MU-NLPC/Calc-aqua_rat huggingface dataset:
The line K represented by which of the following equation does not intersect with the line represented by y = 3x^2+5x+1  Select the correct option.
A) y = 2x^2+5x+1	B) y = x^2+5x+2	C) y = 3x^2+5x+2	D) y = 3x^2+7x+2	E) y = x^2+7x+1

Solution: concept of slope for linesparabolas are different. Bunuel, please correct if I am wrong. Also please help to solve this problem if its a GMAT type question.   The general form of parabolic equ. is y^2= 4ax which implies the axis is x or x^2 = 4ay where axis is y.   We have a similar form as x^2 = 4ay.   here the vertex is origin.   So if we have same values of x and y but constant term changes then we will have parallel parabolas.   This is same as for straight line K which are parallel for different values of constant term c   ax + by +c1 = 0 and ax +by+ c2 =0   We have quadratic equations. These equations when drawn give parabolas, not lines. The question is: which of the following parabolas does not intersect with the parabola represented by y=3x^2+5x+1.y = 3x^2+5x+2
Answer: C
A town's oldest inhabitant is x years older than the sum of the ages of the Lee triplets. If the oldest inhabitants is now J years old, how old will one of the triplets E be in 20 years?
J-X-40/3 is my answers.
J = X + L + L + L is the initial situation
After 20 years
J + 20 = X + L + L + L + 60 ...20 years for each triplet so 60 years totally.
J - X - 40/ 3 = L is my answer.
What wrong am i doing ? Since the age asked is after 20 years i also consider adding 20 years to J .	Answers.
A) (J - 50)/3	B) 3(J + 20)/x	C) (J + x - 50)/3	D) (J - x + 60)/3	E) (J + x - 20)/3

Solution: here it goes:   Oldest inhabitant = sum of age of triplets + X   J = 3L + X so L = (J - X)/3   After 20 years = L + 20   E= (J - X)/3 + 20   = (J - X + 60)/3=(J - x + 60)/3
Answer: D
Circular gears P and Q start rotating at the same time at constant speeds. Gear P makes 10 revolutions per minute and Gear Q makes 40 revolutions per minute. How many seconds after the gears start rotating will gear Q have made exactly 5 more revolutions than gear P?  Options: A) 6 B) 8 C) 10 D) 12 E) 15

Solution: Gear Q makes 30 more revolutions each 60 seconds.   The time to make 5 = 30/6 more revolutions is 60/6= 
60/6 = 10
10 seconds.   The answer is 10.
Answer: C
If n is an integer greater than 5, which of the following must be divisible by 3? Pick one:
A) 1. n (n+1) (n-4)  B) 2. n (n+2) (n-1)  C) 3. n (n+3) (n-5)  D) 4. n (n+4) (n-2)  E) 5. n (n+5) (n-6)

Solution: We need to find out the number which is divisible by three,   In every 3 consecutive integers, there must contain 1 multiple of 3.   So n+4 and n+1 are same if we need to find out the 3's multiple. replace all the numbers which are more than or equal to three   1. n (n+1) (n-4) = > n(n+1)(n-1) = > (n-1)n(n+1)   2. n (n+2) (n-1) = > n(n+2)(n-1) = > (n-1)n(n+1)   3. n (n+3) (n-5) = > n(n+0)(n-2) = > (n-2)n(n)   4. n (n+4) (n-2) = > n(n+1)(n-2) = > (n-2)n(n+1)   5. n (n+5) (n-6) = > n(n+2)(n-0) = > (n)n(n+2)   from the above onlyoption Ais product of consecutive three numbers.   5. n (n+5) (n-6)
Answer: E
What is the least number should be added to 1056, so the sum of the number is completely divisible by 29?  Choose the correct option: A) 17 B) 27 C) 37 D) 47 E) 57

