mathewhe/aqua_rat huggingface dataset:
Question: A line has a slope of 3/4 and intersects the point R (-12, -39). At which point does this line intersect the x-axis?
(A) (40,0)
(B) (30,0)
(C) (0,40)
(D) (40,30)
(E) (0,30)
Rationale: Assume that the equation of the line is y=mx+c, where m and c are the slope and y-intercept.
You are also given that the line crosses the point (-12,-39), this means that this point will also lie on the line above.
Thus you get -39=m*(-12)+c , with m=3/4 as the slope is given to be 3/4.
After substituting the above values, you get c = -30.
Thus the equation of the line is y=0.75*x-30 and the point where it will intersect the x-axis will be with y coordinate = 0.
Put y=0 in the above equation of the line and you will get, x=40.
Thus, the point R of intersection is (40,0).
A is the correct answer.
Answer: (A) (40,0)
Question: A and B enter into partnership with capital as 7:9. At the end of 8 months, A withdraws. If they receive the profits in the ratio of 8:9 find how long B's capital was used?
(A) 8
(B) 4
(C) 5
(D) 7
(E) 6
Rationale: 7 * 8 : 9 * x = 8:9 => x= 7
Answer:D
Answer: (D) 7
Question: A pipe can fill a cistern in 20 minutes whereas the cistern when fill can be emptied by a leak in 28 minutes. When both pipes are opened, find when the cistern will be full?
(A) 27
(B) 76
(C) 70
(D) 21
(E) 28
Rationale: 1/20 - 1/28 = 1/70
70 minutes.Answer: C
Answer: (C) 70
Question: A certain city with a population of 60,000 is to be divided into 11 voting districts , and no district is to have a population that is more than 10 percent greater than the population of any other district What is the minimum possible population that the least populated district could have ?
(A) a) 10,700
(B) b) 10,800
(C) c) 10,900
(D) d) 11,000
(E) e) 5,000
Rationale: Let x = number of people in smallest district
x*1.1 = number of people in largest district
x will be minimised when the number of people in largest district is maximised
10*x*1.1 = 11x = total number of people in other districts
So we have 11x + x = 60k
x = 5,000
Answer : E
Answer: (E) e) 5,000
Question: A and B start a business with Rs.2000 and Rs.8000 respectively. How should they share their profits at the end of one year?
(A) 3:5
(B) 1:4
(C) 3:1
(D) 3:2
(E) 3:9
Rationale: They should share the profits in the ratio of their investments.
The ratio of the investments made by A and B =
2000 : 8000 => 1:4
Answer:B
Answer: (B) 1:4
Question: Find the sum to 200 terms of the series 1 + 4 + 6 + 5 + 11 + 6 + ....
(A) 30,200
(B) 29,800
(C) 30,400
(D) 40,400
(E) None of these
Rationale: Spot the above series is a combination of two APs.
The 1st AP is (1 + 6 + 11 + ....) and the 2nd AP is (4 + 5 + 6 + ...)
Since the terms of the two series alternate
S =(1 + 6 + 11 + .... to 100 terms) + (4 + 5 + 6 + .... to 100 terms)
=> 100[2 x 1 + 99 x 5]/2 + 100[2 x 4 + 99 x 1]/2 --->(Using the formula for the sum of an AP)
=>50[497 + 107] =50[604] = 30200
Alternatively, we can treat every two consecutive terms as one.
So, we will have a total of 100 terms of the nature:
(1 + 4) + (6 + 5) + (11 + 6).... -> 5, 11, 17,....
Now, a= 5, d=6 and n=100
Hence the sum of the given series is
S= 100/2 x[2 x 5 + 99 x 6]
=> 50[604]
=> 30200
ANSWER:A
Answer: (A) 30,200
Question: The average of first six prime numbers which are between 60 and 90 is
(A) 35.4
(B) 42
(C) 45.7
(D) 57
(E) 72.33
Rationale: Explanation :
first six prime numbers which are between 60 and 90 = 61, 67, 71, 73, 79, 83
average = (61 + 67 + 71 + 73 + 79 + 83)/6
= 72.33
Answer : E
Answer: (E) 72.33
Question: P is five times as old as Q, and Q is seven years older than R. If R is z years old, what is P’s age in terms of z?
