MU-NLPC/Calc-aqua_rat huggingface dataset:
Two boys starting from the same place walk at a rate of 5kmph and 5.5kmph respectively. What time will they take to be 8.5km apart, if they walk in the same direction?
Choose the correct choice:
A) 67 hours	B) 47 hours	C) 17 hours	D) 27 hours	E) 16 hours

Solution: Explanation:   In this type of questions we need to get the relative speed between them,   The relative speed of the boys = 5.5kmph â€“ 5kmph   = 0.5 kmph   Distance between them is 8.5 km   Time = Distance/Speed   Time= 8.5km / 0.5 kmph = 17 hrs   Answer: 17 hours
Answer: C
The speed of the boat in still water in 12 kmph. It can travel downstream through 60 kms in 3 hrs. In what time would it cover the same distance upstream?	Choose the correct choice from the following answers:
A) 8 hours	B) 6 hours	C) 4 hours	D) 15 hours	E) 6 hours

Solution: Still Water=12km/hr   15 hoursownstream=60/3= 
60/3 = 20
20km/hr   Upstream=>> still water=(u+v/2) =>> 12=u+20/2 = 4km/hr   So time taken in upstream = 60/4= 
60/4 = 15
15hrs   ANSWER:15 hours
Answer: D
Two stations A and B are 110 km apart on a straight line. One train starts from A at 6 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?
Choose the correct choice from the following answers: A) 11 B) 10 C) 9 D) 12 E) 15

Solution: Suppose they meet x hours after 6 a.m.   Distance covered by A in x hours = 20x km.   Distance covered by B in (x - 1) hours = 25(x - 1) km.   Therefore 20x + 25(x - 1) = 110   45x = 135   x = 3.   So, they meet at 9 a.m.   Answer: 9
Answer: C
A car gets 20 kilometers per gallon of gasoline. How many gallons of gasoline would the car need to travel 180 kilometers? Select.
A) 8.5 gallons	B) 9 gallons	C) 6.5 gallons	D) 5.5 gallons	E) 6 gallons

Solution: Each 20 kilometers, 1 gallon is needed. We need to know how many 20 kilometers are there in 180 kilometers?   180 / 20= 
180 / 20 = 9
9 * 1= 
9 * 1 = 9
9 gallons correct answer 9 gallons
Answer: B
the probability of a student possessing a ball point pen in exam is 3/5 & possessing an ink pen is 2/3. find his probability of possessing at least one of them	Options
A) 10/15  B) 11/15  C) 12/15  D) 13/15  E) 14/15

Solution: the probability of a student possessing a ball point pen in exam is 3/5 .   the probability of a student not possessing a ball point pen in exam is 2/5 & possessing an ink pen is 2/3.   & not possessing an ink pen is 1/3.   his probability of possessing none of them =2/5*1/3=2/15   his probability of possessing one of them =1-2/15 = 13/15   ANSWER:13/15
Answer: D
Camel and carriage for Rs. 5000. He SP the camel at a gain of 20% and the carriage at a loss of 10%. If he gains 3% on the whole, then find the CP of the camel?
Choose one:
A) Rs.2166.67
B) Rs.2145.67
C) Rs.2157
D) Rs.2167.1
E) Rs.2178.34

Solution: Now, in this numerical, there is no common loss and gain %.   Hence, solve it making equations.   Let cost price of camel be x.   As cost of camel and carriage = Rs 5000   Cost of carriage = Rs. (5000 – x)   After selling camel he gains 20% and on carriage a loss of 10%. But on the whole he gains 3%.   Therefore,   20% of x – 10 % of (5000 – x) = 3 % of 5000   20 × x – 10 × (5000 – x) = 3 × 5000   100 100 100   x – (5000 – x) = 150   5 10   10x – (5000 – x) × 10 = 150 × 10   5 10   2x-5000+x=1500   3x=1500+5000   x=2166.67   The cost of camel = Rs.2166.67   Option (Rs.2166.67) is the correct answer
Answer: A
The difference between C.I. and S.I. on an amount of Rs. 15,000 for 2 years is Rs. 294. What is the rate of interest per annum?
Pick.
A) 18 B) 12 C) 9 D) 14 E) 16

