mathewhe/aqua_rat huggingface dataset:
Question: If a quarter kg of potato costs 60 paise, how many paise will 200gm cost ?
(A) 45 paise
(B) 46 paise
(C) 47 paise
(D) 48 paise
(E) None of these
Rationale: Explanation:
Quarter of Kg means 250 gm
Less weight, less price (Direct Proportion)
So,
250:200::60:x=>x=200∗60/ 250=>x=48
So 200 gm will cost 48 paise.
Option D
Answer: (D) 48 paise
Question: Find the odd man out. 15, 25, 30, 51, 85, 90, 115
(A) 15
(B) 25
(C) 51
(D) 90
(E) 91
Rationale: Explanation :
All except 51 are multiples of 5. Answer : Option C
Answer: (C) 51
Question: Find the area of a parallelogram with base 12 cm and height 48 cm?
(A) 122 cm2
(B) 576 cm2
(C) 246 cm2
(D) 42 cm2
(E) 39 cm2
Rationale: Area of a parallelogram
= base * height
= 12 * 48
= 576 cm2
Answer: B
Answer: (B) 576 cm2
Question: A can do a particular work in 6 days . B can do the same work in 8 days. A and B signed to do it for Rs. 3840. They completed the work in 3 days with the help of C. How much is to be paid to C?
(A) s. 380
(B) s. 600
(C) s. 420
(D) s. 400
(E) s. 480
Rationale: Explanation :
Amount of work A can do in 1 day = 1/6
Amount of work B can do in 1 day = 1/8
Amount of work A + B can do in 1 day = 1/6 + 1/8 = 7/24
Amount of work A + B + C can do = 1/3
Amount of work C can do in 1 day = 1/3 - 7/24 = 1/24
work A can do in 1 day: work B can do in 1 day: work C can do in 1 day
= 1/6 : 1/8 : 1/24 = 4 : 3 : 1
Amount to be paid to C = 3840 × (1/8) = 480
Answer : Option E
Answer: (E) s. 480
Question: lexus car agency has 216 cars.he sold some cars at 9% profit and rest at 36% profit thus he gains 17% on the sale of all his cars.the no. of cars sold at 36% profit is?
(A) 36
(B) 64
(C) 38
(D) 39
(E) 40
Rationale: ratio of 36% profit cars to 9% profit cars = 8:19
so no. of cars sold at 36% profit = 216*8/27= 64 cars
ANSWER:B
Answer: (B) 64
Question: Bill made a profit of 10% by selling a product. If he had purchased that product for 10% less and sold it at a profit of 30%, he would have received $ 63 more. What was his original selling price?
(A)  $770
(B)  $660
(C)  $700
(D)  $990
(E)  $840
Rationale: Let the original purchase price be X
So original selling price at 10% profit = 1.1X
If product is purchased at 10% less of original = 0.9X
Profit of 30% on this price = 1.3(0.9X)
He would have received $63 more in second scenario => 1.3(0.9X) - 1.1X = 63
=> 0.07X = 63
=> X = $900
Original purchase price = $900
Hence, original selling price (at 10% of profit) = 1.1(900) = $990
Option D
Answer: (D)  $990
Question: Joe needs to paint all the airplane hangars at the airport, so he buys 360 gallons of paint to do the job. During the first week, he uses 1/2 of all the paint. During the second week, he uses 1/5 of the remaining paint. How many gallons of paint has Joe used?
(A) 18
(B) 144
(C) 175
(D) 216
(E) 250
Rationale: Total paint initially = 360 gallons
Paint used in the first week = (1/2)*360 = 180 gallons.
Remaning paint = 180 gallons
Paint used in the second week = (1/5)*180 = 36 gallons
Total paint used = 216 gallons.
Option D
Answer: (D) 216
Question: For dinner, Sue ate 360 grams of fruit which was five times as much fruit as she ate for lunch, and three times as much fruit as she ate for breakfast. How much fruit did Sue eat in total?
(A) 552
(B) 560
(C) 568
(D) 576
(E) 584
Rationale: For breakfast, Sue ate 360 / 3 = 120 grams.
