MU-NLPC/Calc-aqua_rat huggingface dataset:
2/5 of the fish in an aquarium are red and 1/4 of the fish are brown. 1/4 of the red fish and 2/5 of the brown fish are male. If the rest of the fish in the aquarium are female, what is the probability that a fish randomly picked from the aquarium is male?  Choose the correct choice:
A) 1/4	B) 1/5	C) 1/10	D) 1/12	E) 1/20

Solution: 1/4*2/5 + 2/5*1/4 = 1/5   The answer is 1/5.
Answer: B
If x is the product of three consecutive positive integers, which of the following must be true?
I. x is an integer multiple of 5.
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 partnership between A, B and C. A's capital is Rs.5000. If his share of a profit of Rs.800 is Rs.300 and C's share is Rs.130, what is B's capital?
Choose the correct choice from the following:
A) 19878
B) 12798
C) 6166
D) 11750
E) 22073

Solution: 300 + 130= 
300 + 130 = 430
430   800 - 430= 
800 - 430 = 370
370   300 ---- 5000   370 ---- ?=> 6166   Answer: 6166
Answer: C
If 10/b + 20/b + 30/b is an integer, which of the following must also be an integer? Choose the correct choice from the following answers
A) 20/b
B) b/16
C) 60/b
D) 4b
E) 4+b

Solution: If 10/b + 20/b + 30/b; then (10+20+30)/b is also integer.   i.e. 60/b is an integer.   Answer is 60/b
Answer: C
The president of a country and 2 other dignitaries are scheduled to sit in a row on the 3 chairs represented above. If the president must sit in the center chair, how many different seating arrangements are possible for the 3 people? Choose the correct choice from the following choices:	A) 4	B) 5	C) 20	D) 24	E) 2

Solution: IMO E   Given that one chair is taken, i think the remaining 2 dignitaries can be arranged 2!. That is 2*1= 
2*1 = 2
2.
Answer: E
There are 7 people and 7 chairs. In how many different ways people can occupy the chairs?  Pick
A) 5040
B) 4500
C) 3400
D) 6766
E) 120

Solution: number of ways =7! = 5040   5040nswer is 5040
Answer: A
What is the next number in the sequence below?
1 4 9 16 25 36 __ ? Choose the correct choice from the following:	A) 45	B) 46	C) 47	D) 48	E) 49

Solution: as the series of numbers are squares of numbers   1^2=1   2^2=4   3^2=9   and so on   therefore 7^2=49   ANSW49R:49
Answer: E
The compound ratio of 1:2, 2:5 and 3:10?
Answers
A) 1:2 B) 1:5 C) 3:5 D) 1:50 E) 3:50

Solution: 1/2 * 2/5 * 3/10 = 3/503:50Answer: 3:50
Answer: E
A machine P can print one lakh books in 8 hours, machine Q can print the same number of books in 10 hours while machine R can print them in 12 hours. All the machines are started at 9 a.m. while machine P is closed at 11 a.m. and the remaining two machines complete the work. Approximately at what time will the work be finished?	Choose the correct choice from the following choices:	A) 11 : 30 am	B) 12 noon	C) 12 : 30 pm	D) 1 pm	E) None of these

Solution: (P + Q + R)’s 1 hour’s work = (1⁄8 + 1⁄10 + 1⁄12) = 37⁄120   Work done by P, Q and R in 2 hours = (37⁄120 × 2) = 37⁄60   Remaining work = (1 - 37⁄60) = 23⁄60   (Q + R)’s 1 hour’s work = (1⁄10 + 1⁄12) = 11⁄60   Now, 11⁄60 work is done by Q and R in 1 hour.   So, 23⁄60 work will be done by Q and R in   (60⁄11 × 23⁄60) = 23⁄11 hours ≈ 2 hours.   So, the work will be finished approximately 2 hours after 11 a.m., i.e., around 1 p.m.   Answer 1 pm
Answer: D
Given the following equation 25% of 2475 + 20% of 2115 = x, Find the approximate value should come in place of the x. Choose the most appropriate option:
A) 1046	B) 1048	C) 1049	D) 1047	E) 1040