(A) 5z + 7
(B) 5z − 35
(C) 5z + 35
(D) (z + 7)/5
(E) (z − 7)/5
Rationale: P = 5Q
Q = R+7 = z+7
P = 5(z+7) = 5z + 35
The answer is C.
Answer: (C) 5z + 35
Question: A certain roller coaster ride has between 29 and 150 people waiting in line to board. If riders are let on only in groups of 5 there will be 2 riders that do not get on. If the riders are let on only in groups of 6 all riders will be able to get on. Which of the following is the sum of the greatest possible number of people in the line and the least possible number of people in the line?
(A) 269
(B) 184
(C) 174
(D) 169
(E) 142
Rationale: Let x be the number of people
x=5m+2
x=6n
x=30p+12
Least = 30+12= 42
Highest = 30*4+12 = 132
Total = 174
ANSWER:C
Answer: (C) 174
Question: If money is invested at r percent interest, compounded annually, the amount of the investment will double in approximately 54/r years. If Joe's parents invested $5,000 in a long-term bond that pays 6 percent interest, compounded annually, what will be the approximate total amount of the investment 18 years later, when Joe is ready for college?
(A)  $20000
(B)  $15000
(C)  $12000
(D)  $10000
(E)  $9000
Rationale: Since investment doubles in 54/r years, then for r=6 it'll double in 54/6=~9 years (we are not asked about the exact amount so such an approximation will do). Thus after 18 years investment will become $5,000*2=$10,000 .
Answer: D.
Answer: (D)  $10000
Question: A pair of articles was bought for $50 at a discount of 60%. What must be the marked price of each of the article?
(A) $25
(B) $10
(C) $29.65
(D) $35.95
(E) $45.62
Rationale: S.P. of each of the article = 50/2 = $25
Let M.P = $x
40% of x = 25
x = 25*.4 =$10
Answer is B
Answer: (B) $10
Question: If APPLE is coded as 0 and FLOWER is coded as 63, then BASKET is coded as
(A) 2
(B) 19
(C) 35
(D) 40
(E) None
Rationale: APPLE = 1+16+16+12+5=50 i.e 5*0=0
FLOWER = 6+12+15+23+5+18=79 i.e 7*9=63
BASKET =2+1+19+11+5+20=58 5*8=40
ANSWER:D
Answer: (D) 40
Question: Annie will be half as old as Larry in 3 years. Annie will also be one-third as old as Jerome in 5 years. If Jerome is 12 years older than Larry, how old is Annie?
(A) 5
(B) 8
(C) 19
(D) 26
(E) 34
Rationale: J = L+12
(1) 2(A+3) = L+3
(2) 3(A+5) = J+5 = L+17
Let's subtract equation (1) from equation (2)
A+9 = 14
A = 5
The answer is A.
Answer: (A) 5
Question: Barbara has 8 shirts and 9 pants. How many clothing combinations does Barbara have, if she doesn’t wear 2 specific shirts with 3 specific pants?
(A) 41
(B) 66
(C) 36
(D) 70
(E) 56
Rationale: 8 shirts
9 pants
we can combine 2 shirts with (9-3) pants
2*6=12
we can combine the other shirts (6) with any pants (9)
6*9=54
Thus total :12+54=66	ANS:B
Answer: (B) 66
Question: 4,25,49,121,169,
(A) 149
(B) 169
(C) 289
(D) 209
(E) 219
Rationale: 17^2= 289 because follow sequence of square of the prime numbers
ANSWER:C
Answer: (C) 289
Question: When 1/10 percent of 4,000 is subtracted from 1/10 of 4,000, the difference is
(A) 396
(B) 36
(C) 3996
(D) 40
(E) 400
Rationale: (1/10)*4000 - (1/10)%*4000 =
400 - (1/1000)*4000 =
400 - 4 = 396
The answer is A.