Solution: Explanation:   [15000 * (1 + R/100)2 - 15000] - (15000 * R * 2)/100 = 294   15000[(1 + R/100)2 - 1 - 2R/100] = 294   15000[(100 + R)2 - 10000 - 200R]/10000 = 294   R2 = (294 * 2)/3= 
(294 * 2)/3 = 196
196=> R = 14   Rate = 14%   Answer: Option 14
Answer: D
A certain sum of money is divided among A, B and C so that for each Rs. A has 80 paisa, B has 65 paisa and C 40 paisa. If C's share is Rs.40, find the sum of money?	Pick one
A) Rs.185
B) Rs.410
C) Rs.285
D) Rs.385
E) Rs.475

Solution: Rs.185:B:C = 80:65:40   = 16:13:8   8 ---- 40   37 ---- ? => Rs.185   Rs.185NSWER:Rs.185
Answer: A
The perimeter of a triangle is 28 cm and the inradius of the triangle is 2.5 cm. What is the area of the triangle
Select the correct option:
A) 72 B) 828 C) 729 D) 34 E) 35

Solution: Explanation:   Area of a triangle = r * s   Where r is the inradius and s is the semi perimeter of the triangle.   Area of triangle = 2.5 * 28/2= 
2.5 * 28/2 = 35
35 cm2   Answer: Option 35
Answer: E
How many FIVE letter words are formed using the letters of the word LEADER? Choose the correct choice from the following options
A) 860  B) 720  C) 230  D) 460  E) 940

Solution: The number of letters in the given word is 6.   The number of FIVE letter words that can be formed using these four letters is 6P5=6*5*4*3*2= 
6*5*4*3*2 = 720
720   Answer:720
Answer: B
10 distinct integers are arranged in ascending order. The range of the first 7 is 25 and that of last 7 is 30. What is the maximum range M of the 10 numbers? Answers.
A) 25	B) 27	C) 30	D) 52	E) 55

Solution: Positions: 1 2 3 4 5 6 7 8 9 10   Given: 1st position = x; 4th position = a; 7th position = y; 10th position = b   y - x = 25   Let x be 0 and y = 25. We are asked to maximize the range and the integers are distinct.   b - a = 30 --> b = 30 + a   In order to increase the range, we have to maximize the value of 'b'.   'b' can be maximized by taking the max value of 'a'.   From the assumed values, maximum value of 'a' can be 22.   Therefore, b = 30 + 22= 
30 + 22 = 52
52   Range M= 52 - 0= 
52 - 0 = 52
52   Answer: 52
Answer: D
Keshav runs a factory in three shifts of eight hours each with 210 employees. In each shift minimum of 80 employees are required to run the factory effectively. No employees can be allowed to work for more than 16 hours a day. At least how many employees will be required to work for 16 hours every day? Select:
A) 30
B) 40
C) 50
D) 60
E) 70

Solution: total 210 employees and There are 3 shifts of 8 hrs.   per each shift no of employees = 210/3= 
210/3 = 70
70.   But Per each shift 80 employees are required.   so employess need to work for 16 hrs=80-70= 
80-70 = 10
10.   for 3shifts,10*3=30   i.e 30 employees required to work 16 hrs every day.   30NSWER:30
Answer: A
If x and y are positive integers such that y is a multiple of 5 and 3x + 4y = 600, then x must be a multiple of which of the following?  Pick.
A) 3.	B) 6.	C) 7.	D) 8.	E) 10.