For lunch, Sue ate 360 / 5 = 72 grams.
For dinner, Sue ate 360 grams.
The total is 120 + 72 + 360 = 552 grams.
The answer is A.
Answer: (A) 552
Question: 60 percent of Andrea's living room floor is covered by a carpet that is 4 feet by 9 feet. What is the area of her living room floor?
(A) 14.4
(B) 180/7
(C) 50.4
(D) 60
(E) 90
Rationale: 60% of Area of the floor = 4*9 square feet = 36 square feet
i.e. 100% Area of Floor = (36/60)*100 = 60 square feet
Answer: Option D
Answer: (D) 60
Question: If a wagon wheel had 10 more spokes, the angle between them would decrease by 6 degrees. Can you identify the number of spokes in the wheel?
(A) 20 spokes
(B) 10 spokes
(C) 30 spokes
(D) 15 spokes
(E) 25 spokes
Rationale: A
20 spokes
360/S = A
360/(S +10) = A – 6
Thus there are 20 spokes in the wheel.
Answer: (A) 20 spokes
Question: (5!+6!+4!)/4!*0!*5*6=?
(A) 4/5
(B) 6/5
(C) 5/6
(D) 4/3
(E) 9/8
Rationale: 4!(5+30+1)/4!*1*5*6
36/30=6/5
answer B
Answer: (B) 6/5
Question: Three unbiased coins are tossed. What is the probability of getting 1 heads, 1 Tail?
(A) 3/4
(B) 1/4
(C) 3/8
(D) 7/8
(E) 2/8
Rationale: Let, H --> Head , T --> Tail
Here S = {TTT, TTH, THT, HTT, THH, HTH, HHT, HHH}
Let E = event of getting 3 heads
Then E = {THT, HTH}
P(E) = n(E)/n(S) =2/8
Answer is E
Answer: (E) 2/8
Question: In how many ways can 5 boysand 2 girls be arranged at a table if 2 girls are never together?
(A) 250
(B) 256
(C) 350
(D) 360
(E) 480
Rationale: Total ways of arranging 7 person in a circle = 6! = 720 ways
If we consider two women as one, then we have 5+1=6 persons. Arranging these six persons in circle will take = 5! = 120 ways
And two women can arrange themselves in 2! ways
Total ways in which two women sit together in circle = 5!*2! = 240 ways
Total ways in which two women doesn’t sit together in circle = 6! - 5!*2! = 720 - 240 = 480 ways
E
Answer: (E) 480
Question: If (1 – 1.5)N = 1, then N =
(A)  −400
(B)  −140
(C)  −2
(D)  4
(E)  400
Rationale: (1 – 1.5)N = 1
Simplify to get: -0.5N = 1
Rewrite as (-1/2)N = 1
Multiply both sides by -2 to get: N = -2
Answer: C
Answer: (C)  −2
Question: Aman started a business investing Rs. 70,000. Rakhi joined him after six months with an amount of Rs.. 1,05,000 and Sagar joined them with Rs. 1.4 lakhs after another six months. The amount of profit earned should be distributed in what ratio among Aman, Rakhi and Sagar respectively, 3 years after Aman started the business?
(A) 7 : 6 : 10
(B) 12 : 15 : 16
(C) 42 : 45 : 56
(D) 12 : 18 : 26
(E) Cannot be determined
Rationale: Aman : Rakhi : Sagar =(70,000 x 36):(1,05,000 x 30):(1,40,000 x 24) = 12 : 15 : 16.
Answer: Option B
Answer: (B) 12 : 15 : 16
Question: Andrew started saving at the beginning of the year and had saved $150 by the end of the year. He continued to save and by the end of 2 years had saved a total of $540. Which of the following is closest to the percent increase in the amount Andrew saved during the second year compared to the amount he saved during the first year?
(A) 11%
(B) 25%
(C) 44%
(D) 56%
(E) 125%
Rationale: Percent increase in the amount Andrew saved during the second year compared to the amount he saved during the first year.