Answer: (A) 396
Question: A river 3m deep and 36 m wide is flowing at the rate of 2 kmph the amount of water that runs into the sea per minute is?
(A) 4500
(B) 2678
(C) 3600
(D) 3400
(E) 2500
Rationale: (2000 * 3 * 36)/60
= 3600 M3
Answer:C
Answer: (C) 3600
Question: Rates for having a manuscript typed at a certain typing service are $6 per page for the first time a page is typed and $4 per page each time a page is revised. If a certain manuscript has 100 pages, of which 35 were revised only once, 15 were revised twice, and the rest required no revisions, what was the total cost of having the manuscript typed?
(A) $860
(B) $850
(C) $840
(D) $830
(E) $820
Rationale: 50 pages typed 1x
35 pages typed 2x (original + one revision)
15 pages typed 3x (original + two revisions)
50(6)+35(6+4)+15(6+4+4)=300+350+210=860
Answer - A
Answer: (A) $860
Question: A can do a piece of work in 20 days and B can do it in 15 days and C can do it 20 days. They started the work together and A leaves after 2 days and B leaves after 4 days from the beginning. How long will work lost?
(A) 10 2/5
(B) 10 2/0
(C) 12 2/3
(D) 10 2/1
(E) 10 2/3
Rationale: 2/20 + 4/15 + x/20 = 1
x = 38/3 = 12 2/3 Answer: C
Answer: (C) 12 2/3
Question: At the start of an experiment, a certain population consisted of 3 animals. At the end of each month after the start of the experiment, the population size was double its size at the beginning of that month. Which of the following represents the population size at the end of 6 months?
(A)  2^3
(B)  3^2
(C)  2(3^10)
(D)  3(2^6)
(E)  3(10^2)
Rationale: 3*2^n where n is the #of month --> 3*2^6 Answer (D)
Answer: (D)  3(2^6)
Question: In a bag there are coins of 50 paisa, 25 paisa and one rupee in the proportion 5:6:2. If there are in all Rs.42, the number of 25 paisa coins is?
(A) 16
(B) 42
(C) 16
(D) 84
(E) 26
Rationale: 5x 6x 2x
50 25 100
250x + 150x + 200x = 4200
600x = 4200
x = 7 => 6x = 42
Answer: B
Answer: (B) 42
Question: The HCF of two numbers is 42 and the other two factors of their LCM are 11 and 12. What is the largest number.
(A) 462
(B) 450
(C) 480
(D) 504
(E) 555
Rationale: Explanation:
HCF of the two numbers = 42
HCF will be always a factor of LCM
42 is factor of LCM
other two factors are 11 & 12
Then the numbers are (42 11) and (42 x 12)
= 462 and 504
Answer: Option D
Answer: (D) 504
Question: What will be the percentage increase in the area of the cube's surface if each of the cube's edges grows by 20%?
(A) 33%
(B) 44%
(C) 55%
(D) 56%
(E) 73%
Rationale: The question is very easy. My logic is the following:
A surface = 6*a^2
After 20% increase A surface = 6* ((1.2a)^2) = 6*1.44*a^2
The increase in the surface area = (6*1.44*a^2 - 6*a^2)/6*a^2 = (6*a^2(1.44-1))/(6*a^2) = 1.44-1=0.44 = 44%
ANSWER:B
Answer: (B) 44%
Question: there are 3 girls and 6 boys. how many kids are there?
(A) 10
(B) 19
(C) 20
(D) 9
(E) 12
Rationale: D
Answer: (D) 9
Question: In a class of 40 students, 12 enrolled for both English and German. 22 enrolled for German. If the students of the class enrolled for at least one of the two subjects, then how many students enrolled for only English and not German?