Solution: If y is a multiple of 5, then 4y is also a multiple of 5.   3x = 600 - 4y   600 - 4y is even and it is a multiple of 5.   Thus x must also be even and a multiple of 5.   Therefore x must be a multiple of 10.   The answer is 10..
Answer: E
The captain of a cricket team of 11 members is 26 years old and the wicket keeper is 3 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. Find out the average age of the team.
Pick:
A) 23 years  B) 20 years  C) 24 years  D) 21 years  E) 22 years

Solution: Explanation:   Number of members in the team = 11   Let the average age of of the team = x   => Sum of ages of all 11 members/11=x   => Sum of the ages of all 11 members = 11x   23 yearsge of the captain = 26   23 yearsge of the wicket keeper = 26 + 3= 
26 + 3 = 29
29   Sum of the ages of 9 members of the team excluding captain and wicket keeper=11x−26−29=11x−55   23 yearsverage age of 9 members of the team excluding captain and wicket keeper   =11x−5/59   Given that 11x−55/9=(x−1)   ⇒11x−55=9(x−1)   ⇒11x−55=9x−9   ⇒2x=46   ⇒x=46/2= 
46/2 = 23
23 years   23 yearsnswer: Option 23 years
Answer: A
A circle of radius 10 inches has its center at the vertex C of an equilateral triangle ABC and passes through the other two vertices. The side AC extended through C intersects the circle at D. The number of degrees of angle ADB is:  Choose the correct choice
A) 27	B) 30	C) 837	D) 37	E) 18

Solution: Answer: 30
Answer: B
Jake remembers only the last three letters of his four-letter Klingon name. If he is sure that the first letter is neither "N" nor "X", and assuming that there are only 15 letters in the Klingon alphabet, what is the probability that he will give the correct name when asked for it by the space attendant?
Select the correct option.
A) A)8/100
B) B)9/100
C) C)1/8
D) D)1/13
E) E)9/10

Solution: Total letters 15, out of which the first letter is anything of 10 but N or X...   So there are 13 possible letters for first place..   And only one of them is correct..   So 1/13   Answer: 1/13
Answer: D
? x 12 = 173 x 240  Options:
A) 3460
B) 685
C) 865
D) 495
E) 534

Solution: Let y x 12 = 173 x 240   Then y = (173 x 240) / 12   =3460   3460NSWER :3460
Answer: A
A seller mixed 4 dozen bananas costing Rs.12 per dozen with 6 dozen bananas at Rs.8 per dozen then what is the cost price of mixed bananas per dozen? Choose the correct choice from the following:
A) Rs.6.40	B) Rs.10	C) Rs.9.6	D) Rs.10.2	E) None of the above

Solution: 4 dozens of bananas cost is rs12   then   4*12= 
  4*12 = 48
48   6 dozens of bananas cost is rs8   then   6*8= 
  6*8 = 48
48   48+48/4+6=96/10= 
96/10 = 48/5 = around 9.6
9.6   ANSWER:Rs.9.6
Answer: C
Walking across campus, a student interviewed a group of students. 20% of the students took a finance class last semester, 45% took a marketing class last semester, and 40% took neither a finance nor a marketing class last semester. What percent of the students in the group took both a finance and a marketing class? Choose the correct choice from the following options.
A) 60%
B) 50%
C) 25%
D) 15%
E) 5%

Solution: {Total} = {finance} + {marketing} - {both} + {neither}   100 = 20 + 45 - {both} + 40   {both} = 5%.   The answer is 5%.
Answer: E
In an examination 42% students failed in Hindi and 52% failed in English. If 17% failed in both of these .subjects, what is the percentage of students who passed in both the subjects ? Choose one
A) 52	B) 25	C) 72	D) 35	E) 23