Percentage Change = ( Change in value / Original value ) * 100
Percentage Change = [ (Saving in 2nd year - Saving in 1st year ) / Saving in 1st year ] * 100
Saving in 2nd year + Saving in 1st year = 540
Saving in 2nd year + 150 = 540
Saving in 2nd year = 540 - 150 = 390
Change in Value = 390 - 150 =240
Original Value = 160
Percentage Increase = (160 / 150 ) * 100 = 160% ..... Answer E......
Answer: (E) 125%
Question: A can do a piece of work in 80 days. He works at it for 10 days & then B alone finishes the remaining work in 42 days. In how much time will A and B, working together, finish the work?
(A) 23 days
(B) 25 days
(C) 30 days
(D) 33 days
(E) 35 days
Rationale: Work done by A in 10 days=10/80=1/8
Remaining work=(1-(1/8))=7/8
Now, work will be done by B in 42 days.
Whole work will be done by B in (42*8/7)=48 days
Therefore, A's one day's work=1/80
B’s one day's work=1/48
(A+B)'s one day's work=1/80+1/48=8/240=1/30
Hence, both will finish the work in 30 days.
Answer : C.
Answer: (C) 30 days
Question: which number need to add to 859622 to get a number exactly divisible by 456?
(A) 389999
(B) 543248
(C) 798790
(D) 795320
(E) 859622
Rationale: Dividend = Quotient * Divisor + Reminder
859622 / 456 gives quotient = 1885 and reminder = 62.
So, the next number divisible by 456 is 456 places infront of 456 * 1885
Which means 456 – 62 = 394 should be added to 859622.
E
Answer: (E) 859622
Question: A thief steals at a car at 2.30 p.m. and drives it at 60 km/hr. The theft is discovered at 3 p.m. and the owner sets off in another car at 75 km/hr. When will he overtake the thief?
(A) 2 p.m
(B) 6 p.m
(C) 5 p.m
(D) 7 p.m
(E) 9 p.m
Rationale: Suppose the thief is overtaken x hrs after 2.30 p.m.
Then, distance covered by the owner in (x - 1/2) hrs.
60x = 75(x - 1/2) => x = 5/2 hrs.
So, the thief is overtaken at 5 p.m.
Answer:C
Answer: (C) 5 p.m
Question: X and Y run a 200 m race,where X beats Y by 20 m. To do a favor to Y, X starts 20 m behind the starting line in a second 200 m race. Both run at the same previous speed. Which of the following is true?
(A) X Beats Y by 2m
(B) Y Beats X by 10m
(C) Y Beats X by 11m
(D) Y Beats X by 1m
(E) Y Beats X by 11m
Rationale: Let's suppose that the speed of X is 20m/s and that the speed of Y is 18m/s.
So, in the first race, the results are the following:
X crosses the finish line in 10s. In other words, X has run 200m in 10 s.
In 10s, Y has run 180 meters.
Therefore, there is the difference of 20 meters mentioned in the question.
Now, let's review the second race.
In 11 seconds, X can complete the 200 meters race. We have to remember that X is 20 meters behind the starting line.
But in 11 seconds, Y has covered (180+18) =198 meters. Also, it is important to notice that in 11 seconds Y cannot arrive to the finish line.
So, 200 - 198 = 2 meter
Answer: A
Answer: (A) X Beats Y by 2m
Question: If x and y are unique prime integers, which of the following must be odd?
(A) xy^2
(B) 2x+2y
(C) 2x−2y
(D) 2x/2y
(E) x−y
Rationale: Any number multiplied by 2 has to be an even number hence
Answer E
Answer: (E) x−y
Question: Tough and Tricky questions: Combinations.
The product of the digits of the four-digit number h is 48. No two digits of h are identical. How many different numbers are possible values of h?
(A) 6
(B) 12
(C) 24
(D) 36
(E) 42
Rationale: Answer = C = 24
Let number =abcd
Given that a*b*c*d = 48
a,b,c,d can be 1,2,3,8
Number of ways = 4*3*2 = 24
Answer: (C) 24
Question: The cost price of a radio is Rs.1500 and it was sold for Rs.1230, find the loss %?
