mathewhe/aqua_rat huggingface dataset:
Question: Nine friends go to see a movie at the local movie theater and sit in a row together. If there are two friends who refuse to sit next to each other, how many 9-person seating arrangements are possible?
(A) 122,400
(B) 162,920
(C) 202,180
(D) 242,360
(E) 282,240
Rationale: The number of ways to arrange 9 people in a row is 9!
From this we want to subtract all the arrangements where the two friends are next to each other. If we consider them as one unit, then the number of arrangements of this 2-person unit and the 7 other friends is 8! And the number of arrangements of the two friends within this unit are 2 because the two friends can switch places. So the total number of arrangements of the 9 friends with the 2-person unit together is 8!*2
The total number of permutations where these two friends are not seated next to each other is 9! - 8!*2 = 7*8! = 282,240
The answer is E.
Answer: (E) 282,240
Question: A man is 37 years older than his son. In two years, his age will be twice the age of his son. The present age of this son is
(A) 78 years
(B) 22 years
(C) 88 years
(D) 35 years
(E) 65 years
Rationale: Let's Son age is x, then Father age is x+37.
=> 2(x+2) = (x+37+2)
=> 2x+4 = x+39
=> x = 35 years
Answer: D
Answer: (D) 35 years
Question: 85 white and black tiles will be used to form a 10x10 square pattern. If there must be at least one black tile in every row and at least one white tile in every column, what is the maximum difference between the number of black and white tiles that can be used?
(A) 75
(B) 80
(C) 85
(D) 90
(E) 95
Rationale: Answer = A
Please refer diagram below
85 - 10 = 75
Answer: (A) 75
Question: CONVERT 1.8 hectares in ares
(A) 130 ares.
(B) 160 ares.
(C) 180 ares.
(D) 230 ares.
(E) 250 ares.
Rationale: 1.8 hectares in ares
1 hectare = 100 ares
Therefore, 1.8 hectares = 1.8 × 100 ares
= 180 ares.
ANSWER- C
Answer: (C) 180 ares.
Question: How many 4-letter words with or without meaning can be formed out of the letters of the word,'LOGARITHMS',if repetition of letters is not allowed?
(A) 5040
(B) 2520
(C) 400
(D) 40
(E) 1502
Rationale: 'LOGARITHMS' contains 10 different letters
Required number of words=Number of arrangements of 10 letters taking 4 at a time
=10P4
=10*9*8*7
=5040
Option A
Answer: (A) 5040
Question: A Jar contains a mixture of A & B in the ratio 4:1. When 10 L of Mixture is replaced with liquid B, ratio becomes 2:3. How many liters of liquid A was present in mixture initially.
(A) 12
(B) 15
(C) 16
(D) 20
(E) 25
Rationale: 10 litres of mixture that is replaced will contain 8 litres of A and 2 litres of B (as A:B = 4:1)
Let the initial volume of the mixture be 4K + 1K = 5K
So by condition ,
[ 4K-8 ]/ [ K-2+10 ] = 2/3
Solve for K which is K = 4
So initial volume of liquid A = 4K = 16 litres
ANSWER:C
Answer: (C) 16
Question: Dravid rented a power tool from a rental shop. The rent for the tool was $8 for the first hour and $3 for each additional hour. If Dravid paid a total of $38, excluding sales tax, to rent the tool, for how many hours did she rent it?
(A) 10
(B) 11
(C) 12
(D) 13
(E) 15
Rationale: 8 + 3n = 38
n = 10
Total time = n+1 hrs = 10+1 hrs = 11 hrs
Answer : B
Answer: (B) 11
Question: If x,y ,and z are positive real numbers such that x+y-z =100 , y-z+x =120 , and z-x+y = 50, then find the x+y+z value?
(A) 100
(B) 120
(C) 150
(D) 200
(E) 160
Rationale: x+y-z =100, ------1)
y-z+x =120 , ------2)
z-x+y = 50------3)
from (1)&(2)
2z=20
z=10
from (2)&(3)
2y = 170
y=85
then x=100-75= 25
x+y+z = 120
correct option is B
Answer: (B) 120
Question: A seven-digit phone number is divisible by 7. After adding the two digits of the area code the number is not divisible by 7, which of the following cannot be the area code?
(A) 07.
(B) 07.
(C) 05.
(D) 04.
(E) 02.
