mathewhe/aqua_rat huggingface dataset:
Question: A car traveled the first quarter of a certain distance at four times the speed it traveled the remaining distance. What proportion of the total time traveled, was the time taken to travel the first quarter of the distance?
(A) 1/4
(B) 1/5
(C) 1/6
(D) 1/7
(E) 1/13
Rationale: These problems can be solved through algebra or sly number picking. Being a big fan of solving problems with numbers, let's pick a total distance divisible by 4 (say 40) so we can break it up into quarters, and a speed that can easily be one fourth, say 10. Each quarter is thus 10 kilometers (or miles or feet or angstroms for all it matters), and the runner's speed is 10 km/h for the first quarter and 5/2 km/h for the remaining quarters.
He'll take 1 hour to do the first quarter and then 4 hours for the second quarter, 4 hours for the third and 4 hours for the fourth. On total he will take 13 hours to complete this race, of which 1 hour was spent on the first quarter. So 1/13. Answer E.
Answer: (E) 1/13
Question: Robert purchased $4000 worth of US saving bonds. If bonds are sold in $50 or $100 denominations only, which of the following CANNOT be the number of US saving bonds that Robert purchased?
(A) 20
(B) 47
(C) 50
(D) 80
(E) 90
Rationale: I started off with looking at the answer choices... 20-47-50 are in a tight range, so my guess was to look and rule out the bigger numbers.
The total amount is $4000. So with 90 bonds, each $50 = $4500 , we already exceed the $4000 limit. Hence E is the answer.
E remains.
Answer: (E) 90
Question: Find the perimeter and area of the rectangle of length 11 cm and breadth 9 cm.
(A) 71 cm2
(B) 99 cm2
(C) 141 cm2
(D) 171 cm2
(E) 221 cm2
Rationale: length = 11 cm, breadth = 9 cm
Perimeter of rectangle = 2 (length + breadth)
= 2 (11 + 9) cm
= 2 × 20 cm
= 40 cm
We know that the area of rectangle = length × breadth
= (11 × 9) cm22
= 99 cm2
ANSWER : B
Answer: (B) 99 cm2
Question: What is the least number to be added to 1480 to make it a perfect square?
(A) 105
(B) 160
(C) 200
(D) 71
(E) 120
Rationale: The numbers greater than 1480 and are square of number is 1600.
The least number that should be added 1480 to make it perfect square = 1600 - 1480 = 120.
ANSWER:E
Answer: (E) 120
Question: 8 liters are drawn from a cask full of wine and is then filled with water. This operation is performed three more times . The ratio of the quantity of wine now left in cask to that of the water is 16:65. How much wine did the cask hold originally?
(A) 12
(B) 24
(C) 36
(D) 42
(E) 56
Rationale: Let the quantity of wine in the cask originally be x liters
quantity of wine left in cask after 4 operations = x(1 - 8/x)^4 liters
x(1 - 8/x)^4 /x = 16/81
(1-8/x)^4 = (2/3)^4
x = 24
Answer is B
Answer: (B) 24
Question: In an effort to plan out expenses, the Roberts family is representing its annual budget as a circle graph. Each sector of the graph is proportional to the amount of the budget it represents. If “clothes and shoes” takes up 72° of the chart, how much of the Roberts’s $20,000 annual budget is dedicated to clothes and shoes?
(A) $1,500
(B) $3,000
(C) $4,000
(D) $5,000
(E) $5,400
Rationale: Given for clothes and shoes” takes up 72° of the circular chart.
Then clothes and shoes = 72/360 * 20000.
=> 4000.
IMO option C is correct answer...
Answer: (C) $4,000
Question: If f is a function defined for all k by f(k) = k^5 /16, what is f(3k) in terms of f(k)?
(A) 1/8 f(k)
(B) 5/8 f(k)
(C) 244 f(k)
(D) 243 f(k)
(E) 323 f(k)
Rationale: f(k) = k^5 /16
f(3k) = (3k)^5/16 = 243 * k^5 /16 = 243 * (k^5 /16) = 243 f(k).
