reduce the number of hours worked per week so that the employee's total weekly income would remain unchanged. By what percent should the number of hours worked be reduced?
Select the correct option
A) 9	B) 13	C) 17	D) 20	E) 33.33

Solution: Let original hourly wage be x and let the no of hours worked be y   Total wage will be =x*y   After the increment the wage will be=1.5 x   Now we need to find number of hours worked so that   x*y=1.5x*z i.e z=1/1.5 y = 2/3y   %decrease = (y-2/3y)/y *100=100/3=33.33%.   Thus my answer is 33.33.
Answer: E
A number is said to be prime saturated if the product of all the different positive prime factors of d is less than the square root of d. What is the greatest two digit prime saturated integer ?  Pick: A) 99 B) 98 C) 97 D) 96 E) 95

Solution: Clearly D A number is said to be prime saturated if the product of all the different positive prime factors of d is less than the square root of d.   96 has more number of smaller prime factor thats the clue !!=96
Answer: D
At Company X, senior sales representatives visit the home office once every 18 days, and junior sales representatives visit the home office once every 12 days. The number of visits that a junior sales representative makes in a 2-year period is approximately what percent greater than the number of visits that a senior representative makes in the same period?
Choose one:
A) 10%  B) 25%  C) 33%  D) 50%  E) 67%

Solution: Each 36-day period, senior representatives visit the home office 2 times while junior representatives visit 3 times, thus 50% more.   The answer is 50%.
Answer: D
If the length of a rectangular field is 30 metres more than its breadth and the perimeter of the field is 540 metres, what is the area of the field in square metres? Choose the most appropriate option
A) 18000	B) 40000	C) 31000	D) 19000	E) 16000

Solution: Let breadth is x then length is 30+x   Now the perimeter=2(x+30+x)=540   solving this we get x=120   Now the area is  120*150= 
 120*150 = 18_000
18000   18000NSWER:18000
Answer: A
The length of a rectangular floor is more than its breadth by 200%. If Rs.400 is required to paint the floor at the rate of Rs.3/sq m, what would be the length of the floor?	Select.
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 = 400/3 = 133.33 sq m   l b = 133.33 i.e., l * l/3 = 133.33   l^2 = 400> l = 20.   20
Answer: C
In a certain game, a large container is filled with red, yellow, green, and blue beads worth, respectively, 7, 5, 3, and 2 points each. A number of beads are then removed from the container. If the product of the point values of the removed beads is 3,087,000, how many red beads were removed?
Pick:
A) 1
B) 2
C) 3
D) 4
E) 5

Solution: 3,087,000   = 2^3 * 5^3 * 3087   = 2^3 * 3 * 5^3 * 1029   = 2^3 * 3^2 * 5^3 * 343   = 2^3 * 3^2 * 5^3 * 7^3   The answer is 3.
Answer: C
Each of the squares above is to have exactly one letter and nothing else placed inside it. If 3 of the letters are to be the letter X, 2 of the letters are to be the letter Y, and 1 of the letters is to be the letter Z, in how many different arrangements can the squares have letters placed in them?	Choose the correct choice:
A) 30
B) 60
C) 108
D) 120
E) 150

Solution: take it as a alphabetical problem   XXXYYZ   since those are alphabets, they are identical....   so that's 6!/3!*2!*1! = 60   ANSWER:60
Answer: B
If j and k are integers and j^2 / k is odd, which of the following must be true ?	Choose the correct choice from the following answers:	A) j and k are both even	B) j = k	C) If j is even, k is even	D) j is divisible by k	E) j^2 > k

Solution: Given: j and k are integers and j^2/k=odd--> j^2=k∗odd   (A) j and k are both even: not necessarily true, for example j=1 and k=1   (B) j = k: not necessarily true, for example j=3 and k=1;   (C) If j is even, k is even: as j^2=k∗odd then in order j to be even k must be even too, so this statement must be true;   (D) j is divisible by k: not necessarily true, for example j=3 and k=9;   (E) j^2 > k: not necessarily true, for example j=1 and k=1.Answer: C.   Answer: If j is even, k is even.
Answer: C
Based on this year's costs, an orcharde grower budgets P dollars for planing N new trees next year. If the average cost of planting each tree were to increase 15% from this year's cost, then the greatest number of trees that the orchard grower could plant next year using P dollars would be
Choose the correct choice
A) 13% less than N  B) 25% less than N  C) equal to N  D) 20% greater than N  E) 25% greater than