(A) 18%
(B) 19%
(C) 78%
(D) 48%
(E) 11%
Rationale: 1500 ---- 270
100 ---- ? => 18%
Answer: A
Answer: (A) 18%
Question: What is (19^7+19) / 19?
(A) 45225766
(B) 46855821
(C) 47045882
(D) 48925947
(E) 49325989
Rationale: (19^7+19) / 19 =
19*(19^6+1) / 19 =
19^6 + 1
Clearly this is a number which ends with a 2 in the units place.
The answer is C.
Answer: (C) 47045882
Question: Rs.1500 is divided into two parts such that if one part is invested at 6% and the other at 5% the whole annual interest from both the sum is Rs.87. How much was lent at 5%?
(A) 388
(B) 2998
(C) 277
(D) 300
(E) 271
Rationale: (x*5*1)/100 + [(1500 - x)*6*1]/100 = 87
5x/100 + 90 – 6x/100 = 87
x/100 = 3
=> x = 300.Answer: D
Answer: (D) 300
Question: What is the % profit or loss, if the cost price of 4 mangoes is equal to the selling price of 9 mangoes?
(A) 75.6%
(B) 13.6%
(C) 54.6%
(D) 55.6%
(E) 51.6%
Rationale: Let the cost price of 1 mangoes be Rs 1
Cost of 9 mangoes = Rs 9
Selling price of 9 mangoes = 4
Gain/loss = 9 - 4 = 5
%=5/9âˆ—100= 55.6
Answer: D
Answer: (D) 55.6%
Question: The sum of two numbers is 30 and their difference is 10. Find their product.
(A) 104
(B) 114
(C) 315
(D) 200
(E) 335
Rationale: Let the numbers be x and y.
Then x + y = 30 and x - y = 10
x = 20; y = 10
xy = 20 * 10 = 200
ANSWER:D
Answer: (D) 200
Question: If (x + yi) / i = ( 7 + 9i ) , where x and y are real, what is the value of (x + yi)(x - yi)?
(A) 110
(B) 120
(C) 130
(D) 140
(E) 150
Rationale: (x + yi) / i = ( 7 + 9i )
(x + yi) = i(7 + 9i) = -9 + 7i
(x + yi)(x - yi) = (-9 + 7i)(-9 - 7i) = 81 + 49 = 130
CORRECT ANSWER IS C0130
Answer: (C) 130
Question: How many of the following numbers are divisible by 132?
264, 396, 462, 792, 968, 2178, 5544, 6336
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: A number is divisible by 132, if it is divisible by each one of 11, 3 and 4.
Clearly, 968 is not divisible by 3. None of 462 and 2178 is divisible by 4.
Each one of remaining 5 is divisible by each one of 11, 3 and 4 and therefore, by 132.
ANSWER:B
Answer: (B) 5
Question: What decimal fraction is 20 ml of a litre ?
(A) .2
(B) 0.002
(C) .05
(D) .02
(E) None of these
Rationale: Answer
Required fraction = 20/1000
= 2/100
= .02
Correct Option: D
Answer: (D) .02
Question: A crate of mangoes contains one bruised mango for every thirty mango in the crate. If three out of every four bruised mango are considerably unsaleble and there are 10 unsaleable mangoes in the crate then how msny mango are there in the crate?
(A) 100 mangoes
(B) 110 mangoes
(C) 120 mangoes
(D) 130 mangoes
(E) 125 mangoes
Rationale: 100 mangoes
ANSWER:A
Answer: (A) 100 mangoes
Question: A can finish a work in 18 days and B can do same work in half the time taken by A. then working together, what part of same work they can finish in a day
(A) 1\5
(B) 1\6
(C) 1\7
(D) 1\8
(E) 1\9
Rationale: Explanation:
Please note in this question, we need to answer part of work for a day rather than complete work. It was worth mentioning here because many do mistake at this point in hurry to solve the question
So lets solve now,
A's 1 day work = 1/18
B's 1 day work = 1/9 [because B take half time than A]
(A+B)'s one day work =
(1/18+1/9)
=(1+2 /18)=1/6
So in one day 1/6 work will be done.