Solution: (1056 / 29) gives remainder 12   17 + 12= 
17 + 12 = 29
29, So we need to add 17   17
Answer: A
If a is an integer, what is the greatest possible value for a that would still make the following statement true: 11*10^a < 1/10 ?	Choose one:
A) –4
B) –3
C) –2
D) –1
E) 0

Solution: Just putting values, the LHS becomes   a=0 --> 11   a=-1 --> 11/10   a=-2 --> 11/100   a=-3 --> 11/1000   Anything lower will be smaller than 11/1000. a=-2, equality does not hold but it does for a=-3.   Answer is –3.
Answer: B
The average expenditure of the hotel when there are 10 guests is Rs. 60 per guests and the average expenditure is Rs.40 when there are 20 Guests. If it is known that there are some fixed expenses irrespective of the number of guests then the average expenditure per guest whe there are 40 guests in the hotel? Choose the correct choice from the following choices:
A) Rs.30 B) Rs.32 C) Rs.31 D) Rs.39 E) Rs.12

Solution: Answer: A) Rs. 30   Explanation:   Let the fixed expenditure of the hotel be Rs.x and the variable expenditure ( which is dependent on the guest ) is Rs.y , then   x + 10y = 600 ---------(1)   x + 20y = 800 ----------(2)   10y = 200   y = Rs. 20 and x= 400   Hence the total expenditure when there are 40 guests = 400 + 40 x 20 = 1200   average expenditure ={1200}/{40}   = Rs. 30   Rs.30nswer: Rs.30
Answer: A
If x - 2 < 8 and x + 6 > 4, which of the following inequalities expresses all possible values of x?
Choose the correct answer
A) 2 < x < 10 B) 4 < x < 8 C) -2 < x < 10 D) -4 < x < 8 E) -8 < x < 4

Solution: x - 2 < 8   So, x < 10   2. x + 6 > 4   So, x > -2   -2 < x < 10ombine the two you get -2 < x < 10   Answer will be (-2 < x < 10)
Answer: C
Glen is having his big family over for Christmas. Out of 25 people coming, 40 percent are lactose intolerant and 72% are vegetarians. Glen wants to prepare the good in advance. Can you calculate how many of the guests are both vegetarians and lactose intolerant?  Pick
A) 1	B) 2	C) 3	D) 4	E) 5

Solution: The total number of guests coming over for Christmas is n=25.   The number of lactose intolerant guests is 40% of it, thus   n (A)=40/100×25=40/4= 
40/4 = 10
10.   The number of guests who are vegetarians is 72%, thus   n (B)=72/100×25=72/4= 
72/4 = 18
18.   In order to calculate the number of guests who are both lactose intolerant and vegetarians we can use the following equation:   n (AnB)=n (A)+n (B) -n =10+18-25=28-25= 
28-25 = 3
3.   So, 3 of Glen's guests are both lactose intolerant and vegetarians.   ANSWER: 3
Answer: C
How long does a train 110 m long running at the speed of 72 km/hr takes to cross a bridge 132 m length? Choose the correct choice from the following answers:
A) 12.6
B) 12.0
C) 12.1
D) 12.3
E) 12.2

Solution: Speed = 72 * 5/18= 
72 * 5/18 = 20
20 m/sec   Total distance covered= 110 + 132= 
110 + 132 = 242
242 m.   Required time= 242/20= 
242/20 = 121/10 = around 12.1
12.1 sec.Answer: 12.0
Answer: B
A bag contains 8 red and 3 white balls. One ball is drawn at random. What is the probability that the ball drawn is white? Choose one:	A) 4/7	B) 2/3	C) 8/11	D) 1/4	E) 5/7

Solution: Total number of balls = 8+3= 
8+3 = 11
11   number of white balls= 8   Probability = 8/11 = 8/11   Answer is 8/11
Answer: C
Each term of a certain sequence is 3 less than the previous term. The first term of this sequence is 18. If the sum of the first n terms of the sequence is n, what is the value of positive integer n?  Choose one
A) 1 B) 13 C) 15 D) 19 E) 47