Solution: Correct answer is (A).   This year, the price of a tree is price1=P/N.   If this price increases by 15% it becomes price2=P/N*1.15   Then with P dollars, you can grow P/price2 tress i.e. P/(P/N*1.15) i.e. N/1.15 i.e. .87%
Answer: A
If a survey shows that 60 citizens out of a sample of 200 support a particular Senate bill, what percent of the sample does not support the bill?	Choose the correct choice:	A) 56%	B) 70%	C) 72%	D) 82%	E) 86%

Solution: Those who support = 60.   % of those who don't support it is (200-60)/ 200 = 70%   Answer 70%
Answer: B
A dishonest dealer professes to sell his goods at Cost Price but still gets 20% profit by using a false weight. What weight does he substitute for a kilogram?  Choose the correct choice from the following choices:
A) 833 1/6 grams	B) 833 1/3 grams	C) 873 1/3 grams	D) 733 1/3 grams	E) 837 1/3 grams

Solution: If the cost price is Rs.100, then to get a profit of 20%, the selling price should be Rs.120.   If 120kg are to be sold, and the dealer gives only 100kg, to get a profit of 20%.   How many grams he has to give instead of one kilogram(1000 gm).   120 gm ------ 100 gm   1000 gm ------ ?   (1000 * 100)/120 = 2500/3 = 833 1/3 grams.   Answer: 833 1/3 grams
Answer: B
A straight line in the xy- plane has y-intercept of 17 . If the slope is half its y-intercept, and the x-coordinate of the point in this line is 7, find the y-coordinate.	Select:
A) -100
B) 34
C) 76.5
D) 75.6
E) 74.3

Solution: Eq of line = Y = MX +76.5   76.5= 17   M=76.5/2 = 17/2 =   X = 7   Substitute givens:   Y=(17/2*7) + 17= 
(17/2*7) + 17 = 153/2 = around 76.5
76.5   correct option is 76.5
Answer: C
There are 20 pieces of candy and 4 kids. How many pieces of candy does each kid get?
Select the correct option:
A) 7
B) 5
C) 13
D) 20
E) 4

Solution: If you split 20 pieces of candy between 4 kids each kid will get 5 pieces of candy   5
Answer: B
The perimeter of a triangle is 40 cm and the in radius of the triangle is 2.5 cm. What is the area of the triangle?
Choose the correct choice from the following options:
A) 76  B) 88  C) 66  D) 55  E) 50

Solution: Area of a triangle = r * s   Where r is the in radius and s is the semi perimeter of the triangle.   Area of triangle = 2.5 * 40/2= 
2.5 * 40/2 = 50
50 cm2   Answer:50
Answer: E
In ΔPQS above, if PQ =2 and PS = 3, then Choose the correct choice:
A) 3/2  B) 12/5  C) 16/5  D) 15/4  E) 20/3

Solution: there are two ways to calculate area of PQS. area remains same, so both are equal.   2*3/2 = PR*4/2   PR = 3/2   3/2
Answer: A
A train running at a speed of 60 kmph crosses a pole in 12 seconds.What is the length of the train?	Choose the correct choice from the following answers:
A) 200 m
B) 180 m
C) 190 m
D) 150 m
E) 160 m

Solution: 60 kmph=50/3 m/sec   50/3*12= 
50/3*12 = 200
200 m   200 mNSWER:200 m
Answer: A
In how many different ways can the letters of the word "NEGLIGENCE" be rearrangement? Choose the correct choice
A) 3628800  B) 3628800  C) 3628812  D) 3428800  E) 3368800

Solution: Option '3628800'   The total number of arrangements is   10P10 = 10! = 3628800
Answer: B
In the sequence S, each term after the first is twice the previous term. If the first term of sequence S is 3, what is the sum of the 14th and 15th terms in sequence S?	Choose the correct choice from the following answers.
A) 3(2^16)  B) 9(2^15)  C) 21(2^14)  D) 9(2^14)  E) 9(2^13)