(A) 30
(B) 10
(C) 18
(D) 28
(E) 32
Rationale: Answer
Let A be the set of students who have enrolled for English and B be the set of students who have enrolled for German.
Then, (A U B) is the set of students who have enrolled at least one of the two subjects. As the students of the class have enrolled for at least one of the two subjects, A U B = 40
We know A U B = A + B - (A n B)
i.e, 40 = A + 22 - 12
or A = 30 which is the set of students who have enrolled for English and includes those who have enrolled for both the subjects.
However, we need to find out the number of students who have enrolled for only English = Students enrolled for English - Students enrolled for both German and English
= 30 - 12 = 18.
choice is (C)
Answer: (C) 18
Question: There are 10 points in a plane out of which 4 are collinear. Find the number of triangles formed by the points as vertices.
(A) 102
(B) 116
(C) 103
(D) 512
(E) 105
Rationale: The number of triangle can be formed by 10 points = 10C3.
Similarly, the number of triangle can be formed by 4 points when no one is collinear=4C3.
In the question, given 4 points are collinear, Thus, required number of triangle can be formed,
= 10C3-4C3 = 120-4 = 116.
Ans: B
Answer: (B) 116
Question: If 99<x<199 and 10<y<100, then the product xy CANNOT be equal to:
(A) 19,104
(B) 19,903
(C) 19,356.732
(D) 19,502
(E) 19,880
Rationale: Correct Answer: (B)
Determine the range of xy by multiplying the two extremes of each individual range together. The smallest value of xy must be greater than 99 * 10. The largest value must be less than 199 * 100. This means that 990 < xy < 19,900. (B) is outside of this range, so it is not a possible product of xy.
Answer: (B) 19,903
Question: Three numbers are in the ratio 4 : 5 : 6 and their average is 25. The largest number is :
(A) 30
(B) 98
(C) 27
(D) 21
(E) 22
Rationale: Explanation:
Let the numbers be 4x, 5x and 6x, Then, (4x + 5x + 6x ) / 3 = 25
=> 5x = 25
=> x = 5.
Largest number 6x = 30.'
Answer: A) 30
Answer: (A) 30
Question: If x and y are integers such that x^2= 2y and xy = 256, then x – y = ?
(A) -30
(B) -24
(C) -5
(D) 5
(E) 20
Rationale: here x and y are integers .
x^2=2y,xy =256.
substitute (x^2)/2=y in xy => x^3=256*2=>x^3=512.
here x^3 is positive ,
x is also positive.
x=8 then y=32.
x-y=-24
so option B is correct
Answer: (B) -24
Question: The entire contents of a full sack of flour can be used to make 15 cupcakes and 8 pizzas. The same full sack of flour can be used to make 5 cupcakes and 14 pizzas. If a full sack of flour is used to make only pizzas, how many pizzas can be made?
(A) 18 1/4
(B) 18 1/2
(C) 18 3/4
(D) 17
(E) 19 1/4
Rationale: 15x+8y=5x+14y
x=3/5y. Answer D
Answer: (D) 17
Question: If an article is sold at 19% profit instead of 12% profit, then the profit would be Rs. 105 more. What is the cost price?
(A) Rs.1520
(B) Rs.1570
(C) Rs.1500
(D) Rs.1550
(E) Rs.1700
Rationale: Let the cost price of an article be Rs. x.
(19% of x) - (12% of x) = 105
19x/100 - 12x/100 = 105 => 7x = 105 * 100
=> x = 1500
Cost price = Rs.1500
Answer:C
Answer: (C) Rs.1500
Question: A manufacturer is using glass as the surface for the multi-touch screen of its smartphone. The glass on the manufactured phone has a 7% probability of not passing quality control tests. The quality control manager bundles the smartphone in groups of 10. If that bundle has any smartphone that does not pass the quality control test, the entire bundle of 10 is rejected.