Solution: x = 25% of 2475 + 20% of 2115   x = 25/100*2475 + 20/100*2115= 
25/100*2475 + 20/100*2115 = 4_167/4 = around 1_041.75
1041.75   ≈ 1040   Answer 1040
Answer: E
A circle and a rectangle have the same perimeter. The sides of the rectangle are 18 cm and 26 cm. What is the area of the circle ? Choose the correct choice from the following.
A) 88 cm2 B) 154 cm2 C) 1250 cm2 D) 616 cm2 E) None of these

Solution: Perimeter of the circle = 2πr = 2(18 + 26)   ⇒ 2 × 22⁄7 × r = 88 ⇒ r = 14   ∴ Area of the circle   = πr2 = 22⁄7 × 14 × 14 = 616 cm2   Answer 616 cm2
Answer: D
A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. The sum is:  Choose the correct choice from the following answers:
A) Rs. 650	B) Rs. 690	C) Rs. 698	D) Rs. 700	E) None of these

Solution: Explanation :   S.I. for 1 year = Rs. (854 - 815) = Rs. 39.   S.I. for 3 years = Rs.(39 x 3) = Rs. 117.   Principal = Rs. (815 - 117) = Rs. 698.   Answer : Rs. 698
Answer: C
Find the number of factors R of 180 that are in the form (4*k + 2), where k is a non-negative integer?	Choose the correct choice from the following options.
A) 1
B) 2
C) 3
D) 4
E) R=6

Solution: As for the question, the most straightforward way is to list out the factors (this is fine for this question as 180 is a relatively small number). Number of factors of 180 R (=2^2*3^2*5) = 18. So listing the factors gives us:   1, 180   2, 90   3, 60   4, 45   5, 36   6, 30   9, 20   10, 18   12, 15   As the question asks us about the factors of the form 4k+2 ---> eliminate all ODD factors. You are now left with   2,4,6,10,12,18,20,30,36,60,90,180   For the form 4k+2, the first few values are 2, 6, 10, 14, 18, 22, 26, 30 ... already giving you 5 factors (=2,6,10,18,30). You can stop here and mark 6 (6th one = 90) as the correct answer as 5 is not given.   For checking any particular factor whether they conform to the form 4k+2---> do the following   4k+2 = 36 ---> 4k = 34 --> this will NOT give you an integer value for k ---> reject. Proceed with others until you find all the values asked.   R=6 is thus the correct answer.
Answer: E
A bus leaves Santa Barbara at 8:00 a.m. traveling east at 80 miles per hour. At 3:00 p.m. a plane leaves Santa Barbara traveling east at 360 miles per hour. At what time will the plane overtake the bus? Choose the most appropriate option:
A) 5:00 p.m.  B) 6:00 p.m.  C) 4:00 p.m.  D) 5:30 p.m.  E) 4:30 p.m.

Solution: 5:00 p.m.t 3:00pm, the bus is 560 miles ahead of plane   The plane travels at 360 mph, which gains 250 mph on bus   560/280= 4/3 hours = 120 minutes   3:00 + 2:00 = 5:00   The plane will overtake bus at 5:00pm   5:00 p.m.nswer:5:00 p.m.
Answer: A
Mary charges $8.50 per hour to clean a house. If she works 25 hours, how much
does she earn in one week?  Choices.
A) $612.50
B) $112.50
C) $212.50
D) $412.50
E) $312.50

Solution: Multiply 25 hours x $8.50 =   Answer: $212.50   correct answer $212.50
Answer: C
A train passes a station platform in 36 seconds and a man standing on the platform in 24 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
Choose the correct choice from the following:
A) 180
B) 240
C) 288
D) 267
E) 211

Solution: Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train = (15 x 24)m = 360 m. Let the length of the platform be x meters. Then, (x + 360)/36 = 15 ==> x + 360 = 540 ==> x = 180 m.180nswer: 180
Answer: A
There are 8 books in a shelf that consist of 3 paperback books and 5 hardback books. If 3 books are selected at random without replacement, how many different combinations are there that at least one paperback book is selected? Choose the correct choice:
A) 40	B) 46	C) 50	D) 55	E) 60

Solution: 8C3 [Select any four] -5C3 [Select all hard backs] = 46   46
Answer: B
The difference of the areas of two squares drawn on two line segments of different lengths is 32 sq	.cm. Find the length of the greater line segment if one is longer than the other by 2cm. Pick one.
A) 6 cm B) 7 cm C) 9 cm D) 11 cm E) None