So answer is D.
Answer: (D) 243 f(k)
Question: A, B and C enter into a partnership with a capital in which A's contribution is Rs. 10,000. If out of a total profit of Rs. 1000, A gets Rs. 500 and B gets Rs. 300, then C's capital is?
(A) 4002
(B) 4029
(C) 4129
(D) 4000
(E) 4019
Rationale: A : B : C = 500 : 300 : 200 = 5 : 3 : 2.
Let their capitals be 5x, 3x and 2x respectively.
Then, 5x = 10000
=> x = 2000.
C's capital = 2x = Rs. 4000.
Answer: D
Answer: (D) 4000
Question: Taps A and B can fill a bucket in 12 minutes and 15 minutes respectively. If both are opened and A is closed after 4minutes, how much further time would it take for B to fill the bucket?
(A) 6 min.
(B) 4 min.
(C) 5 min.
(D) 3 min.
(E) 2 min.
Rationale: Explanation:
Part filled in 4 minutes =
4∗(1/12+1/15)=4∗9/60=3/5
Remaining part =1−3/5=2/5
=>1/15:2/5=1:X
=>X=6
=>X=6 min.
So it will take further 6 min. to fill the bucket.
Option A
Answer: (A) 6 min.
Question: Adam borrowed some money at the rate of 6% p.a. for the first two years, at the rate of 9% p.a. for the next three years, and at the rate of 14% p.a. for the period beyond four years. If he pays a total interest of 11,500 at the end of nine years, how much money did he borrow?
(A) 10,105
(B) 12,105
(C) 14,105
(D) 16,105
(E) None of these
Rationale: Let the sum borrowed be x. Then,
(x×6×21/00)+(x×9×3/100)+(x×14×4/100)= 11500
⇒ (3⁄25x + 27⁄100x + 14⁄25x) = 11400 ⇒ 95⁄100x = 11500
⇒ x = (11500×100/95)= 12105
Hence, sum borrowed = 12,105
Answer B
Answer: (B) 12,105
Question: 3 women and a few men participated in a chess tournament. Each player played two matches with each of the other players. If the number of matches that men played among themselves is 78 more than those they played with the women, how many more men than women participated in the tournament?
(A) 14
(B) 13
(C) 11
(D) 10
(E) 8
Rationale: let the number of men=m..
so 3 women and m men will play= 2*3m=6m games
m will play each other in mC2 way so number of games = 2*mC2= m(m-1)
Difference in two = m(m-1)-6m=78
m^2-7m-78=0
m^2-13m+6m-78=0
(m-13)(m+6)=0
so m = 13 or -6
cannot be -ive so m=13
difference in number of women and men= 13-3=10.. Imp that we do not choose 13 as the answer
ANS D
Answer: (D) 10
Question: Kamal started a business with Rs.25000 and after 4 months, Kiran joined him with Rs.60000. Kamal received Rs.58000 including 10% of profit as commission for managing the business. What amount did Kiran receive?
(A) 72000
(B) 720
(C) 82000
(D) 92000
(E) 7200
Rationale: Ratio of the profits = 25000*12 : 60000*8
= 25*12 : 60*8	= 5*3 : 12:2 = 5 : 4*2
= 5:8
Let the total profit = x.
Then Kamal received 10x/100 = x/10 as commission for managing the business
Remaining profit = x- x/10 = 9x/10 which is shared in the ration 5:8
Kamal's share = x/10 + (9x/10) * (5/13) = 58000
=> x + 9x(5/13) = 580000
=> x(1 + 45/13) = 580000
=> x ( 58/13) = 580000
=> x ( 1/13) = 10000
=> x = 130000
Kiran's share = 130000 - 58000 = 72000
Answer is A
Answer: (A) 72000
Question: Rs 12200 divided among 5 women, 4 boys and 7 men , such that the share a woman, a boy and a man are in the ratio of 7:3:2. Find the share of a girl?