Rationale: Given that 7 digit number is divisible by 3
we know any number will not be divisible by 7 if the sum of all digits of the number is not the multiple of 7.
Hence looking at the option we can say that the number that should be added to the seven digit number must be 07 as adding it will make it divisible by 7... hence answer is B
Answer: (B) 07.
Question: Find the principle on a certain sum of money at 11% per annum for 2 2/5 years if the amount being Rs.1120?
(A) 1000
(B) 812.88
(C) 827.78
(D) 826.82
(E) 886.08
Rationale: 1120 = P [1 + (5*12/5)/100]
P= 886.08
Answer: E
Answer: (E) 886.08
Question: The ratio of buses to cars on River Road is 1 to 3. If there are 40 fewer buses than cars on River Road, how many cars are on River Road?
(A) 60
(B) 75
(C) 85
(D) 95
(E) 105
Rationale: B/C=1/3
C-B=40.........> B=C-40
(C-40)/C=1/3
Testing answers. Clearly Eliminate BCDE
Put C=60.........> (60-40)/60=20/60=1/3
Answer: A
Answer: (A) 60
Question: Three numbers are in the ratio 5 : 4 : 6 and their average is 750. The largest number is :
(A) 30
(B) 98
(C) 900
(D) 21
(E) 22
Rationale: Explanation:
Let the numbers be 5x, 4x and 6x, Then, (5x + 4x + 6x ) / 3 = 750
=> 15x = 750*3
=> x = 150
Largest number 6x = 6*150 = 900
Answer: C
Answer: (C) 900
Question: The sides of a square region, measured to the nearest centimeter, are 9 centimeters long. The least possible value of the actual area of the square region is
(A) 60.25 sq cm
(B) 66.25 sq cm
(C) 56.25 sq cm
(D) 72.25 sq cm
(E) 58.25 sq cm
Rationale: Though there might be some technicalities concerning the termnearest(as 7.5 is equidistant from both 7 and 8) the answer still should be : 7.5^2=56.25.
Answer: C
Answer: (C) 56.25 sq cm
Question: 3x^2 - 10x + 8 =
(A) (3x-4)(x-2)
(B) (3x-4)(x+2)
(C) (3x-4)(x-3)
(D) (3x-2)(x+4)
(E) none of above
Rationale: 3x^2 - 2x + 8
= 3x^2 - 6x - 4x + 8
= 3x (x - 2) - 4 (x-2)
= (3x-4) (x-2)
Option A
Answer: (A) (3x-4)(x-2)
Question: In a garden, 26 trees are planted at equal distances along a yard 500 metres long, one tree being at each end of the yard. What is the distance between two consecutive trees?
(A) 20
(B) 8
(C) 12
(D) 14
(E) 16
Rationale: 26 trees have 25 gaps between them.
Length of each gap = 500/25 = 20
i.e., distance between two consecutive trees = 20
Answer is A.
Answer: (A) 20
Question: Micheal and Adam can do together a piece of work in 20 days. After they have worked together for 18 days Micheal stops and Adam completes the remaining work in 10 days. In how many days Micheal complete the work separately.
(A) 25 days
(B) 100 days
(C) 120 days
(D) 110 days
(E) 90 days
Rationale: Rate of both = 1/20
Together they do = 1/20*18 = 9/10
Left work = 1 - 9/10 = 1/10
Adam completes 1/10 work in 10 day
so he took 10*10 = 100 days to complete the left work alone.
Thus the rate of adam is 1/100
Rate of Micheal = 1/20 - 1/100 = 1/25
Thus micheal takes 25 days to complete the whole work.
ans. A.
Answer: (A) 25 days
Question: In a given set of X = {70,55,98,45,62} what is the difference of median and mean of the set X?
(A) 25
(B) 30
(C) 32
(D) 40
(E) 45
Rationale: mean = 70+55+98+45+62 / 5 = 330/5 = 66
Median = 98
Difference = 98-66 = 32
Answer is C
Answer: (C) 32
Question: Four extra-large sandwiches of exactly the same size were ordered for m students, where m > 8. Three of the sandwiches were evenly divided among the students. Since 4 students did not want any of the fourth sandwich, it was evenly divided among the remaining students. If Carol ate one piece from each of the four sandwiches, the amount of sandwich that she ate would be what fraction of a whole extra-large sandwich?