What is the probability that a smartphone bundle that will be rejected by quality control?
(A)  0.25
(B)  1-0.93^10
(C)  1-0.95^10
(D)  1-0.05^10
(E)  0.95^10
Rationale: Find the probability of the opposite event and subtract from 1.
The opposite event is that bundle will NOT be rejected by quality control, which will happen if all 10 phones pass the test, so P(all 10 phones pass test)=0.93^10.
P(at least one phone do not pass the test)=1- P(all 10 phones pass test)=1-0.93^10.
Answer: B.
Answer: (B)  1-0.93^10
Question: If there are half as many women as men in a group and an equal number of men and women do not own cars - a group that is 30% of the total. What fraction of the total is men who own cars?
(A) 3⁄20
(B) 31⁄60
(C) 9⁄40
(D) 1⁄3
(E) 11⁄20
Rationale: Consider a group of 100 women and 200 men, a total of 300 people. 30% of them, which is 90, form a group of people who don't own a car.
Half of them are men, and the other half are women, more precisely 45.
It means that there are 200 - 45 = 155 men who own a car, and this represents 155/300 = 31/60 of the total.
Answer B
Answer: (B) 31⁄60
Question: The radius of the two circular fields is in the ratio 3: 5 the area of the first field is what percent less than the area of the second?
(A) 74%
(B) 44%
(C) 68%
(D) 64%
(E) 234%
Rationale: r = 3 πr2 = 9
r = 5 πr2 = 25
25 π – 16 π
100 ---- ? => 64%
Answer: D
Answer: (D) 64%
Question: Running at the same constant rate, 6 identical machines can produce a total of 390 bottles per minute. At this rate, how many bottles could 10 such machines produce in 4 minutes?
(A) 648
(B) 1800
(C) 2600
(D) 10800
(E) 10900
Rationale: Let the required number of bottles be x.
More machines, More bottles (Direct Proportion)
More minutes, More bottles (Direct Proportion)
Machines	6	:	10	:: 390 : x
Time (in minutes)	1	:	4
6 x 1 x x = 10 x 4 x 390
x =	(10 x 4 x 390)/(6)
x = 2600.
ANSWER:C
Answer: (C) 2600
Question: Each child has 2 pencils and 13 Skittles. If there are 11 children, how many pencils are there in total?
(A) 16
(B) 12
(C) 18
(D) 22
(E) 08
Rationale: 2*11=22.Answer is D.
Answer: (D) 22
Question: Line R has the equation 3x + y = 7. Which of the following lines is perpendicular to Line R?
(A)  y = 3x + 4
(B)  y = –3x – 6
(C)  y = (1/3)x – 1
(D)  y = (–1/3)x + 2
(E)  y = (–7/3)x – 5
Rationale: I first rewrote the equation in the standard y=mx+b form. Therefore, Line R as presented, 3x + y = 7, can be rewritten as follows: y=-3x+7.
Thought process next is what line would be perpendicular to Line R? Any line with a reciprocal of the slope but in the opposite direction. The reciprocal of any fraction/integer is 1 over that number/integer. Therefore the reciprocal of -3 is -1/3 - need to drop the negative sign because the line would kinda run parallel and we want perpendicular. Scan the answers choices and notice C as the only one.
Answer: (C)  y = (1/3)x – 1
Question: In a village the average age of n people is 42 years. But after the verification it was found that the age of a person had been considered 20 years less than the actual age, so the new average, after the correction,increased by 1. The value of n is?
(A) 33
(B) 20
(C) 88
(D) 37
(E) 16
Rationale: It is the same as a person with 20 years more age replaces an existing person of the group ( or village)
Since the total age of the village having n persons, is being increased by 20 years and the average age of village is being increased by 1 year, hence there are total 20 people in the village.