(A) Rs 100
(B) Rs200
(C) Rs300
(D) Rs 2000
(E) Rs 600
Rationale: Total amount paid = (5 x 7x) + (4 x 3x) +(7 x 2x) =61x = 12200
=>35x+12x+14x=12200
=>61x=12200 =>x=200
The share of a girl= 3x = 3 x Rs 200 = Rs 600
Answer:E
Answer: (E) Rs 600
Question: The speed of a boat in upstream is 60 kmph and the speed of the boat downstream is 80 kmph. Find the speed of the boat in still water and the speed of the stream?
(A) 10
(B) 99
(C) 77
(D) 55
(E) 22
Rationale: Speed of the boat in still water = (60+80)/2 = 70 kmph. Speed of the stream
= (80-60)/2
= 10 kmph.
Answer: A
Answer: (A) 10
Question: find two integers, neither of which ends in a zero, and whose product is exactly 100
(A) 4 and 25
(B) 60 and 15,625
(C) 64 and 15,620
(D) 64 and 15,635
(E) 64 and 16,625
Rationale: 100=10^2
=10x10
=(2x5)x(2x5)
=(2^2)x(5^2)
= 4x25
so the numbers are 4 and 25
ANSWER:A
Answer: (A) 4 and 25
Question: 600 km journey it will take 8hrs, if 120 km is done by bus and the rest by car. It takes 20 minutes more, if 200 km is done by busand the rest by car. The ratio of the speed of the train to that of the cars is?
(A) 1 : 3
(B) 3 : 4
(C) 2 : 5
(D) 1 : 4
(E) 3 : 5
Rationale: Let the speed of the train be x km/hr and that of the car be y km/hr.
Then, 120 + 480 = 8 1 + 4 = 1 ....(i)
x y x y 15
And, 200 + 400 = 25 1 + 2 = 1 ....(ii)
x y 3 x y 24
Solving (i) and (ii), we get: x = 60 and y = 80.
Ratio of speeds = 60 : 80 = 3 : 4.
B
Answer: (B) 3 : 4
Question: Country X imported approximately $1.44 billion of goods in 1996. If Country X imported $360 million of goods in the first two months of 1997 and continued to import goods at the same rate for the rest of the year, by how much would Country Xs 1997 imports exceed those of 1996?
(A)  $24 million
(B)  $120 million
(C)  $644 million
(D)  $540 million
(E)  $720 million
Rationale: Convert units to millions as answer is in millions
1996 Imports = $1.44 bill = $1440 mill
i.e. 1440/12 = $120 mill/month
1997 Imports = $360 mill/2 month
i.e. $180 mill/month
Difference/month = 180-120 = 60
Difference/year = $60 mill * 12 = $720 mill
ANSWER: E
Answer: (E)  $720 million
Question: Two alloys A and B are composed of two basic elements. The ratios of the compositions of the two basic elements in the two alloys are 5 : 3 and 1 : 5, respectively. A new alloy X is formed by mixing the two alloys A and B in the ratio 4 : 3. What is the ratio of the composition of the two basic elements in alloy X ?
(A) 1 : 1
(B) 3 : 4
(C) 5 : 2
(D) 4 : 3
(E) 7 : 9
Rationale: Mixture A has a total of 5 + 3 = 8 parts. If in the final mixture this represents 4 parts, then the total number of parts in mixture B should be (8/4)*3 = 6.
So, we should take of mixture B a quantity with 1 and 5 parts, respectively.
This will give us in the final mixture (5 + 1) : (3 + 5), which means 6:8, or 3:4.
Answer B.
Answer: (B) 3 : 4
Question: A father said to his son, "I was as old as you are at present at the time of your birth." If the father's age is 38 years now, the son's age five years back was:
(A) 9 years
(B) 14 years
(C) 25 years
(D) 12 years
(E) 11 years
Rationale: Answer: Option B
Let the son's present age be x years.
Then, (38 - x) = x
2x = 38 => x = 19
Son's age 5 years back = (19 - 5) = 14 years.
Answer: (B) 14 years
Question: You choose at random ten points inside of a circle, so that no two of them are
on any diameter. What is the probability that the circle has some diameter, so that exactly
five points are on one side and exactly five points are on the other?