Solution: Solution   Let the lengths of the line segments be x cm and (x + 2) cm.   Then (x+2)2 - x2 = 32   <=> x2+4x+4-x2 = 32   <=> 4x = 28   Therefore x = 7.   Length of longer line segment	= (7 + 2)= 
(7 + 2) = 9
9 cm.   Answer 9 cm
Answer: C
John makes $50 a week from his job. He earns a raise andnow makes $90 a week. What is the % increase?	Choices: A) 15% B) 16.66% C) 17.8% D) 80% E) 21%

Solution: Increase = (40/50)*100 = (4/5)*100= 
(4/5)*100 = 80
80%.   80%
Answer: D
You collect balls. Suppose you start out with 16. Mike gives you another 17 balls. How many balls do you have at the end?	Choose the correct choice from the following choices
A) 33 B) 34 C) 35 D) 36 E) 37

Solution: Solution   Start with 16 balls.   Mike gives you 17 balls:   16 + 17= 
  16 + 17 = 33
33 balls.   So you have 33 at the end.   Correct answer: 33
Answer: A
In your classes you counted 120 hands. How many students were at the class?  Choose the correct choice from the following options.
A) 60  B) 61  C) 85  D) 86  E) 88

Solution: Total number of hands = 120   We have 2 hands.   To find how many students were at the class, divide the total number of hands by the number of hands we have.   We get, divide 120 by 2   220 ÷ 2 = 60   Therefore, there were 60 students at the class.   60NSWER IS 60
Answer: A
In a certain candy store, 22% of the customers are caught sampling the candy and are charged a small fine, but 10% of the customers who sample the candy are not caught. What is the total percent of all customers who sample candy?  Choices.
A) 22%	B) 23%	C) 24.4%	D) 25%	E) 34%

Solution: Since 10% of the customers who sample the candyare notcaught, then 90% of the customers who sample the candyarecaught:   {% of customers who sample candy}*0.90 = 0.22;   {% of customers who sample candy} = 0.25.   Answer: 24.4%.
Answer: C
Find the area of the quadrilateral of one of its diagonals is 26 cm and its off sets 9 cm and 6 cm?	Choose the correct answer:
A) 188 cm2
B) 150 cm2
C) 168 cm2
D) 195 cm2
E) 987 cm2

Solution: 1/2 * 26(9 + 6)   = 195 cm2   Answer: 195 cm2
Answer: D
A rectangular park 60 m long and 40 m wide has two concrete crossroads running in the middle of the park and rest of the park has been used as a lawn. If the area of the lawn is 2109 sq. m, then what is the width of the road?	Choose the most appropriate option.
A) 2  B) 3.5  C) 3  D) 4  E) 5

Solution: Area of the park = (60 x 40) m2 = 2400 m2.   Area of the lawn = 2109 m2.   Area of the crossroads = (2400 - 2109) m2 = 291 m2.   Let the width of the road be x metres. Then,   60x + 40x - x2 = 291   x2 - 100x + 291 = 0   (x - 97)(x - 3) = 0   x = 3.   3)
Answer: C
A diet contains 400 grams of a mixture of two foods, food X and food Y. Food X contains 10 percent protein and food Y contains 15 percent protein. If a diet provides exactly 50 grams of protein daily, how many grams of food X are in the mixture?  Choose the correct choice from the following
A) 120 B) 140 C) 150 D) 160 E) 200

Solution: Let x be the number of grams of food X in the mixture.   0.1x + 0.15(400-x) = 50   0.05x = 10   x = 200   The answer is 200.
Answer: E
he number of sequences in which 5 players can throw a ball, so that the youngest player may not be the last is?	Options.
A) 96
B) 12
C) 50
D) 42
E) 18

Solution: x Not younger_______ ↑   The last ball can be thrown by any of the remaining 4 players. The first 4 players can throw the ball in 4P4 ways.   The required number of ways = 4(4!) = 4320   96nswer:96
Answer: A
The ratio of numbers is 3:4 and their H.C.F is 4. Their L.C.M is?  Choose the correct option.
A) 23
B) 77
C) 88
D) 48
E) 11