(A) (4m-10)/[m(m-8)]
(B) (4m-24)/[m(m-2)]
(C) (4m-24)/[m(m-3)]
(D) (4m-24)/[m(m-6)]
(E) (4m-24)/[m(m-8)]
Rationale: Three of the sandwiches were evenly divided among the students
i.e. Amount of Sandwiches with each students = 3/m
Amount of 4th Sandwich with remaining (m-8) students = 1/(m-8)
The amount of Sandwich that carol ate = 3/m + 1/(m-8) = (3m-24+m)/[m(m-8)] = (4m-24)/[m(m-8)]
Answer: E
Answer: (E) (4m-24)/[m(m-8)]
Question: Two partners in a business (Carol and Ben) invested $500 and $850 in a business respectively. At the end of the year they made a profit of $250. Find share of each partner?
(A) $92.59,$157.41
(B) $96.59,$157.41
(C) $92.59,$159.41
(D) $92.59,$127.41
(E) $12.59,$157.41
Rationale: A:B = 500:850
A:B = 10 : 17
A's share = 250*10/27 = $92.59
B's share = 250*17/27 = $157.41
Answer is A
Answer: (A) $92.59,$157.41
Question: There are 13 clubs in a full deck of 52 cards. In a certain game, you pick a card from a standard deck of 52 cards. If the card is a club, you win. If the card is not a club, the person replaces the card to the deck, reshuffles, and draws again. The person keeps repeating that process until he picks a club, and the point is to measure how many draws it took before the person picked a club and, thereby, won. What is the probability that one will pick the first club on the forth draw or later?
(A) 1/2
(B) 3/4
(C) 7/8
(D) 27/32
(E) 27/64
Rationale: Favorable case = the club is picked in the third draw or later
Unfavorable cases = The club is picked in either first draw, second draw or third draws
Probability = Favorable outcomes / Total out comes
Also probability = 1-(Unfavorable outcomes / Total out comes)
Unfavorable case 1: probability of club picked in first draw = 13/52 =1/4
Unfavorable case 2: probability of club picked in Second draw (i.e. first draw is not club)= (39/52)*(13/52) =(3/4)*(1/4)= 3/16
Unfavorable case 3: probability of club picked in Third draw (i.e. first and 2nd draws are not clubs)= (39/52)*(39/52)*(13/52) =(3/4)*(3/4)*(1/4)= 9/64
Total Unfavorable Probability = (1/4)+(3/16)+(9/64) = (16/64)+(12/64)+(9/64)=37/64
i.e., Favorable Probability = 1 - (37/64) = 27/64
Answer: Option E
Answer: (E) 27/64
Question: If a and b are positive integers of T such that a/b=2.86, which of the following must be a divisor of a?
(A) 10
(B) B.13
(C) 18
(D) 26
(E) 50
Rationale: The prompt gives us a couple of facts to work with:
1) A and B are positive INTEGERS
2) A/B = 2.86
We can use these facts to figure out POSSIBLE values of A and B. The prompt asks us for what MUST be a divisor of A. Since we're dealing with a fraction, A and B could be an infinite number of different integers, so we have to make both as SMALL as possible; in doing so, we'll be able to find the divisors that ALWAYS divide in (and eliminate the divisors that only SOMETIMES divide in).
The simplest place to start is with...
A = 286
B = 100
286/100 = 2.86
These values are NOT the smallest possible values though (since they're both even, we can divide both by 2)...
A = 143
B = 50
143/50 = 2.86
There is no other way to reduce this fraction, so A must be a multiple of 143 and B must be an equivalent multiple of 50. At this point though, the value of B is irrelevant to the question. We're asked for what MUST divide into A....
Since A is a multiple of 143, we have to 'factor-down' 143. This gives us (11)(13). So BOTH of those integers MUST be factors of A. You'll find the match in the answer choices.
Final Answer:
B
Answer: (B) B.13
Question: If f(a)=2a+2, what is the value of (f(2a)+f(a)) ?
(A) 2a-4
(B) 8a-7
(C) 9a+5
(D) 6a+12
(E) 6a+4
Rationale: f(a)=2a+2
f(2a)= 4a+2
(f(2a)+f(a)) = 4a+2+2a+2 = 6a+4
Answer is E
Answer: (E) 6a+4
Question: John was 35 years old when he married Betty. They just celebrated their fifth wedding anniversary, and Betty's age is now 7/8 of John's. How old is Betty?