(A) 63/256
(B) 1/2
(C) 2/3
(D) 5/6
(E) 1
Rationale: The randomness is a red herring: There is some diameter dividing the points 5 - 5
no matter what!
Note that none of the points can be in the center of the circle. (Then any diameter going
through any of the points would contain two points.) Choose any diameter. If five points
are on either side, we're done. Otherwise, let n be the larger number of points and rotate
the diameter gradually 180 degrees. As we do this, the number of points on the side with
n changes whenever the diameter crosses a point, eventually dropping to 10 - n. Since 5 is
between n and 10-n, and this number of points changes one at a time, it must be 5 at some point
correct answer E
Answer: (E) 1
Question: The first train leaves the station at 7:00 am with a speed of 60 km/hr. The second train leaves at 8:30 am, in the same direction from the same station, with a speed of 80 km/hr. What time will the second train catch the first train?
(A) 11:00 am
(B) 12:00 noon
(C) 1:00 pm
(D) 2:00 pm
(E) 3:00 pm
Rationale: In ninety minutes, the first train travels 90 km.
The second train catches the first train with a relative speed of 20 km/h.
The second train will catch the first train in 4.5 hours.
The second train will catch the first train at 1:00 pm.
The answer is C.
Answer: (C) 1:00 pm
Question: John found that the average of 15 numbers is 40. If 13 is added to each number then the mean of number is?
(A) 53
(B) 45
(C) 65
(D) 78
(E) 64
Rationale: (x+x1+...x14)/15 = 40
53
Option A
Answer: (A) 53
Question: Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is:
(A) 2:3
(B) 1:2
(C) 7:9
(D) 5:11
(E) 4:5
Rationale: Explanation:
Let the third number be x.
Then, first number = 120% of x=120x/100=6x/5
Second number = 150% of x =150 x/100=3x/2
Ratio of first two numbers =(6x/5:3x/2)=12x:15x=4:5
Answer:E
Answer: (E) 4:5
Question: When 6 is added to half of one-third of one-fifth of a number, the result is one-fifteenth of the number. Find the number?
(A) 32
(B) 180
(C) 60
(D) 27
(E) 11
Rationale: Explanation:
Let the number be
26+ 1/2[1/3(a/5)] = a/15
=> 6 = a/30 => a = 180
Answer:B
Answer: (B) 180
Question: How many times will the digit 5 be written when listing the integers from 1 to 1000?
(A) 300
(B) 380
(C) 180
(D) 415
(E) 264
Rationale: Many approaches are possible. For example:
Consider numbers from 0 to 999 written as follows:
1. 000
2. 001
3. 002
4. 003
...
...
...
1000. 999
We have 1000 numbers. We used 3 digits per number, hence used total of 3*1000=3000 digits. Now, why should ANY digit have preferences over another? We used each of 10 digits equal # of times, thus we used each digit (including 5) 3000/10=300 times.
Answer: A.
Answer: (A) 300
Question: Mary's income is 70 percent more than Tim's income, and Tim's income is 40 percent less than Juan's income. What percent of Juan's income is Mary's income?
(A)  124%
(B)  102%
(C)  96%
(D)  80%
(E)  64%
Rationale: Juan's income = 100 (assume);
Tim's income = 60 (40 percent less than Juan's income);
Mary's income = 102 (70 percent more than Tim's income).
Thus, Mary's income (102) is 102% of Juan's income (100).
Answer: B.
Answer: (B)  102%
Question: In 1995 a certain store had ,2000 tools in stock that had been purchased for $30 each. If 1,000 of these tools were sold in 1995 for $40 each and the remaining 800 were sold in 1996 for $50 each, how many greater was the gross profit on the tools sold in 1996 than the gross profit on those sold in 1995?
(A) $0
(B) $6,000
(C) $8,000
(D) $32,000
(E) $10,000
Rationale: The keyword here isGross Profit:
Gross Profit = (Selling Price - Original Price)*(# of Items Sold)
So lets figure out what the Gross Profit for 1995:
GP1995 = (40-30)*(1000) = 10000
And the Gross Profit for 1996:
GP1996 = (50-30)*(1000) = 20000
So the difference would be:
20000-10000 = 10000
ANSWER: E.