Alternatively : ( n x 42 ) + 20 = ( n x 43 )
=> n=20
Answer: B
Answer: (B) 20
Question: The average (arithmetic mean) of the even integers from 0 to 80 inclusive is how much greater than the average (arithmetic mean) of the even integers from 0 to 40 inclusive?
(A) 20
(B) 24
(C) 28
(D) 36
(E) 40
Rationale: The sum of even numbers from 0 to N is 2 + 4 +...+ N
= 2(1 + 2 + ...+ N/2)
= 2(N/2)(N/2+1)/2 = (N/2)(N/2+1)
The average is (N/2)(N/2+1)/(N/2+1) = N/2
The average of the even numbers from 0 to 80 is 80/2 = 40
The average of the even numbers from 0 to 40 is 40/2 = 20
The answer is A.
Answer: (A) 20
Question: A train, 130130 metres long travels at a speed of 4545 km/hr crosses a bridge in 3030 seconds. The length of the bridge is
(A) 270 metres
(B) 245 metres
(C) 235 metres
(D) 220 metres
(E) 260 metres
Rationale: Explanation:
Solution 1Speed =45 km/hr=45Ã—518 m/s=12.5 m/s=45 km/hr=45Ã—518 m/s=12.5 m/s
Time =30 s=30 s
Distance travelled =12.5Ã—30=375 m=12.5Ã—30=375 m
Length of the bridge =375âˆ’130=245 m
ANSWER IS B
Answer: (B) 245 metres
Question: Jake, Lena, Fred, John and Inna need to drive home from a corporate reception in an SUV that can seat 8 people. If only Inna or Jake can drive, how many seat allocations are possible?
(A) 30
(B) 42
(C) 120
(D) 360
(E) 1680
Rationale: 5 people ,8 seats, only 2 can drive
if inna is in one seat remaining, 4 people can be arranged in 4p4 i.e 4! =24 ways
since any one can drive total ways = 24 *2= 48 ways
4 seats can be chosen out of remaining 7 seats in 7c4 ways = 7!/(5!*2!)= 35 ways
48*35=1680
E
Answer: (E) 1680
Question: At what rate percent per annum will the simple interest on a sum of money be 1/5 of the amount in 10 years?
(A) 2%
(B) 7%
(C) 9%
(D) 3%
(E) 1%
Rationale: Let sum = x. Then, S.I. = x/5, Time
= 10 years.
Rate = (100 * x) / (x * 5 * 10)
= 2%
Answer: A
Answer: (A) 2%
Question: 45 x ? = 35% of 900
(A) 16.2
(B) 7
(C) 5
(D) 500
(E) None
Rationale: Answer
Let 45 x A = (35 x 900)/100
∴ A = (35 x 9)/45 = 7
Correct Option: B
Answer: (B) 7
Question: If a% of b is the same as 8/9 of 450, then the value of ab is?
(A) 40000
(B) 45120
(C) 65200
(D) 32560
(E) 45878
Rationale: a/100 * b = 8/9 * 450
xy = 400*100 = 40000
Answer is A
Answer: (A) 40000
Question: How many four-digit numbers are there, if the two leftmost digits are even, the other digits are odd and the digit 4 cannot appear more than once in the number.
(A) 480
(B) 475
(C) 485
(D) 490
(E) 495
Rationale: N=(4*5-1)*5*5=475
where
4 cases of first digit {2,4,6,8}
5 cases of second digit {0,2,4,6,8}
1 case of 44 for two leftmost digit
5 cases of third digit {1,3,5,7,9}
5 cases of fourth digit {1,3,5,7,9}
B
Answer: (B) 475
Question: The dimensions of a room are 25 feet * 15 feet * 12 feet. What is the cost of white washing the four walls of the room at Rs. 5 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each?
(A) Rs. 4800
(B) Rs. 3600
(C) Rs. 3560
(D) Rs. 4530
(E) None of these
Rationale: Area of the four walls = 2h(l + b)
Since there are doors and windows, area of the walls = 2 * 12 (15 + 25) - (6 * 3) - 3(4 * 3) = 906 sq.ft.