Solution: Let the numbers be 3x and 4x.   Then their H.C.F = x. So, x = 4.   So, the numbers are 12 and 16.   L.C.M of 12 and 16 = 48.   Answer:48
Answer: D
In an election, candidate Smith won 52% of the total vote in Counties A and B. He won 61% of the vote in County A. If the ratio of people who voted in County A to County B is 3:1, what percent of the vote did candidate Smith win in County B ? Choose the correct choice from the following choices:
A) 25%
B) 27%
C) 34%
D) 43%
E) 49%

Solution: Let total votes in County A = 3x.   Let total votes in County B = x.   Hence total votes in Count 25% & B together = 4x   Given that, 0.52(4x) = 0.61(3x) + n(x)   So, 2.08x = 1.83x + nx   So, n = 0.25 = 25%   Hence option 25%
Answer: A
A square mirror has exactly half the area of the rectangular wall on which it is hung. If each side of the mirror is 34 inches and the width of the wall is 54 inches, what is the length of the wall, in inches? Choose the correct choice from the following answers.
A) 22.8	B) 33.8	C) 42.8	D) 63.8	E) 56.8

Solution: Since the mirror is 42 inches in all sides, it must be a square. Area of a square is A=a^2; 34^2=1156.Area of rectangle is double of that 2 *1156= 
2 *1156 = 2_312
2312.Now A=lw and we need find w so A/l=w ; 2312/54= 42.8 Answer!   Answer is 42.8
Answer: C
A man can hit a target once in 4 shots. If he fires 4 shots in succession, what is the probability that he will hit his target?  Choose the correct choice from the following answers
A) 564/123  B) 646/458  C) 456/847  D) 175/256  E) 256/175

Solution: The man will hit the target if he hits it once or twice or thrice or all four times in the four shots that he takes.   So, the only possibility when the man will not hit the target is when he fails to hit the target in even one of the four shots that he takes.   The event of not hitting the target even once is the complement of the event of hitting the target at least once.   The probability that he will not hit the target in any given shot = 1 – 1/4 = ¾   Therefore, the probability that he will not hit the target in any of the four shots =3/4*3/4*3/4*3/4=81/256   The probability that he will hit the target at least in one of the four shots=1-81/256   =175/256   Ans: 175/256
Answer: D
In a certain zoo, the ratio of horses to penguins is 5 to 11. If there are 80 more penguins than horses at the zoo, how many horses are there? Pick:
A) 24	B) 36	C) 66	D) 72	E) 132

Solution: 5/11 = x / x+80   5*80 = 6x   x=66   C. 66
Answer: C
A watch was sold at a loss of 10%. If it was sold for Rs.190 more, there would have been a gain of 4%. What is the cost price?	Choose the correct option:
A) s.1000  B) s.1009  C) s.1007  D) s.1357.1  E) s.1002

Solution: Explanation:   90%   104%   --------   14% ---- 190   100% ---- ? => Rs.1357.1   Answer:s.1357.1
Answer: D
The C.P of 10 pens is equal to the S.P of 20 pens. Find his gain % or loss%?
Answers:
A) loss 16 2/8%
B) loss 50%
C) loss 16 2/3%
D) loss 18 2/3%
E) loss 16 25%

Solution: 10 CP = 20 SP   20 --- 10 CP loss   100 --- ? => 50% loss   Answer:loss 50%
Answer: B
A man has Rs. 160 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?	Pick:
A) 30  B) 60  C) 75  D) 90  E) 105

Solution: Answer : A   Let number of notes of each denomination be x.   Then, x + 5x + 10x = 160   16x = 160   x = 10.   Hence, total number of notes = 3x = 30.
Answer: A
Sarah is driving to the airport. After driving at 50 miles per hour for one hour, she realizes that if she continues at that same average rate she will be an hour late for her flight. She then travels 100 miles per hour for the rest of the trip, and arrives 30 minutes before her flight departs. How many miles did she drive in all?
Choose the correct choice.
A) 140  B) 175  C) 200  D) 245  E) 280

Solution: After driving at 50 miles per hourfor one hour, this distance left to cover is d-50. Say this distance is x miles.   Now, we know that the difference in time between covering this distance at 50 miles per hour and 100 miles per hour is 1+ 1/2 = 3/2 hours.   So, we have that x/50 - x/100 = 3/2 --> 2x/100 - x/100 = 3/2 --> x/100 = 3/2 --> x = 150   Total distance = x + 50 = 200 miles.   Answer: 200.
Answer: C
If v equals the sum of the odd integers from 5 to 505, inclusive, and q equals the sum of the odd integers from 3 to 303, inclusive, what is the value of v - q? Choose the correct choice from the following answers:
A) 1616
B) 153007
C) 40902
D) 1147612
E) 50503