Solution: Hindi = 42% - 17% =25%   English 42  - 17= 
42  - 17 = 25
25%   English= 52% - 17% = 35%   Middle is 17%.   so 35 in 23nglish and 25 in Hindi which means that 35+25+17 52  - 17= 
52  - 17 = 35
35%   Middle is 17%.   so 35 in 23nglish and 25 in Hindi which means that 35+25+17= 
35+25+17 = 77
77% 100%-77%= 23%   Therefore 23% passes both   Answer : 23
Answer: E
Find the least number that must be subtracted from 1387 so that the remaining number is divisible by 15.
Choose the correct option.
A) 1
B) 5
C) 7
D) 9
E) 13

Solution: On dividing 1387 by 15 we get the remainder 7, so 7 should be subtracted. The answer is 7.
Answer: C
A 270 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train? Choose one: A) 230m B) 240m C) 250m D) 260m E) 270m

Solution: speed = (120 + 80)km/h (because direction is opposite hence relative velocity is added)= 500/9 m/s   time= 9sec   let the lenght of second train is x   total distance covered= 270 + x   therefore, D= speed*time   thus 270 + x = 500/9 * 9= 
500/9 * 9 = 500
500-270= 
500-270 = 230
230 m   230mNSWER:230m
Answer: A
The probabilities of solving a question by 3students A, B & C are 1/2,1/3 &1/4, respectively. The probability that the problem will be solved is?	Choose the correct choice from the following answers:
A) 2/3 B) 3/4 C) 3/5 D) 3/7 E) 4/7

Solution: Sol. First, we find the probability of not solving the problem x PTO x = (1 — D x - D x - D   1 2 3 1 =iXiX71=4;   1 3 Required probability 3/4   3/4
Answer: B
A classroom has equal number of boys and girls. TEN girls left to play kho-kho, leaving twice as many boys as girls in the classroom. What was the total number of girls and boys present initially?	Options:
A) 16
B) 24
C) 32
D) 48
E) 40

Solution: after 10 girls left remaining 10 girls   now boys 20 are twice as many as remaining girls.   initially boys=20 and girls=20.   ANSW40R:40
Answer: E
Celine worked for h hours each day for d consecutive days. If she earns $7.50 per hour, what is the total amount she earned?
Choose the correct choice.
A) 7.50/d + h  B) 7.50 + d + h  C) 7.50 + dh  D) 7.50dh  E) 7.50h + d

Solution: H hours for d days.   Income each day = 7.5*h   Total income = 7.5*h*d   Correct option: 7.50dh
Answer: D
The ‘moving walkway’ is a 300-foot long conveyor belt that moves continuously at 3 feet per second. When Bill steps on the walkway, a group of people that are also on the walkway stands 120 feet in front of him. He walks toward the group at a combined rate (including both walkway and foot speed) of 6 feet per second, reaches the group of people, and then remains stationary until the walkway ends. What is Bill’s average rate of movement Q for his trip along the moving walkway?
Pick one
A) 2 feet per second
B) 2.5 feet per second
C) 3 feet per second
D) 4 feet per second
E) 5 feet per second

Solution: I get E.   Their rate is 3 ft/sec and his is 6 ft/sec. Their distance is d-120 and his distance is d.   So we get two equations:   3t=d-120   6t=d   Substituting, we get 3t=6t-120, or t=40 which means that d=240 so Bill traveled 240 ft and they traveled 120 ft. (They were at 240 on the conveyor belt when they met.   So, Bill's average rate of movement Q is:   He traveled 6 ft/sec for 240 ft and 40 seconds. He traveled 3 ft/sec for the remaining 60 ft for 20 seconds.   (240+60)/(20+40)= 
(240+60)/(20+40) = 5
5 ft/sec=5 feet per second
Answer: E
What percentage of numbers from 1 to 70 have 1 or 9 in the unit's digit?
Answers
A) 6 B) 9 C) 24 D) 20 E) 29