Solution: The terms in the sequence can be shown as   a(n) = 2* a(n-1)   So, the sequence will look like: 3, 2*3, (2^2) *3,...   And the nth term will be given as 2^(n-1) *3   Therefore, a(14) = (2^13)*3, a(15) = (2^14) *3,   So, a(14) + a(15) = (2^13) *3 + (2^14) *3   = 3* (2^13) *(1+2) = 3* (2^13) *3   = 9 * (2^13)   Answer : 9(2^13)
Answer: E
Express a speed of 342 kmph in meters per second?	Choose the correct choice from the following options
A) 10 mps  B) 59 mps  C) 79 mps  D) 90 mps  E) 19 mps

Solution: 342 * 5/18 = 90 mps   Answer: 90 mps
Answer: D
The juice stall at the circus stocked just 2 brands of orange juice tetra packs. Brand A costs $1 per pack and brand B costs $1.5 per pack. Last week , brand A contributed to m% of stall’s revenue and accounted for n% of sales of juice tetra packs. Which of the following expresses m in terms of n? Options
A) 100n/(150 – n)
B) 200n/(250-n)
C) 200n/(300-n)
D) 250n/(400-n)
E) 300n/(500-n)

Solution: Let the number of units sold be 100. Then n units of A are sold and (100-n) units of B are sold.   Total revenue= Revenue due to A + Revenue due to B   = (No.of units of A sold * Cost/unit of A) + (No.of units of B sold * cost/unit of B)   = n *1 + (100-n) *1.5   = n + (150-1.5n) --- (1)   2. But we know, revenue due to A = m%. of the total revenue --- (2)   3. To express m in terms of n we need to relate (1) and (2)   4. m% = n / ( n + (150-1.5n))   or m= 100n / 150-0.5n = 200n/(300-n)   ANSWER:200n/(300-n)
Answer: C
A man started driving at a constant speed, from the site of a blast, the moment he heard the blast. He heard a second blast after a time of 30 mins and 25 seconds. If the second blast occurred exactly 30 mins after the first, how many meters was he from the site when he heard the second blast? ( speed of sound = 330 m/s) Choose the correct choice from the following answers
A) 8250 B) 9350 C) 10,450 D) 11,550 E) 12,650

Solution: The distance the sound traveled to the man is 25*330= 
25*330 = 8_250
8250 meters   The answer is 8250.
Answer: A
If 5 machines can produce 20 units in 10 hours, how long would it take 20 machines to produce 120 units?
Choose the correct choice:
A) 50 hours B) 40 hours C) 15 hours D) 12 hours E) 8 hours

Solution: Here, we're told that 5 machines can produce 20 units in 10 hours....   That means that EACH machine WORKS for 10 hours apiece. Since there are 5 machines (and we're meant to assume that each machine does the same amount of work), then the 5 machines equally created the 20 units.   20 units/5 machines = 4 units are made by each machine every 10 hours   Now that we know how long it takes each machine to make 4 units, we can break THIS down further if we choose to...   10 hours/4 units = 2.5 hours per unit when 1 machine is working.   The prompt asks us how long would it take 20 machines to produce 120 units.   If 20 machines each work for 2.5 hours, then we'll have 20 units. Since 120 units is '6 times' 20, we need '6 times' more TIME.   (2.5 hours)(6 times) = 15hours   Final Answer:   [Reveal]Spoiler:   15 hours
Answer: C
The length of the side of square A is twice the length of the side of square B. What is the ratio of the area of square A to the area of square B? Choose the correct choice from the following options.
A) 4:1  B) 1:1  C) 2:1  D) 1:2  E) 1:21

Solution: Solution   Let x be the length of the side of square A and y be the length of the side of square B with x = 2 y. Area of A and B are given by   A = x^2 and B = y^2   But x = 2y. Hence   4:1 = (2y)^2 = 4 y^2   The ratio of 4:1 to B is   4 y^2 / y^2 = 4 / 1 or 4:1   4:1NSWER IS 4:1
Answer: A