Answer: (E) $10,000
Question: In how many different ways can the letters of the word 'SCHOOL' be arranged so that the vowels always come together?
(A) 120
(B) 140
(C) 145
(D) 150
(E) 160
Rationale: 'SCHOOL' contains 6 different letters.
vowels OO are always together
we have to arrange the letters (OO)SCHL
Now 5 letters can be arranged in 5! = 120 ways
The vowels (OO) can be arranged 2! = 2 ways.
= (120 x 2) = 240
again you have to divided 2 common vowels so answer is 120.
A)
Answer: (A) 120
Question: Two vessels A and B contain 62.5% and 87.5% of alcohol respectively. If 2 litres from vessel A is mixed with 4 litres from vessel B , the ratio of alcohol and water in the resulting mixture is?
(A) 19:5
(B) 17:2
(C) 27:2
(D) 21:5
(E) 11:1
Rationale: A
19:5
Quantity of alcohol in vessel A = 62.5/100 * 2 = 5/4 litres
Quantity of alcohol in vessel B = 87.5/100 * 4 = 7/2 litres
Quantity of alcohol in the mixture formed = 5/4 + 7/2 = 19/4 = 4.75 litres
As 6 litres of mixture is formed, ratio of alcohol and water in the mixture formed = 4.75 : 1.25 = 19:5.
Answer: (A) 19:5
Question: In a class of 150 students 55 speak English;85 speak Telugu and 30 speak neither English nor Telugu
How many speak both English and Telugu?
(A) 10
(B) 20
(C) 30
(D) 40
(E) 50
Rationale: Total=150
English=55
Telugu=85
none/ neither English nor Telugu=30
No. of Students who speak only one or both=150-30=120
so, 120 stud's can speak english or telugu or both.
then,
No. of Stud's speak only English= 120-85(telugu)=35
" " " " " Telugu= 120-55=65
Remaining 120-(65+35)=20 stud's can speak both.
B)
Answer: (B) 20
Question: A total of 5 liters of gasoline is to be poured into two empty containers with capacities of 2 liters and 6 liters, respectively, such that both containers will be filled to the same percent of their respective capacities. What amount of gasoline, in liters, must be poured into the 6-liter container?
(A) 4 1/2
(B) 4
(C) 3 3/4
(D) 3
(E) 1 1.4
Rationale: Let x be the amount of gasoline in 2 lt container.
(x/2)*100 = ((5 - x)/6)*100
x = (5 - x)/3
3x = 5 - x
x = 1.25
Amount of gasoline in 6 lt container = 5 - 1.25 = 3.75
Answer: C
Answer: (C) 3 3/4
Question: One hour after Yolanda started walking from X to Y, a distance of 31 miles, Bob started walking along the same road from Y to X. If Yolanda's walking rate was 3 miles per hour and Bobт's was 4 miles per hour, how many miles had Bob walked when they met?
(A) 24
(B) 23
(C) 22
(D) 21
(E) 16
Rationale: When B started walking Y already has covered 3 miles out of 31, hence the distance at that time between them was 31-3=28 miles.
Combined rate of B and Y was 3+4=7 miles per hour, hence they would meet each other in 28/7=4 hours. In 6 hours B walked 4*4=16 miles.
Answer: E.
Answer: (E) 16
Question: There are some passengers riding on a bus. At the first stop, half the passengers get off and nobody gets on the bus. This pattern continues as the bus goes to the next stops. If only one passenger gets off at stop number 5, how many passengers were on the bus originally?
(A) 128
(B) 64
(C) 32
(D) 16
(E) 8
Rationale: Before stop 5, there were 2 passengers on the bus.
Before stop 4, there were 4 passengers on the bus.
etc...
Before stop x, there were 2^(6-x) passengers on the bus.
Before stop 1, there were 2^5 = 32 passengers on the bus.