Solution: Use following formulae for such problems:   Sum of evenly spaced integers = (# of integers)*(mean of integers)   # of integers = [(last - first)/2] + 1   Mean of integers = (last + first)/2   In above problem:   # of integers = [(505 - 5)/2] + 1= 251 and [(303-3)/2]+ 1 (505 - 5)/2  + 1= 
(505 - 5)/2  + 1 = 251
251 and [(303-3)/2]+ 1 = 151   Mean of integers (303-3)/2 + 1= 
(303-3)/2 + 1 = 151
151   Mean of integers= (505 + 5)/2= 
(505 + 5)/2 = 255
255 and   (303 + 3)/2= 
  (303 + 3)/2 = 153
153   Sum of integers= (251*255)= 
(251*255) = 64_005
64005 and   (151*153)= 
  (151*153) = 23_103
23103   Thus their difference (v - q)= 40902   ANSWER:40902
Answer: C
The compound ratio of 5:7, 3:2 and 4:5? Choose the correct choice from the following options
A) 1:7  B) 6:5  C) 6:7  D) 4:7  E) 6:9

Solution: 5/7 * 3/2 * 4/5 = 6/7   6:7   ANSWER:6:7
Answer: C
A computer wholesaler sells eight different computers and each is priced differently. If the wholesaler chooses three computers for display at a trade show, what is the probability (all things being equal) that the two most expensive computers will be among the three chosen for display?	Choose the correct choice from the following answers.
A) 15/56 B) 3/28 C) 1/28 D) 1/56 E) 1/168

Solution: Since, two of the choices are prefixed, we are free to choose 1 from the rest of the 6 avilable. so 6C1 is the numerator.   Total no of ways we can choose 3 from 8 is 8c3, which is the denominator.   So, the probability: 6c1/8c3= 3/28 ans is 3/28.
Answer: B
In how many ways, a committee of 5 members can be selected from 6 men and 5 ladies, consisting of 3 men and 2 ladies? Answers.
A) 150  B) 180  C) 200  D) 310  E) 250

Solution: (3 men out 6) and (2 ladies out of 5) are to be chosen   Required number of ways = 62003*52002 = 200   Answer is 200
Answer: C
Jerry and Michelle play a card game. In the beginning of the game they have an equal number of cards. Each player, at her turn, gives the other a third of her cards. Michelle plays first, giving Jerry a third of her cards. Jerry plays next, and Michelle follows. Then the game ends. Jerry ended up with 28 more cards than Michelle. How many cards did each player have originally?  Select:	A) 51	B) 52	C) 53	D) 54	E) 56

Solution: GameMichelle Jerry   Initially 54 54 assume   After game 1 36 72   After game 2 60 48   After game 3 40 68   Now Merry has 28 cards more than Michelle. This option gives us exactly what number of cards they had initially.   So the answer is 54
Answer: D
If a certain number is divisible by 12 and 10, it is NOT necessarily divisible by which of the following?  Choose the correct option
A) 4	B) 6	C) 15	D) 20	E) 24

Solution: If a certain number is divisible by 12 and 10, it is NOT necessarily divisible by which of the following?   let the certain number be 60, which is both divisible by 12 and 10.   60/24 = 5/2   ANSW24R:24
Answer: E
Each Machine of type X has 3 steel parts and 2 chrome parts. Each machine of type Y has 4 steel parts and 7 chrome parts. If a certain group of type X and type Y machines has a total of 20 steel parts and 22 chrome parts, how many machines are in the group	Choose the correct choice.
A) 2  B) 3  C) 6  D) 8  E) 9

Solution: Look at the below representation of the problem:   Steel Chrome total   X 3 2 20 >>no. of type X machines=20/5= 
20/5 = 4
4   Y 4 7 22 >>no. of type Y machines=22/11= 
22/11 = 2
2   So the answer is 6 i.e 6.
Answer: C
The average age of students in section A of 115 students is 15 years and the average age of students in section B of 120 students is 22 years. Find the average age of students in both sections taken together?  Select.
A) 26 years B) 30years C) 18years D) 25years E) 20years