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 70 are 1, 9, 11, 19, 21, 29, 31, 39, 41, 49, 51, 59, 61, 69.   Number of such number =14   Required percentage =14	x 100	% = 20%   Answer:24
Answer: C
A salesperson received a commission of 3 percent of the sale price for each of the first 100 machines that she sold and 4 percent of the sale price for each machine that she sold after the first 100. If the sale price of each machine was $10,000 and the salesperson received a $38,000 commission, how many machines did she sell? Select:
A) 90
B) 103
C) 105
D) 115
E) 120

Solution: First 100 machines = 3% commission = 0.03*100*10000= 
0.03*100*10000 = 30_000
30000   Commission from sale of next machines= 38000 - 30000= 
38000 - 30000 = 8_000
8000   So 20 more machines..   Total= 120 machines   IMO 120...
Answer: E
The cost of an article is decreased by 10%. If the original cost is $100, find the decrease cost.
Choose the correct choice from the following answers:
A) 33
B) 11
C) 68
D) 36
E) 90

Solution: Original cost = $100   Decrease in it = 10% of $100   = 10/100 Ã—100   = 1000/100= 
1000/100 = 10
$10   Therefore, decrease cost= $100 - $10 = $90   Answer:90100 -  10= 
100 -  10 = 90
$90   Answer:90
Answer: E
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 $1.95?	Choose the correct choice from the following answers
A) 980	B) 1170	C) 1530	D) 1720	E) 1960

Solution: The charge is 65 cents for the first 250 grams.   This leaves a charge of $1.95 - $0.65 = $1.30   The charge for the next 1200 grams is $1.20 which leaves a charge of $0.10   The weight is somewhere between 1450 and 1550.   The answer is 1530. 1.95 -  0.65= 
 1.95 -  0.65 = 1.3
$1.30   The charge for the next 1200 grams is $1.20 which leaves a charge of $0.10   The weight is somewhere between 1450 and 1550.   The answer is 1530.
Answer: C
A cistern has a leak which would empty the cistern in 20 minutes. A tap is turned on which admits 6 liters a minute into the cistern, and it is emptied in 24 minutes. How many liters does the cistern hold? Choose the correct answer:
A) 480  B) 487  C) 720  D) 729  E) 268

Solution: 1/x - 1/20 = -1/24   x = 120   120 * 6= 
120 * 6 = 720
720   Answer:720
Answer: C
A person spent Rs. 6,040 from his salary on food and 8,000 on house rent. After that he was left with 70% of his monthly salary. What is his monthly salary ? Choose the correct choice from the following choices:
A) 46,800
B) 66,800
C) 56,800
D) 26,800
E) 76,800

Solution: Total money spent on food and house rent = 6,040+8,000 = 14,040   Which is 100 - 70= 
100 - 70 = 30
30% of his monthly salary   ∴ His salary= 14040x100/30 = 46800   46,800nswer : 46,800
Answer: A
Mary passed a certain gas station on a highway while traveling west at a constant speed of 40 miles per hour. Then, 15 minutes later, Paul passed the same gas station while traveling west at a constant speed of 60 miles per hour. If both drivers maintained their speeds and both remained on the highway for at least 2 hours, how long after he passed the gas station did Paul catch up with Mary?
Choose the correct choice from the following answers:  A) 1/2  B) 2  C) 1  D) 4  E) 5

Solution: d = rt   M: r = 40 mph, t = t + 1/4hr   d = 40 (t + 1/4)   P: r = 60, t = t   d = 60t   since they went the same distance:   40t + 40/4 = 60t   20t = 40/4   t = 1/2 or 1/2 hr   1/2
Answer: A
Two men A and B start from place X walking at 4 ½ kmph and 5 ¾ kmph respectively. How many km apart they are at the end of 3 ½ hours if they are walking in the same direction?  Choose the correct choice from the following answers:
A) 7 km
B) 6 km
C) 4 3/8 km
D) 9 km
E) 5 km