Solution: We know that it is a decreasing sequence i.e. the terms keep decreasing till 0 and then negative terms start.   What does this imply?If the sum of the first n terms of the sequence is n   Since number of terms will definitely be positive, we are looking for a positive sum.   19 + 16 + 13 + 10 + 7 + 4 + 1 -2 -5 -7 -10 .... and so on   Note that the first 7 terms are positive and all others negative. Every negative term has greater absolute value than the corresponding positive terms i.e. -2 absolute value is greater than 1 absolute value, -5 absolute value is greater than 4 absolute value, and so on...   Since we have 7 positive terms, we must have less than 7 negative terms to get the sum as positive. If we have 6 negative terms, we will have a total of 13 terms. Of the given options, only 13 is possible and hence it must be the answer.   Answer (15)
Answer: C
A shopkeeper bought 150 calculators at the rate of 250 per calculator.He spent 2500 on transportation and packing. If the marked price of calculator is 320 per calculator and the shopkeeper gives a discount of 5% on the marked price then what will be the percentage profit gained by the shopkeeper? Pick one.
A) 20%  B) 14%  C) 15%  D) 16%  E) None of these

Solution: CP of 150 calculators = 150 × 250 = 37,500.   \ total CP = 37,500 + 2500 = 40,000   Marked price of 150 calculators = 150 × 320 = 48,000   Selling price after discount = 4800 × 95⁄100   = 45,600   \ Percentage profit = 45,600−40,000/40,000×100 = 14%   Answer 14%
Answer: B
The 20th term of the series a, b , b, c, c, c, d, d, d, d, e, e, e, e, e, .... is
Choose one
A) a B) b C) c D) d E) e

Solution: a is one time, b,2 times so on...   so 20=n(n+1)/2..   0r n(n+1)= 40... now 6*7=30... 5*6<40 so n= 6.. and 20th alphabet is e..ans e
Answer: E
After decreasing 50% in the price of an article costs Rs.620. Find the actual cost of an article?
Answers.
A) 1400	B) 1240	C) 1200	D) 1100	E) 1500

Solution: CP* (50/100) = 620   CP= 12.4 * 100 => CP = 1240   ANSWER:1240
Answer: B
A researcher computed the mean, the median, and the standard deviation R for a set of performance scores. If 5 were to be added to each score, which of these three statistics would change? Choose the correct choice
A) The mean only
B) The median only
C) The standard deviation only
D) The mean and the median
E) The mean and the standard deviation

Solution: If we add or subtract a constant to each term in a set the standard deviation R will not change..   If we add (or subtract) a constant to each term in a set the mean and the median will increase (decrease) by the value of that constant.   Answer: The mean and the median.
Answer: D
CP of 2 buffaloes are $30,000. By selling 1 at a loss of 15% and other at a profit of 19%, he foundthat SP of both buffaloes is the same. Find the CP of each?	Options.
A) $10,500	B) $10,500	C) $11,500	D) $12,000	E) $12,500

Solution: Let the C.P of 1st buffalo = x   ∴C.P of 2nd buffalo = 30,000 - x   S.P of 1st buffalo = ( 100 - loss% )   ------------------- x C.P   100   S.P = 100 - 15x   -----------= 85x/ 100   100   S.P of 2nd buffalo = ( 100 - Profit%)   --------------------- x C.P   100   S.P = (100 + 19)(30,000- x) 119(30,000 -x)   -------------------- = ----------------   100 100   S.P of 1st buffalo = S.P of 2nd buffalo   85x/ 100 = 119 ( 30,000 - x)/ 100   ⇒ 85x = 119(30,000 - x)   ⇒ 85x = 3,570,000 - 119x   ⇒ 85x + 119 x = 3,570,000   ⇒ 204x = 3,570,000   ⇒ x = 3,570,000 / 204   ⇒ x = $17,500   C.P of 1st buffalo = $17,500   C.P of 2nd buffalo = 30,000 - 17,500 = $12,500   $12,500
Answer: E
Ben is driving on the highway at y miles per hour. (One mile equals 5,280 feet.) Ben's tires have a circumference of x feet. Which of the following expressions gives the number of revolutions each wheel turns in one hour? Options
A) 5,280(x/y)  B) 5,280(y/x)  C) 5,280(xy)  D) 5,280/(xy)  E) (xy)/5,280