Total cost = 906 * 5 = Rs. 4530
ANSWER:D
Answer: (D) Rs. 4530
Question: A watch was sold at a loss of 15%. If it was sold for Rs.400 more, there would have been a gain of 5%. What is the cost price?
(A) 1600
(B) 2998
(C) 2778
(D) 2788
(E) 2991
Rationale: 85%
120%
--------
25% ---- 400
100% ---- ? => Rs.1600
Answer:A
Answer: (A) 1600
Question: Look at this series: 22, 21, 23, 22, 24, 23, ... What number should come next?
(A) 22
(B) 24
(C) 25
(D) 26
(E) 27
Rationale: Explanation: In this simple alternating subtraction and addition series; 1 is subtracted, then 2 is added, and so on.
Answer: Option C
Answer: (C) 25
Question: If the Average of 10 consecutive integers is 22.5 then the 10th integer is :-
(A) 15
(B) 20
(C) 23
(D) 27
(E) 25
Rationale: The average falls between the 5th and 6th integers,
integer 5 = 22, integer 6 = 23.
Counting up to the tenth integer
we get 27.
ANSWER:D
Answer: (D) 27
Question: The entrance ticket at the Imax theatre in Chennai is worth Rs 250. The sale of tickets increased by 50% when the price of the ticket was lowered. However, the collections recorded a decrease of 17.5%. The price of the ticket is reduced by how much rupees?
(A) Rs150
(B) Rs112.50
(C) Rs105
(D) Rs120
(E) Rs180
Rationale: let the no. of tickets sold before = x
then the no. of tickets sold after = 1.5x
Collection Before = x*250
Collection after = 1.5x* = (250x*82.5)100
=137.5
change in price =250 - 137.5
=112.5
ANSWER:B
Answer: (B) Rs112.50
Question: Harkamal purchased 8kg of grapes at the rate of 90 per kg and 9 kg of mangoes at the rate of 55 per kg. How much amount did he pay to the shopkeeper?
(A) A)1055
(B) B)1215
(C) C)1065
(D) D)1070
(E) E)1080
Rationale: Cost of 8 kg grapes = 90 × 8 = 720.
Cost of 9 kg of mangoes = 55 × 9 = 495.
Total cost he has to pay = 720 + 495 = 1215.
B)
Answer: (B) B)1215
Question: 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 R 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: 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 is R:
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)= 5 ft/sec=E
Answer: (E) 5 feet per second
Question: A store sells eight different kinds of shirts. If we want to buy two different kinds of shirts, how many possible combinations of two shirts can we buy?
(A) 22
(B) 24
(C) 26
(D) 28
(E) 30
Rationale: 8C2=28.
The answer is D.
Answer: (D) 28
Question: A 280 m long train running at the speed of 120 km/hr crosses another train running in opposite direction at the speed of 80 km/hr in 9 sec. What is the length of the other train?
(A) 230
(B) 288
(C) 267
(D) 256
(E) 220
Rationale: Relative speed = 120 + 80 = 200 km/hr.
= 200 * 5/18 = 500/9 m/sec.
Let the length of the other train be x m.
Then, (x + 280)/9 = 500/9 => x = 220.
Answer: E
Answer: (E) 220
Question: In a barrel of juice there is 40 liters; in a barrel of beer there are 80 liters. If the price ratio between barrels of juice to a barrel of beer is 3:4, what is the price ratio between one liter of juice and one liter of beer?
(A) 3:2.
(B) 2:1.
(C) 3:1.
(D) 4:3.
(E) 3:4
Rationale: Price of 40 L juice= 3x
1L= 3x/40
Price of 80 L beer= 4x
1L= 4x/80
Ratio of 1 L price = 3x/40/4x/80= 3:2
A is the answer
Answer: (A) 3:2.