The answer is C.
Answer: (C) 32
Question: A can do a work in 15 days and B in 20 days. If they work on it together for 7 days, then the fraction of the work that is left is
(A) 8/17
(B) 7/15
(C) 3/15
(D) 8/15
(E) 11/60
Rationale: Person ( A ) ( B ) ( A+B )
Time - ( 15 ) ( 20 ) (-)
Rate - ( 20 ) ( 15 ) ( 35 )
Work -(300) (300) (300)
therefore A+B requires (300/35) days to complete entire work
For 1st 4 days they work 35 * 7 = 245
Remaining work is 300 - 245 = 55
Remaining fraction of work is = 55/300 = 11/60
Answer E
Answer: (E) 11/60
Question: On Monday, a certain animal shelter housed 70 cats and dogs. By Friday, 1/5 of the cats and 1/4 of the dogs had been adopted; no new cats or dogs were brought to the shelter during this period. What is the greatest possible number of pets that could have been adopted from the animal shelter between Monday and Friday?
(A) 13
(B) 15
(C) 17
(D) 19
(E) 21
Rationale: To maximize the number of pets adopted, we should maximize the number of dogs adopted since 1/4 > 1/5.
The greatest multiple of 4 less than 70 is 60 (such that the remaining number is divisible by 5), so let's assume there were 60 dogs and 10 cats.
Then the maximum number of adopted pets is 1/4*(60) + 1/5*(10) = 15 + 2 = 17.
The answer is C.
Answer: (C) 17
Question: A circle graph shows how the budget of a certain company was spent: 60 percent for salaries, 9 percent for research and development, 5 percent for utilities, 4 percent for equipment, 2 percent for supplies, and the remainder for transportation. If the area of each sector of the graph is proportional to the percent of the budget it represents, how many degrees of the circle are used to represent transportation?
(A) 18°
(B) 36°
(C) 54°
(D) 72°
(E) 90°
Rationale: The percent of the budget for transportation is 100 - (60+9+5+4+2)= 20%
100% of the circle is 360 degrees.
Then (20%/100%)*360 = 72 degrees
The answer is D.
Answer: (D) 72°
Question: A sum of Rs. 4000 amounts to Rs. 4600 in 5 years at a certain rate of simple interest. What would be the amount, if the rate of interest is increased by 3 %.
(A) Rs. 4900
(B) Rs. 5000
(C) Rs. 5200
(D) Rs. 5600
(E) None of these
Rationale: Explanation:
Principal = Rs. 4000, Amount = Principal + SI = Rs. 4600
SI = Amount – Principal = 4600 – 4000 = Rs. 600
Given : Principal = Rs. 4000, Time = T = 5 years and SI = Rs. 600
SI =PRT/100
600 = 4000 *R * 5/100
600 = 200R
R = 3 % p.a.
Now the new interest rate is = 3% + 3% = 6 % p.a.
SI = PRT/ 100 = 4000 * 6 * 5/ 100 = Rs. 1200
Amount = Principal + SI
= 4000 + 1200
= 5200
ANSWER C
Answer: (C) Rs. 5200
Question: The length of a rectangle is two - fifths of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 1225 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 10 units?
(A) 140 sq.units
(B) 158 sq.units
(C) 187 sq.units
(D) 607 sq.units
(E) 815 sq.units
Rationale: Given that the area of the square = 1225 sq.units
=> Side of square = √1225 = 35 units
The radius of the circle = side of the square = 35 units Length of the rectangle = 2/5 * 35 = 14 units
Given that breadth = 10 units
Area of the rectangle = lb = 14 * 10 = 140 sq.units
Answer: A
Answer: (A) 140 sq.units
Question: In an election only two candidates contested. A candidate secured 70% of the valid votes and won by a majority of 176 votes. Find the total number of valid votes?
(A) 440
(B) 570
(C) 480
(D) 520
(E) 550
Rationale: Let the total number of valid votes be x.