Solution: In one hour, at the rate of y miles per hour, Ben covers y miles, so 5,280y feet.   The number of revolutions = distance/circumference = 5,280y/x.   Answer: 5,280(y/x).
Answer: B
A train speeds past a pole in 15 seconds and a platform 100 m long in 20 seconds. Its length is?
Choices:
A) 188 m  B) 876 m  C) 251 m  D) 300 m  E) 145 m

Solution: Let the length of the train be x meters and its speed be y m/sec.   They, x / y = 15 => y = x/15   x + 100 / 20 = x / 15   x = 300 m.   Answer: 300 m
Answer: D
If x dollars is invested at 10 percent for one year and y dollars is invested at 8 percent for one year, the annual income from the 10 percent investment will exceed the annual income from the 8 percent investment by $92. If $2,000 is the total amount invested, how much is invested at 8 percent? Choose the correct choice:
A) $600	B) $700	C) $800	D) $900	E) $1000

Solution: 0.1x = 0.08(2000-x)+92   0.18x = 252   x = 1400   Then the amount invested at 8% is $2000 - $1400 = $600   The answer is $600.2000 -  1400= 
2000 -  1400 = 600
$600   The answer is $600.
Answer: A
A grocer has a sale of Rs. 5435, Rs. 5927, Rs. 5855, Rs. 6230 and Rs. 5562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 5500?  Choices.
A) 4991  B) 5991  C) 3991  D) 6542  E) 6995

Solution: Total sale for 5 months = Rs. (5435 + 5927 + 5855 + 6230 + 5562) = Rs. 29009.   Required sale = Rs. [ (5500 x 6) - 29009 ]   = Rs. (33000 - 29009)   = Rs. 3991   Answer: Option 3991
Answer: C
P is faster than Q. P and Q each walk 24 km. The sum of their speeds is 7 km/hr and the sum of times taken by them is 14 hours. Then, P's speed is equal to ?  Options.
A) 9 km/hr	B) 4 km/hr	C) 6 km/hr	D) 5 km/hr	E) 3 km/hr

Solution: Explanation:   Let P's speed = x km/hr. Then, Q's speed = (7 - x) km/ hr.   So, 24/x + 24/(7 - x) = 14   - 98x + 168 = 0   (x - 3)(x - 4) = 0 => x = 3 or 4.   Since, P is faster than Q,   so P's speed = 4 km/hr and Q's speed = 3 km/hr.   Answer: 4 km/hr
Answer: B
John got Rs.6000 as his share out of a total profit of Rs.9000 which he and Rick earned at the end of one year. If John invested Rs.20,000 for 6 months, where as Rick invested his amount for the whole year, what was the amount invested by Rick? Choices:
A) 3400	B) 3500	C) 4500	D) 5000	E) 5500

Solution: (5000)   Let the amount invested by Ramesh = Rs.x.Then, 20000×6 : 12x=6000:3000   or 12000012x=21 or x = 5000
Answer: D
What is the greatest value of positive integer x such that 2^x is a factor of 100^70? Choose the most appropriate option:
A) 120
B) 140
C) 130
D) 150
E) 160

Solution: Put in simple words, we need to find the highest power of 2 in 100^70   100 = 2^2*5^2   Therefore 100^70 = (2^2*5^2)^70 = 2^140*5^140   Answer : 140
Answer: B
A certain factory employed 600 men and 400 women and the average wager was Rs. 25.50 per day, If a woman got Rs. 5 less than a man, then what are their daily wages ?  Choose the correct choice from the following answers:
A) M :23.50 w:22.50
B) M :27.50 w:22.50
C) M :27.50 w:22.51
D) M :27.50 w:22.53
E) M :27.50 w:22.66