Solution: The required average = (115*15+120*22)/115+120 = 18 years   Answer is 18years
Answer: C
The average of 10 numbers is calculated as 15. It is discovered later on that while calculating the average, one number namely 36 was wrongly read as 26. The correct average is? Options
A) 29 B) 8 C) 16 D) 99 E) 12

Solution: 10 * 15 + 36 – 26 = 160/10= 
160/10 = 16
16   Answer: 16
Answer: C
A man desired to get into his work building, however he had forgotten his code.
However, he did recollect five pieces of information
-> Sum of 5th number and 3rd number is 14.
-> Difference of 4th and 2nd number is 1.
-> The 1st number is one less than twice the 2nd number.
->The 2nd number and the 3rd number equals 10.
->The sum of all digits is 30.
Crack the code ?	Choose the correct choice from the following choices
A) 54658  B) 74658  C) 84658  D) 14658  E) 34658

Solution: 74658   74658   * 8 + 6 =14   * 5 - 4 = 1   * 7 = 2*4 - 1   * 4 + 6 = 10   * 7+4+6+5+8 = 30
Answer: B
In how many ways can the letters of the word, ‘KEYBOARD’ be arranged in such a way that the vowels always come together?
Pick:
A) 4250
B) 4520
C) 4320
D) 4230
E) 4530

Solution: In the word ‘KEYBOARD’ we treat the vowels EOA as one letter. Thus, we have KYBRD (EOA).   Thus we have 6 letters can be arranged in 6! = 720 ways   The vowels (EOA) can be arranged among themselves in 3! = 6 ways   Therefore, Required number of ways= (720*6)= 
(720*6) = 4_320
4320   ANSWER:4320
Answer: C
If a certain sample of data has a mean of 21.0 and the value 42.0 is more than 2.5 standard deviations from the mean, which of the following could be the standard deviation of the sample
Choose the most appropriate option.
A) 8.3  B) 7.3  C) 7.5  D) 6.5  E) 6.2

Solution: 42.0 is more than 2.5 standard deviations from 21 --> 42 > 21 + 2.5*{SD} --> 2.5*{SD} < 21 --> {SD} < 8.4. Only option A offers the standard deviation less than 8.4.   8.3nswer: 8.3
Answer: A
There r 3 boys & 4 girls; Howmany ways they r arranged such that boys should be always together ?
Choices
A) 120ways B) 220ways C) 420ways D) 720ways E) 520ways

Solution: By kept 3boys together(1) and arranging 4 girls with them   5! = 5*4*3*2*1= 
5*4*3*2*1 = 120
120ways. (i.e., 4+1=5)   Possible arrangements of 3 boys in following ways   3! = 3*2*1= 
3*2*1 = 6
6ways   Now, arrange all with the boys together     120*6= 
  120*6 = 720
720ways   ANSWER:720ways
Answer: D
Five machines, each working at the same constant rate, together can complete a certain job in 20 days. How many additional machines, each working at the same constant rate, will be needed to complete the job in 10 days?
Answers.
A) 4	B) 6	C) 8	D) 5	E) 10

Solution: Rate of one machine = 1 job / (20*5) days   let X = number of machines needed to complete the job in 10 days   1/(5*20) * 10 * X = 1 job   X = 10   10-5= 
10-5 = 5
5   ANSWER: 5
Answer: D
Jeya decided to save a certain amount of her monthly salary each month and her salary was unchanged from month to month. If Jeya's savings by the end of the year from these monthly savings were two times the amount she spent per month, what should be the fraction of her salary that she spent each month?	Pick one:
A) 5/7
B) 6/7
C) 9/7
D) 5/7
E) 4/7

Solution: Let Jeya's monthly savings = S   Jeya's monthly pay = P   Jeya's monthly expenditure = P-S   Jeya's savings by the end of the year from these monthly savings were two times the amount she spent per month   12S = 2*(P-S)   =>6S = P-S   => P = 7S   Jeya's monthly expenditure = P-S = 7S-S = 6S   fraction of her salary that Jeya spent each month = 6S / 7S=P-S/P = 6/7. Answer is 6/7
Answer: B