Solution: RS = 5 ¾ - 4 ½ = 1 ¼   T = 3 ½ h.   D = 5/4 * 7/2 = 35/8   = 4 3/8 km   Answer:4 3/8 km
Answer: C
In a particular gumball machine, there are 4 identical blue gumballs, 3 identical red gumballs, 2 identical green gumballs, and 1 yellow gumball. In how many different ways can the gumballs be dispensed, 1 at a time, if the 3 red gumballs are dispensed last?
Select: A) 105 B) 210 C) 315 D) 420 E) 630

Solution: Since the red gumballs are being dispensed last they will not impact the number of permutations of the other gumballs, so we can effectively ignore them. (There is only one way for the three red gumballs to be dispensed last (RRR), so we will multiply the number of permutations of the other colours by 1).   The remaining gumballs are: 4 blue, 2 green, 1 yellow. 7 gumballs in total, so they can be arranged in 7! ways. But since the gumballs of each colour are identical, we must divide by the arrangements of each colour.   Total arrangements of the 7 gumballs = 7!/4!∗2!∗1!=7∗6∗5/2=105   So total arrangements of the 10 gumballs, with all 3 reds chosen last is 105 *1= 
105 *1 = 105
105   105nswer: 105
Answer: A
A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:	Answers.
A) 35 km/hr	B) 50 km/hr	C) 45 km/hr	D) 65 km/hr	E) 87 km/hr

Solution: Speed of the train relative to man   = (125/10) m/sec = (25/2) m/sec. [(25/2) * (18/5)] km/hr   = 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed   = (x - 5) km/hr. x - 5 = 45 ==> x = 50 km/hr.   Answer: 50 km/hr
Answer: B
What least number must be subtracted from 427398 so that remaining number is divisible by 15	Options:
A) 3 B) 5 C) 7 D) 9 E) None of these

Solution: Explanation:   On dividing 427398 by 15 we get the remainder 3, so 3 should be subtracted   3nswer: Option 3
Answer: A
A man gains 20% by selling an article for a certain price. If the sells it at double the price, the percentage of profit will be:	Choose the correct choice from the following:
A) 130  B) 220  C) 140  D) 120  E) 145

Solution: C   140%   Let C.P. = $x.   Then, S.P. = $(12% of x) = $6x/5   New S.P. = 2 * 6x/5 = $12x/5   Profit = 12x/5 - x = $7x/5   Profit = 7x/5 * 1/x * 100 = 140%.
Answer: C
The age of teacher is the same as the digit in the student's age, but in reverse order. In five years teacher will be twice as old as student will be then. what is the difference in their current age ?	Select the correct option
A) 18  B) 12  C) 25  D) 13  E) 7

Solution: Teacher's age= 10x+y so student's age= 10y+x..   after 5 years , 10x+y+5=2*(10y+x+5)....   so 5+19y=8x... check for odd values of y, y=1 satisfies the eqn with x=3... so ages are 31 and 13 and ans as found correctly by u is 18..18
Answer: A
A farm has only chickens and pigs. When the manager of the farm counted the heads of the animals on the farm, the number totaled up to 80. When the number of legs was counted, the number totaled up to 218. How many more chickens than pigs are there on the farm? Note: Each pig has 4 legs and each chicken had 2 legs.  Choose the correct option:
A) 16  B) 18  C) 20  D) 22  E) 24

Solution: Let x be the number of chickens.   Then 80-x is the number of pigs.   2x+4(80-x)=218   2x=102   x=51 (chickens)   70-x=29 (pigs)   There are  51-29= 
 51-29 = 22
22 more chickens on the farm.   The answer is 22.
Answer: D
In what time will a train 400 meters long cross an electric pole, if its speed is 144 km/hr
Answers:
A) 5 seconds B) 4.5 seconds C) 10 seconds D) 2.5 seconds E) None of these