70% of x = 70/100 * x = 7x/10
Number of votes secured by the other candidate = x - 7x/100 = 3x/10
Given, 7x/10 - 3x/10 = 176 => 4x/10 = 176
=> 4x = 1760 => x = 440.
ANSWER:A
Answer: (A) 440
Question: With # andeach representing different digits in the problem below, the difference between #and ## is 445. What is the value of?
#
-##
____
445
E
(A) 7
(B) 8
(C) 9
(D) 6
(E) 5
Rationale: 100x
-(10x +x)
-----------
89 x= 445
x = 5
E
Answer: (E) 5
Question: If the length of a certain rectangle is decreased by 4 cm and the width is increased by 3 cm, a square with the same area as the original rectangle would result. Find the perimeter of the original rectangle.
(A) 50 cm
(B) 70 cm
(C) 60 cm
(D) 30 cm
(E) 40 cm
Rationale: Let x and y be the length and breadth of the rectangle respectively.
Then, x - 4 = y + 3 or x - y = 7 ----(i)
Area of the rectangle =xy; Area of the square = (x - 4) (y + 3)
(x - 4) (y + 3) =xy<=> 3x - 4y = 12 ----(ii)
Solving (i) and (ii), we get x = 16 and y = 9.
Perimeter of the rectangle = 2 (x + y) = [2 (16 + 9)] cm = 50 cm.
ANSWER A 50 cm
Answer: (A) 50 cm
Question: Goldenrod and No Hope are in a horse race with 6 contestants. How many different arrangements of finishes are there if No Hope always finishes before Goldenrod and if all of the horses finish the race?
(A) 720
(B) 360
(C) 120
(D) 24
(E) 21
Rationale: All 6 horses can finish the race in 6! way (assuming no tie).
If no tie is possible between No Hope and Goldenrod, then in half of these cases No Hope will be before Goldenrod and in half of these cases after (not necessarily right before or right after). How else? So, there are 6!/2=360 different arrangements of finishes where No Hope always finishes before Goldenrod.
Answer: B.
Answer: (B) 360
Question: If n is a positive integer and n^2 is divisible by 50, then what is the largest positive integer that must divide n?
(A) 5
(B) 8
(C) 10
(D) 20
(E) 25
Rationale: 50 = 2 * 5^2
If 50 divides n^2, then n must be divisible by 2 * 5 = 10
The answer is C.
Answer: (C) 10
Question: Raju age after 35 years will be 5 times his age 5 years back, What is the present age of Raju
(A) 28
(B) 17
(C) 15
(D) 77
(E) 66
Rationale: Clearly,
x+35 = 5(x-5)
<=> 4x = 60 => x = 15
Answer:C
Answer: (C) 15
Question: What will be the least number which when doubled will be exactly divisible by 12, 18, 21 and 30 ?
(A) 1260
(B) 630
(C) 2524
(D) 1680
(E) 2250
Rationale: L.C.M. of 12, 18, 21 30 2 | 12 - 18 - 21 - 30
----------------------------
= 2 x 3 x 2 x 3 x 7 x 5 = 1260. 3 | 6 - 9 - 21 - 15
----------------------------
Required number = (1260 ÷ 2) | 2 - 3 - 7 - 5
= 630. ANSWER : B
Answer: (B) 630
Question: In the xy-coordinate system, line k passes through points (-4m, 0) and (0, 2m). Which of the following is a possible equation of line k?
(A) y = -2x + 2m
(B) y = 1/2*x - 4m
(C) y = 2x + 2m
(D) y = 1/2*x + 2m
(E) y = -1/2*x - 5m
Rationale: The slope of the line is 2m/4m=1/2.
The y-intercept is 2m.
the equation of the line is: y = 1/2*x +2m
The answer is D.
Answer: (D) y = 1/2*x + 2m
Question: What is the units digit of 13^4*17^2*29^3?
(A) 9
(B) 7
(C) 5
(D) 3
(E) 1
Rationale: 3^1=3
3^2=9
3^3=7
3^4=1, it is first digit
7^2=9, it is second digit
9^3=9, it is third digit
1*9*9=1
ANSWER:E
Answer: (E) 1