(A) 24
(B) 35
(C) 28
(D) 30
(E) 32
Rationale: Assume Betty's age on marriage = x years.
John's age on marriage = 35
John's age after 5 years = 40 years.
Betty's age after 5 years = x + 5
Given: x + 5 = 7/8 (40) = 35
Therefore Betty's current age = 35
Option B
Answer: (B) 35
Question: five mobsters have arrived at the theater for the premiere of the film “Goodbuddies.” One of the mobsters, Frankie, is an informer, and he's afraid that another member of his crew, Joey, is on to him. Frankie, wanting to keep Joey in his sights, insists upon standing behind Joey in line at the concession stand, though not necessarily right behind him. How many ways can the five arrange themselves in line such that Frankie’s requirement is satisfied?
(A) 80
(B) 66
(C) 60
(D) 72
(E) 75
Rationale: 5 mobsters can stand in 5! ways = 120
in half of the cases one person will be ahead and in the other person in the other half.
thus 60 cases.
C
Answer: (C) 60
Question: A sum of money deposited at C.I. amounts to Rs.2420 in 2 years and to Rs.3146 in 3 years. Find the rate percent?
(A) 11
(B) 30
(C) 28
(D) 24
(E) 82
Rationale: Explanation:
2420 --- 726
100 --- ? => 30%
Answer: Option B
Answer: (B) 30
Question: If 16^y = 4^14, what is y?
(A) 2
(B) 3
(C) 4
(D) 6
(E) 7
Rationale: 16^y = 4^2y = 4^14
2y=14
y = 7
The answer is E.
Answer: (E) 7
Question: The circumference of a circle is equal to 72 pi. Find the radius of this circle.
(A) 32
(B) 33
(C) 36
(D) 37
(E) 39
Rationale: The circumference of a circle is given by
C = 2 pi r, where r is the radius of the circle.
Substitute C by 72 pi to obtain the equation
72 pi = 2 pi r
Simplify and solve for r to obtain
r = 36
correct answer C
Answer: (C) 36
Question: The city of Boston decided to reconstruct its major tunnels. It estimated the job would require 612 mini projects spread evenly over an 18 month plan of completion. Only 108 mini projects had been successfully completed after 4 months. At this time, the construction was behind schedule by how many projects?
(A) 28
(B) 96
(C) 198
(D) 204
(E) 504
Rationale: Project/month : 612/18 = 34
Project in 6 month to be completed = 34*4 =136
Lag :136-108 = 28
A is the answer
Answer: (A) 28
Question: A squirrel runs up a cylindrical post , in a perfect spiral path making one circuit for each rise of 4 feet . How many feet does the squirrel travels if the post is 16 feet tall and 3 feet in circumference?
(A) 12
(B) 13
(C) 14
(D) 15
(E) 16
Rationale: total circuit=16/4=4
total feet squirrel travels=4*3=12 feet
ANSWER:A
Answer: (A) 12
Question: The difference of the squares of two consecutive odd integers is divisible by which of the following integers ?
(A) 4
(B) 6
(C) 2
(D) 8
(E) 0
Rationale: Let the two consecutive odd integers be (2n + 1) and (2n + 3). Then,
(2n + 3)^2 - (2n + 1)^2 = (2n + 3 + 2n + 1) (2n + 3 - 2n - 1)
= (4n + 4) x 2
= 8(n + 1), which is divisible by 8.
ANSWER D
Answer: (D) 8
Question: Having scored 94 runs in the 19th inning, a cricketer increases his average score by 4. What will be his average score after 19 innings?
(A) 28
(B) 27
(C) 26
(D) 22
(E) 24
Rationale: Explanation :
Let the average score of the first 18 innings be n
18n + 94 = 19(n+4)=> n = 18
So, Average score after 19th innings = x+4 =22.
Answer : D
Answer: (D) 22
Question: The probability that A speaks truth is 3/5 and that of B speaking truth is 3/7. What is the probability that they agree in stating the same fact?
(A) 17/35
(B) 17/37
(C) 17/39
(D) 17/33
(E) 17/31
Rationale: If both agree stating the same fact, either both of them speak truth of both speak false.
Probability = 3/5 * 3/7 + 2/5 * 4/7
= 17/35
Answer:A
Answer: (A) 17/35
Question: A certain sum of money at simple interest amounted Rs.840 in 10 years at 3% per annum, find the sum?