Solution: Let the daily wage of a man be Rs. x.   Then, daily wage of a woman = Rs. (x - 5).   Now, 600x + 400 (x - 5) = 25.50 * (600 + 400) <=> 1000x = 27500 <=> x = 27.50.   Man's daily wages = Rs. 27.50; Woman's daily wages = (x - 5) = Rs. 22.50.   Answer: M :27.50 w:22.50
Answer: B
Two good train each 100 m long, are running in opposite directions on parallel tracks. Their speeds are 45 km / hr and 30 km /hr respectively. Find the time taken by the slower train to pass the driver of the faster one.	Choose the correct choice from the following answers:
A) 1.2 sec	B) 2.4 sec	C) 4.8 sec	D) 9.6 sec	E) None

Solution: Sol.   Relative Speed = (45 + 30) km / hr   = (75 x 5 / 18) m/sec   = (125/6) m/sec.   Distance covered = (100+ 100) m = 1000 m.   Required time = (200 x 6 / 125) sec = 9.6 sec.   Answer 9.6 sec
Answer: D
If PINTU is coded as 79523 in a certain code language, how would you code JUMBO in the same language?
Choose the most appropriate option
A) 13426  B) 14236  C) 13436  D) 14263  E) 15263

Solution: 1 2 3 4 5 6 7 8 9   a b c d e f g h i   j k l m n o p q r   s t u v w x y z   sooo...JUMBO is 13426...   13426NSWER:13426
Answer: A
A person crosses a 800 m long street in 6 minutes. What is his speed in km per hour?  Choose the correct choice from the following options:
A) 5.2 km/hr.
B) 8.0 km/hr.
C) 7.2 km/hr.
D) 3.2 km/hr.
E) 4.2 km/hr.

Solution: B   8.0 km/hr.   Speed=(800/6 * 60) m/sec   = 2.2 m/sec.   Converting m/sec to km/hr   =(2.2*18/5) km/hr   = 8.0 km/hr.   Answer is 8.0 km/hr.
Answer: B
Let us say that a table tennis tournament was going on with knock out terms which means the one who loses the match is out of the tournament. 100 players took part in that tournament.
How many matches were played?  Choose the correct option
A) 99 matches	B) 79 matches	C) 69 matches	D) 99 matches	E) 59 matches

Solution: D   99 matches.   The number of matches will always sum up to one less than the number of players in a knock out tournament. You may calculate it in any manner. Thus 99 matches were played.
Answer: D
The average age of 5 boys is 25 years and their ages are in the proportion 3:5:7. The age of the youngest boy is? Pick:
A) 10years B) 15years C) 20years D) 25years E) 18years

Solution: Total age of 5 boys = 25*5= 
25*5 = 125
125   ratio of their ages= 3:5:7   Age of the youngest = 125*3/15= 
125*3/15 = 25
25 years   Answer is 25years
Answer: D
What is the least integer that is a sum of four different prime numbers?  Choose the correct option
A) 15 B) 17 C) 19 D) 21 E) 23

Solution: The sum of the four smallest primes is 2+3+5+7= 
2+3+5+7 = 17
17.   The answer is 17.
Answer: B
A tradesman by means of his false balance defrauds to the extent of 40%? in buying goods as well as by selling the goods. What percent does he gain on his outlay?	Answers
A) 99%	B) 47%	C) 84%	D) 96%	E) 43%

Solution: g% = 40 + 40 + (40*40)/100= 
40 + 40 + (40*40)/100 = 96
96%   Answer: 96%
Answer: D
Ramesh purchased a refrigerator for Rs. 12500 after getting a discount of 20% on the labelled price. He spent Rs. 125 on transport and Rs. 250 on installation. At what price should it be sold so that the profit earned would be 10% if no discount was offered? Choose the correct choice from the following:
A) 12880 B) 12789 C) 27108 D) 17600 E) 18291