Solution: Explanation:   First convert speed into m/sec   Speed = 144*(5/18)= 
144*(5/18) = 40
40 m/sec   Time= Distance/speed   = 400/40= 
400/40 = 10
10 seconds   Answer: 10 seconds
Answer: C
If 2 cards are selected at random from the deck of 52 cards then What is the probability of one of the selected cards will be 10 and other will be Queen?
A deck of cards has a total of 52 cards, consisting of 4 suits; (spades(Black), hearts(Red), diamond(Red)s, and clubs(Black)); and 13 cards including 1 king, 1 queen and 1 jack in each suit Select:
A) 8/2652
B) 1/2652
C) 12/2652
D) 18/2652
E) 16/2652

Solution: 2 possible cases:   10 - Queen or Queen -10 (4 kings and 4 queens).   Either way,   the total probability = 2( 10 -Queen) = 2 (4/52 * 4/51) = 18/2652. 18/2652 is the correct answer.
Answer: D
If a positive odd integer N has p positive factors, how many positive factors will 4N have ? Choose the correct choice:
A) p
B) 2p
C) P+1
D) 2p+1
E) Cannot be determined

Solution: I have added some extra text to make this question more GMAT-like:   Let's TEST some values of N   Try N = 3   The factors of 3 are {1, 3}. Here, p =2   So, 2N = (2)(3) = 6   The factors of 6 are {1, 2, 3, 6}. So, we have a total of4   Now check the answer choices:   A) p =2No good. We want an output of4. ELIMINATE   B) 2p = (2)(2) = 4. PERFECT! KEEP B   C) P+1 =2+ 1= 
2+ 1 = 3
3 No good. We want an output of4. ELIMINATE   D) 2p+1= (2)(2) + 1 = 5 No good. We want an output of4. ELIMINATE   E) Cannot be determined. POSSIBLE. KEEP E   Let's TEST another value of N   Try N = 7   The factors of 7 are {1, 7}. Here, p =2   So, 2N = (2)(7) = 14   The factors of 14 are {1, 2, 7, 14}. So, we have a total of4   Now check the REMAINING answer choices:   B) 2p = (2)(2) =4. PERFECT! KEEP B   E) Cannot be determined. POSSIBLE. KEEP E   Let's TEST one more (non-prime) value of N   Try N = 9   The factors of 9 are {1, 3, 9}. Here, p =3   So, 2N = (2)(9) = 18   The factors of 18 are {1, 2, 3, 6, 9}. So, we have a total of6   Now check the REMAINING answer choices:   B) 2p = (2)(3) =6. PERFECT! KEEP B   E) Cannot be determined. POSSIBLE. KCannot be determinedCannot be determinedP Cannot be determined   At this point, it SCannot be determinedCannot be determinedMS LIKCannot be determinedLY that the correct answer is Cannot be determined
Answer: E
A man rows his boat 84 km downstream and 60 km upstream, taking 4 hours each time. Find the speed of the stream?
Answers:	A) 76 kmph	B) 6 kmph	C) 14 kmph	D) 8 kmph	E) 3 kmph

Solution: Speed downstream = d/t = 84/(4)= 
84/(4) = 21
21 kmph   Speed upstream= d/t = 60/(4)= 
60/(4) = 15
15 kmph   The speed of the stream= (21 - 15)/2= 
(21 - 15)/2 = 3
3 kmph   Answer:3 kmph
Answer: E
Running at their respective constant rate, machine X takes 2 days longer to produce w widgets than machines Y. AT these rates, if the two machines together produce 5w/4 widgets in 3 days, how many days would it take machine X alone to produce 2w widgets. Choose the correct choice from the following answers
A) 4	B) 6	C) 8	D) 10	E) 12

Solution: rx*(t+2) = w   ry*(t) = w.   Also, w/(t+2) + w/t = (5w/4)*(1/3)   or 1/t + 1/(t+2) = 5/12 --> (3+2)/12 = 1/4+1/6   Thus, t = 4. Replacing, rx = w/6,   w/6*T = 2w   or T = 12 days.   ANSW12R:12
Answer: E