(A) 337
(B) 268
(C) 198
(D) 646
(E) 168
Rationale: 840 = P [1 + (10*3)/100]
P = 646'
Answer:D
Answer: (D) 646
Question: Sum of three numbers 264, If the first number be twice then second and third number be one third of the first, then the second number is
(A) 70
(B) 71
(C) 72
(D) 73
(E) 74
Rationale: Explanation:
Let the second number is x, then first is 2x, and third is 1/3(2x)
=>2x+x+2x/3=264
<=>11x/3=264
=>x=72
Answer: Option C
Answer: (C) 72
Question: Two different solutions of alcohol with respective proportions of alcohol to water of 3:1 and 2:3 were combined. What is the concentration of alcohol in the new solution if the first solution was 4.6 times the amount of the second solution?
(A) 62.0
(B) 65.25
(C) 68.75
(D) 70.15
(E) 72.35
Rationale: SOL:
Lets assume that 46L of sol1 was mixed with 10L of sol2.
Alcohol in Sol1: 46*3/4 = 34.5L
Alcohol in Sol2: 10*2/5 = 4L
Total Alcohol in the mixed solution of 56L = 34.5 + 4 = 38.5L
Alcohol concentration in the new sol: (38.5/56)*100 = 68.75%
ANSWER:C
Answer: (C) 68.75
Question: A shopkeeper bought 600 oranges and 400 bananas. He found 15% of oranges and 5% of bananas were rotten. Find the percentage of fruits in good condition?
(A) 92.5%
(B) 89.0%
(C) 85.2%
(D) 96.8%
(E) 78.9%
Rationale: Total number of fruits shopkeeper bought = 600 + 400 = 1000
Number of rotten oranges = 15% of 600
= 15/100 × 600
= 9000/100
= 90
Number of rotten bananas = 5% of 400
= 20
Therefore, total number of rotten fruits = 90 + 20= 110
Therefore Number of fruits in good condition = 1000 - 110 = 890
Therefore Percentage of fruits in good condition = (890/1000 × 100)%
= (89000/1000)%
= 89.0%
Answer:B
Answer: (B) 89.0%
Question: A man is walking at a speed of 10 km per hour. After every kilometre, he takes rest for 10 minutes. How much time will be take to cover a distance of 10 kilometres?
(A) 148 min.
(B) 150 min.
(C) 145 min.
(D) 155 min.
(E) None of these
Rationale: Rest time = Number of rest Ã— Time for each rest
= 9 Ã— 10 = 90 minutes
Total time to cover 10 km
= (10 â„10 Ã— 60)minutes + 90 minutes = 150 minutes
Answer B
Answer: (B) 150 min.
Question: The average of runs of a cricket player of 20 innings was 36. How many runs must he make in his next innings so as to increase his average of runs by 4 ?
(A) 96
(B) 106
(C) 122
(D) 116
(E) 120
Rationale: Average = total runs / no.of innings = 36
So, total = Average x no.of innings = 36 * 20 = 720
Now increase in avg = 4 runs. So, new avg = 36+4 = 40 runs
Total runs = new avg x new no. of innings = 40 * 21 = 840
Runs made in the 11th inning = 840-720 = 120
ANSWER:E
Answer: (E) 120
Question: Find the length of a rectangle isdecreased by 40cm & the width is increased by 3cm, a square with the samearea as the original rectangle result. Find the perimeter of the original rectangle?
(A) 30 cm
(B) 40 cm
(C) 50 cm
(D) 64 cm
(E) 70 cm
Rationale: Let x and y be the length and breadth of the rectangle respectively.
Then, x - 4 = y + 3 or x - y = 7 ----(1)
Area of the rectangle =xy; Area of the square = (x - 4) (y + 3)
(x - 4) (y + 3) =xy <=> 3x - 4y = 12 ----(2)
Solving 1 & 2 , we get x = 16 and y = 9.
Perimeter of the rectangle = 2 (x + y) = [2 (16 + 9)] cm = 50 cm.
C
Answer: (C) 50 cm
Question: If the LCM of two integers M, N (where N> M and M>1) is M*N, then which of the following can not be true?
(A) Both M and N can be Prime Numbers.
(B) Both M and N can be consecutive integers.
(C) M and N do not share any Prime factors.
(D) All Prime factors of M must be Prime factors of N.
(E) M and N do not have a common factor.
Rationale: If LCM of two numbers M and N is the product MN then both numbers are Co- prime.