Solution: Explanation:   Price at which the TV set is bought = Rs. 12,500   Discount offered = 20%   Marked Price = 12500 * 100/80 = Rs. 15625   The total amount spent on transport and installation = 125 + 250 = Rs. 375\Total price of TV set = 15625 + 375 = Rs. 16000   The price at which the TV should be sold to get a profit of 10% if no discount was offered = 16000 * 110/100 = Rs. 17600
Answer: D
What quadrants do the line y = 2x - 4 go through?  Choose the correct answer
A) 1 and 2  B) 1 and 3  C) 1 and 4  D) 1,2 and 3  E) 1,3 and 4

Solution: Find the x-intercept and the y-intercept of the line.   To find the x intercept, set y = 0 and solve for x.   0 = 2x - 4   x = 2   To find the y intercept, set x = 0 and solve for y.   y = 0 - 4   y = -4   Draw the line using the two intercepts.   Thus, the line goes through the 1st, 3rd and 4th quadrants.   Answer is 1,3 and 4
Answer: E
January 13, 2016, fell on a Wednesday. On which day of the week did June 25, 2016, fall? (Note: 2016 was a leap year.)	Choose the correct choice:
A) Sunday  B) Tuesday  C) Thursday  D) Friday  E) Saturday

Solution: The date range contains a partial year. The number of days in the partial year is:   January - 18, February - 29, April - 30, March and May - 31, and June - 25.   18 + 29 + 30 + (2 * 31) + 25= 
18 + 29 + 30 + (2 * 31) + 25 = 164
164 total days in the date range.   Divide by 7 to determine how much the day of the week advances: 164 / 7= 23 remainder 3.   Since the first date was a Wednesday, advance the day of the week by 3; the second date fell on a Saturday. The answer is Saturday.
Answer: E
Anand and Deepak started a business investing Rs. 20,500 and Rs. 30,000 respectively. Out of a total profit of Rs. 13,000, Deepak's share is?
Choose the correct answer
A) Rs. 9400  B) Rs. 8900  C) Rs. 8400  D) Rs. 7722.8  E) Rs. 8440

Solution: Ratio of their shares = 20500 : 30000 = 41 : 60   Deepak's share = 13000 * 60/101 = Rs. 7722.8   Answer:Rs. 7722.8
Answer: D
If A, B and C together can finish a piece of work in 4 days. A alone in 12 days and B in 18 days, then C alone can do it in?
Choose the correct choice:
A) 7 days B) 3 days C) 9 days D) 8 days E) 2 days

Solution: 9 days   9 days   9 days = 1/4 - 1/12 – 1/18 = 1/9 => 9 days
Answer: C
For each month of a given year except December, a worker earned the same monthly salary and donated one-tenth of that salary to charity. In December, the worker earned N times his usual monthly salary and donated one-fifth of his earnings to charity. If the worker's charitable contributions totaled one-seventh of his earnings for the entire year, what is the value of N? Select the correct option:
A) 31/4
B) 33/4
C) 29/4
D) 27/4
E) 25/4

Solution: Let monthly salary for each of the 11 months except December was x, then   11x*1/10 + Nx*1/5 = 1/7(11x + Nx);   11/10 + N/5 = 1/7(11 + N)   11+2N/10 = 11+N/7 =>77+14N = 110+10N =>4N=33   N = 33/4   Answer: 33/4
Answer: B
The number of circles that can be drawn out of 10 points of which 7 are collinear is
Choose the correct choice from the following answers:
A) 130
B) 85
C) 45
D) 72
E) 82