Option B
Answer: (B) 1\6
Question: A train moves fast a telegraph post and a bridge 264 m long in 8 sec and 20 sec respectively. What is the speed of the train?
(A) 22.3 km/hr
(B) 22.9 km/hr
(C) 29.2 km/hr
(D) 79.2 km/hr
(E) 19.2 km/hr
Rationale: Let the length of the train be x m and its speed be y m/sec.
Then, x/y = 8 => x = 8y
(x + 264)/20 = y
y = 22
Speed = 22 m/sec = 22 * 18/5 = 79.2 km/hr.
Answer:D
Answer: (D) 79.2 km/hr
Question: If Q is a positive integer, and Q/15 = 8.2, what is the remainder when Q is divided by 15?
(A) A.1
(B) B.2
(C) C.3
(D) D.4
(E) E.8
Rationale: If Q were a multiple of 15, the quotient Q/15 would be an integer. The fact that it's a decimal tells us that 15 goes into Q eight whole times and some decimal part of a time. This decimal part, 0.2 is the remainder divided by the divisor. Let R be the remainder.
R/15 = 0.2 = 1/5
R = (15)*(1/5) = 3
Answer =(C)
Answer: (C) C.3
Question: If 2a = 4b = 10, then 40ab =
(A) 50
(B) 100
(C) 250
(D) 450
(E) 500
Rationale: 2a * 4b = 10 * 10 = 100
8 ab = 100
i.e. 40 ab = 500
Answer: Option E
Answer: (E) 500
Question: If 35 percent of 400 is 20 percent of x, then x =
(A) 200
(B) 350
(C) 700
(D) 900
(E) 1,400
Rationale: 5/100(400) = 2/10(x)
X = 700..
ANSWER:C
Answer: (C) 700
Question: The following sets each have a mean of 10 and the standard deviations are given in variable form.
Set I = {10, 10, 10, 10, 10, 10}, standard deviation = P
Set II = { 7, 8, 9, 11, 12, 13}, standard deviation = R
Set III = {6, 6, 6, 14, 14, 14}, standard deviation = Q
Rank these three standard deviations from least to greatest.
(A) P, Q, R
(B) P, R, Q
(C) R, Q, P
(D) Q, R, P
(E) R, Q, P
Rationale: SD is minimum when the terms are closer to the mean.
In set 1, we have all terms equal to mean. hence, its SD is 0.(The Lowest)
Comparing Set 2 and Set 3, Set 2 has terms more closer to mean than set 3. hence, Set 3 Sd is the highest.
So, Answer is C
Answer: (C) R, Q, P
Question: In a race with 20 competitors, the first-place finisher receives a gold medal, the second-place finisher receives a silver medal, and the third-place finisher receives a bronze medal. If there are no ties, in how many different ways may these three medals be awarded?
(A) 35
(B) 120
(C) 720
(D) 840
(E) 6,840
Rationale: Well in this case since there are 3 positions and they can be taken by 3 persons only ,so order matters over here .For gold there are 20 choices ,for silver 19 remain (one who got gold cannot be given silver) and for bronze 18 choices remain.
So total possibilities=20*19*18
Correct answer E=6,840
Answer: (E) 6,840
Question: What percent is 400 gm of 1 kg?
(A) 25%
(B) 40%
(C) 10%
(D) 8%
(E) 12%
Rationale: 1 kg = 1000 gm
400/1000 Ã— 100 = 40000/1000
=40 %
Answer is B
Answer: (B) 40%
Question: Three photographers, Lisa, Mike and Norm, take photos of a wedding. The total of Lisa and Mikes photos is 70 less than the sum of Mike's and Norms. If Norms photos number 10 more than twice the number of Lisa's photos, then how many photos did Norm Take?