(Co-prime numbers are any two numbers which have an HCF of 1 i.e. when two numbers have no common prime factor apart from the number 1).
Numbers that can be Co-Prime are :
1) Two consecutive natural numbers.
2) Two consecutive odd numbers.
3) Two prime numbers.
4) One prime number and the other a composite number such that the composite number is not a multiple of the prime number.
With above four statements it can be concluded that Options A, B, C and E are all true.
Only Option D cannot be true.
Hence answer is D.
Answer: (D) All Prime factors of M must be Prime factors of N.
Question: An outlet pipe can empty 2/3 rd of a cistern in 12 minutes. In 8 minutes, what part of the cistern will be emptied?
(A) 4/9
(B) 4/1
(C) 4/7
(D) 4/2
(E) 4/9
Rationale: 2/3 ---- 12
? ----- 8 ==> 4/9
Answer:A
Answer: (A) 4/9
Question: An old man distributed all the gold coins he had to his two sons into two different numbers such that the difference between the squares of the two numbers is 16 times the difference between the two numbers. How many coins did the old man have?
(A)  24
(B)  26
(C)  30
(D)  16
(E)  40
Rationale: Let the number of coins one son got be x and the number of coins another got be y. Total = x + y.
x^2 - y^2 = 16(x - y) --> x + y = 16.
Answer: D.
Answer: (D)  16
Question: At a meeting, 3 people are to be seated around a circular table. Two seating arrangements are considered different only when the positions of the people are different relative to each other. What is the total number of different possible seating arrangements for the group?
(A) 2
(B) 7
(C) C)120
(D) D)144
(E) E)720
Rationale: The number of arrangements of n distinct objects in a row is given by n!
The number of arrangements of n distinct objects in a circle is given by (n−1)!
"The difference between placement in a row and that in a circle is following: if we shift all object by one position, we will get different arrangement in a row but the same relative arrangement in a circle. So, for the number of circular arrangements of n objects we have:
R=n!-n=(n−1)!
(n−1)!=(7−1)!=720
Answer: E
Answer: (C) C)120
Question: Having received his weekly allowance, John spent 3/5 of his allowance at the arcade. The next day he spent one third of his remaining allowance at the toy store, and then spent his last $0.96 at the candy store. What is John’s weekly allowance?
(A) $2.40
(B) $3.00
(C) $3.20
(D) $3.60
(E) $4.80
Rationale: Total allowance=X
Amount spent at the arcade=3/5X
Amount Remaining=2/5X
Amount Spent at the toy store=2/5*1/3X=2/15X
Amount Remaining=2/5X-2/15X=4/15X
Now, 4/15X=$0.96
Therefore, X=$3.60. Answer D
Answer: (D) $3.60
Question: If (c - a)/(c - b) = 3, then (5b - 5a)/(c - a) =
(A) 0.5
(B) 1
(C) 1.5
(D) 3.33
(E) 2.5
Rationale: Let's say c=7, b=5, a=1 so that our 1st expression holds true. Now, ibsert those numbers in the second expression and we'll get 3.33
Answer D (hopefully )))
Answer: (D) 3.33
Question: In the faculty of Reverse-Engineering, 220 second year students study numeric methods, 423 second year students study automatic control of airborne vehicles and 134 second year students study them both. How many students are there in the faculty if the second year students are approximately 80% of the total?
(A) 515.
(B) 545.
(C) 618.
(D) 644.
(E) 636.
Rationale: Answer is E :636
Solution : Total number of students studying both are 423 + 220 - 134 = 509 (Subtracting the 134 since they were included in the both the other numbers already).
So 80% of total is 509, so 100% is approx. 636.
Answer: (E) 636.
Question: Two trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively The ratio of their speeds is
(A) 2 : 3
(B) 4 : 3
(C) 6 : 7
(D) 9 : 16
(E) None
Rationale: Solution
Let us name the trains
as A and B.	= (A'S speed) : (B's speed)
=√b : √a
= √16 : √9
= 4 : 3
Answer B
Answer: (B) 4 : 3
Question: 10x + 2y = -6
2x + y = 3
In the system of equations above, what is the value of x?
(A) 3
(B) 2
(C) 1
(D) -1
(E) -2
Rationale: 10x + 2y = -6 can be written as 5x + y = -3
Let's subtract the second equation from this equation.
3x = -6
x = -2
The answer is E.
Answer: (E) -2