Solution: For drawing a circle we need 3 non collinear points.   This can be done in:   3C3 + 3C2 x 7C1 + 3C1 x 7C2 = 1 + 21 + 63= 
1 + 21 + 63 = 85
85   ANSWER:85
Answer: B
A number is increased by 11% and then reduced by 10%. After these operations, the number : Pick one:
A) does not change	B) decreases by 1%	C) increases by 1%	D) increases by 0.1%	E) None of these

Solution: Let the original number be 100.   Then, the new number = 100 × 1.1 × 0.9 = 99   i.e. the number decreases by 1%.   Answer decreases by 1%
Answer: B
Bruno and Sacha are running in the same direction around a stadium. Sacha runs at a constant speed of 7 meters per second, and Bruno runs at a constant speed of 5 meters per second. At a certain point Sacha overtakes Bruno. If one minute afterward, Sacha stops and waits for Bruno to reach him, then how many seconds does he have to wait?
Pick one.
A) 12  B) 24  C) 36  D) 60  E) 72

Solution: the difference of the speed is 2m per second so in one minute Sacha will be 120 m ahead of Bruno..   Bruno will cover this in  120/5= 
 120/5 = 24
24 secs..   24
Answer: B
If the simple interest on a certain amount in at 4% rate 5 years amounted to Rs.2160 less than the principal. What was the principal?  Choose the correct choice from the following answers:
A) 1500
B) 2500
C) 2700
D) 3200
E) 11500

Solution: P - 2160 = (P*5*4)/100   P = 2700   Answer: 2700
Answer: C
39! is divided by 41. Then what is the remainder for this?	Choose the most appropriate option
A) 1  B) 3  C) 5  D) 6  E) 7

Solution: Substituting p = 41 in the wilson's theorem, we get   40!+141=0   40×39!+141=0   −1×39!41=−1   Cancelling -1 on both sides,   39!41=1   1
Answer: A
4x − 12 = 4y
5y + 5x = 15
Which of the following is the number of solutions to the system of equations shown above?
Choose the correct choice from the following answers.
A) More than three B) Exactly three C) Exactly two D) Exactly one E) None

Solution: 4x − 12 = 4y   => 4x - 4y = 12   => x- y =3 -- 1   5y + 5x = 15   =>x + y = 3 -- 2   From equation 1 and 2 , we get   2x = 6   => x=3   y=0   Therefore , the given system will have Exactly one solution   Exactly one
Answer: D
Three workers have a productivity ratio of 1 to 2 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 9th 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?	Select the correct option: A) 12 to 1 B) 10 to 1 C) 5 to 1 D) 1 to 6 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 1 unit of job worked for only   4+2= 
  4+2 = 6
6 hours (first 4 hours and last 2 hours), so he did   1*6= 
  1*6 = 6
6 units of job;   The ratio thus is 60 to 6, or 10 to 1.   Answer: 10 to 1
Answer: B
Someone on a skateboard is traveling 5 miles per hour. How many feet does she travel in 45 seconds? (1 mile = 5280 feet)  Choose the correct choice from the following choices.
A) 380 ft	B) 400 ft	C) 410.05 ft	D) 329.85 ft	E) 420.85 ft

Solution: per second => 5*5280 ft/60*60 =7.33 ft   45 seconds => 7.33 * 45= 
7.33 * 45 = 329.85
329.85 ft   Answer : 329.85 ft
Answer: D
In Set T, the average (arithmetic mean) equals the median T. Which of the following must be true?
I. Set T consists of evenly spaced numbers.
II. Set T consists of an odd number of terms.
III. Set T has no mode.
IV. None of the above. Select
A) I only
B) I and II
C) II and III
D) I, II, and III
E) IV only

Solution: This is a very good 'trap question'.   Consider Set A= { 0,0,0,0 } Mean=Median=Mode=0- Eliminates 1,2 and 3 OR   Consider Set B= {1,2,2,3 } Mean=Median=Mode=2- Eliminates 1,2 and 3   If you think that only in 'consecutive integers' the average is equal to the median T you might fall for 'D'.   Ans: IV only
Answer: E