(A) 40
(B) 50
(C) 60
(D) 80
(E) 130
Rationale: L+M=M+N-70 / N=2L+10
70=M+N-L-M
70=N-L
70=2L+10-L
60=L
2(60)+10=130
E
Answer: (E) 130
Question: The timing of a college is from 12 p.m to 4.00 p.m. Five lectures are held in the given duration and a break of 5 minutes after each lecture is given to the students. Find the duration of each lecture.
(A) 52 minutes
(B) 45 minutes
(C) 30 minutes
(D) 48 minutes
(E) 44 minutes
Rationale: Explanation:
Total time a student spends in college = 4 hours 00 minutes = 240 minutes
As there are 5 lectures, the number of breaks between lectures is 4. Total time of the break = 20 minutes
Hence, the duration of each lecture is = (240 â€“ 20)/5
= 44 minutes
ANSWER E
Answer: (E) 44 minutes
Question: If pq = p + q^2 – 2pq, for what value of q is pq equal to p for all values of p?
(A) -2
(B) -1
(C) 1
(D) 0
(E) 2
Rationale: C
p + q2 â€“ 2pq = p
=> q2 - 2pq = 0
=> q (q - 2p) = 0
=> q = 0 or q = 2p
im not following the logic you used here.. how did you replace pq with 0 could someone help explain it in MORE DETAI
D
Answer: (D) 0
Question: A women sells 3 different size(in kgs) packs of sugar which are multiples of 1.A person who buys sugar should buy all types of packs.4 different people buys 20,21,23,29 kgs .what will the maximum and minimum amounts a person can buy??
(A) 22
(B) 33
(C) 34
(D) 54
(E) 85
Rationale: packet are 11,6 and 7
7+7+6=20
7+7+7=21
6+6+11=23
7+11+11=29
and min 6+6+6=18
and max 11+11+11=33
ANSWER:B
Answer: (B) 33
Question: A fence consists of m lengths of fence that are each n feet long. A fence post separates each length of fence by its width of x feet. What is the total length Q of the fence including the fence posts on each end?
(A) mn
(B) m(n + x)
(C) Q=m(n + x) + x
(D) m(n + x) + 2x
(E) 2mn
Rationale: Notice that since a fence post separates each length of fence, then there will be m+1 posts, for example if there are m=2 fences, then there will be 3 posts: PFPFP. Thus the total length of the posts is (m+1)x.
The total length Q of the fence is mn, therefore the total length of the fence including the fence posts on each end is (m+1)x+mn=mx+x+mn=m(n+x)+x.
Answer: C.
Answer: (C) Q=m(n + x) + x
Question: At the end of the month, a certain ocean desalination plant’s reservoir contained 6 million gallons of water. This amount is twice the normal level. If this amount represents 60% of the reservoir’s total capacity, how many million gallons short of total capacity is the normal level?
(A) 15
(B) 10
(C) 5
(D) 20
(E) 25
Rationale: the Q talks of total capacity, normal level, present level, shortage etc..
so it is all about not going wrong in these terms
6 MG= 60% of Total..
total = 6/.6=10MG..
Normal level= 1/2 of 10=5MG..
shortage of normal level=10-5=5MG..
C
Answer: (C) 5
Question: What least no. must be subtracted from 5026 so that remaining no.is divisible by 5?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 1
Rationale: Explanation:
On dividing 5026 by 5 we get the remainder 1, so 1 should be subtracted
Option E
Answer: (E) 1
Question: A piece of work can be done by 6 men and 5 women in 6 days or 3 men and 4 women in 10 days. It
can be done by 9 men and 15 women in how many days ?
(A) 3 days
(B) 4 days
(C) 5 days
(D) 6 days
(E) None of these
Rationale: Explanation:
To calculate the answer we need to get 1 man per day work and 1 woman per day work.
Let 1 man 1 day work =x
and 1 woman 1 days work = y.
=> 6x+5y = 1/6
and 3x+4y = 1/10
On solving, we get x = 1/54 and y = 1/90
(9 men + 15 women)'s 1 days work =
(9/54) + (15/90) = 1/3
9 men and 15 women will finish the work in 3 days
Answer: A
Answer: (A) 3 days
Question: A man can row at 4 kmph in still water. If the velocity of current is 1 kmph and it takes him 1 hour to row to a place and come back, how far is the place?
(A) 2.4 km
(B) 2.9 km
(C) 3.4 km
(D) 1.9 km
(E) 5.6 km
Rationale: Explanation:
Speed in still water = 4 kmph
Speed of the current = 1 kmph
Speed downstream = (4+1) = 5 kmph
Speed upstream = (4-1) = 3 kmph
Let the required distance be x km
Total time taken = 1 hour
â‡’ x/5+x/3=1
â‡’3x+5x=15
â‡’8x=15
â‡’x=1.9 km
Answer: Option D
Answer: (D) 1.9 km
Question: The ‘moving walkway’ is a 300-foot long walkway consisting of a 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 rate of 3 feet per second. Once Bill reaches the group of people, he stops walking and stands with them until the walkway ends. What is Bill’s average rate W of movement for his trip along the moving walkway?
(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
Rationale: A, B, and C don't make ANY sense! we know for some time...(a majority of the 300ft) Bill will walk at a pace of 6ft per second...and then at some later time he will stop and move at 3 ft per second... The average W MUST bebetween3-6 ft per second or the Earth is FLAT!!!.
So we are down to DE, D doesn't make sense on a weighted averages level because we know when Bill gets on the walkway the patrons are already 40% of the way down the 300ft walkway AND they are still moving at half the rate of Bill!! So for Bill to average 4 ft per second he would have had to spend a majority of the 300 ft at 3ft per second because 4 is much closer (when you factor in the size of the values we're dealing with 2 is double 1) to 3 than to 6. We know from the information that isn't possible. Billmust havespent the majority of his time at 6 ft per second before he stopped walking. That leaves only answer E as plausible.
Answer: (E) 5 feet per second
Question: If A = d% of y and B = y% of d, then which of the following is true?
(A) 1) A is smaller than B.
(B) 2) A is greater than B
(C) 3) Relationship between A and B cannot be determined.
(D) 4) If x is smaller than y, then A is greater than B.
(E) 5) None of the above
Rationale: Basically A = B = dy/100
None of the options mentions this; hence E.
Answer: (E) 5) None of the above
Question: A certain characteristic in a large population has a distribution that is symmetric about the mean m. If 64 percent of the distribution lies within one standard deviation d of the mean, what percent of the distribution is less than m + d ?
(A)  16%
(B)  32%
(C)  48%
(D)  82%
(E)  92%
Rationale: This is easiest to solve with a bell-curve histogram. m here is equal to µ in the Gaussian normal distribution and thus m = 50% of the total population.
So, if 64% is one st.Dev, then on either side of m we have 64/2 = 32%. So, 32% are to the right and left of m (= 50%). In other words, our value m + d = 50 + 32 = 82% goingfrom the mean m, to the right of the distributionin the bell shaped histogram.. This means that 82% of the values are below m + d.
Like I said, doing it on a bell-curve histogram is much easier to fullygethow this works, or you could apply GMAT percentile jargon/theory to it
D
Answer: (D)  82%
Question: If |x + 10| = 10 what is the sum of all the values of x.
(A) 20
(B) 40
(C) -20
(D) 0
(E) -40
Rationale: There will be two cases
x+10 = 10 and x+10 = -10
Solve for x => x=10-10=> x=0 or x= -10 - 10 => x= -20
The sum of both values will be 0 + -20 =-20
Answer is C
Answer: (C) -20
Question: Machine A produces 100 parts twice as fast as Machine B does. Machine B produces 100 parts in 80 minutes. If each machine produces parts at a constant rate, how many parts does Machine A produce in 20 minutes?
(A) 60
(B) 80
(C) 70
(D) 40
(E) 50
Rationale: Machine B produces 100 part in 80 minutes. Machine A produces 100 parts twice as fast as B, so Machine A produces 100 parts in 80/2=40 minutes.
Now, Machine A produces 100 parts in 40 minutes which is 100/40 = 10/4 parts/minute.
10/4 parts X a total of 20 minutes = 10/4 * 20 =50
E
Answer: (E) 50