mathewhe/aqua_rat huggingface dataset:
Question: x - y =2
2x = 2y + 4
The system of equations above has how many solutions?
(A)  None
(B)  Exactly one
(C)  Exactly two
(D)  Infinitely many
(E)  Exactly three
Rationale: x-y=2 ---------------1
2x=2y+4 ---------------2
Divide equation 2 by 2:
2x/2=(2y+4)/2
x=y+2
x-y=2----------------3
Equation 1 and 3 are equal and thus have infinitely many solutions:
x-y=2
x=4, y=2
x=6, y=4
x=7, y=5
Ans:D
Answer: (D)  Infinitely many
Question: In a ratio which is equal to 7:9, if the antecedent is 42, then the consequent is?
(A) 72
(B) 54
(C) 64
(D) 51
(E) 45
Rationale: We have 7/9 = 42/x
7x = 42*9
x = 54
consequent = 54
Answer is B
Answer: (B) 54
Question: Two stations A and B are 110 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?
(A) 11 a.m
(B) 10 a.m
(C) 09 a.m
(D) 08 a.m
(E) 06 a.m
Rationale: Suppose they meet x hours after 7 a.m.
Distance covered by A in x hours = 20x km.
Distance covered by B in (x - 1) hours = 25(x - 1) km.
Therefore 20x + 25(x - 1) = 110
45x = 135
x = 3.
So, they meet at 10 a.m.
Answer: B
Answer: (B) 10 a.m
Question: A triangle has a perimeter 15. The two shorter sides have integer lengths equal to x and x + 1. Which of the following could be the length of the other side?
(A) 7
(B) 6
(C) 8
(D) 9
(E) 10
Rationale: The SHORTER sides have integral lengths equal to x and x + 1
Let the longest side be 'a'
So, a + x + (x +1) = 15
a + 2x = 14.......eqn (1)
We know that the sum of the lengths of the shorter sides has to be more than the length of the longer one. i.e 2x+1> a
a =6
B
Answer: (B) 6
Question: A can do a work in 15 days and B in 20 days. If they work on it together for 2 days, then the fraction of the work that is left is :
(A) 23/20
(B) 5
(C) 23/30
(D) 23/12
(E) 2
Rationale: Ans is:C
A's 1 day's work =1/15
B's 1 day's work =1/20
(A + B)'s 1 day's work =(1/15+1/20)=7/60
(A + B)'s 2 day's work =(7/60*2)=7/30
Therefore, Remaining work =(1-7/30)=23/30. Ans: C
Answer: (C) 23/30
Question: A committee of three people is to be chosen from five married couples. What is the number of different committees that can be chosen if two people who are married to each other cannot both serve on the committee?
(A) 16
(B) 24
(C) 48
(D) 64
(E) 80
Rationale: Each couple can send only one representative to the committee. Let's see in how many ways we can choose 3 couples (as there should be 3 members) out of 5 to send only one representatives to the committee: 5C3=10.
But each of these 3 couples can send two persons (husband or wife): 2*2*2=2^3=8.
Total # of ways: 5C3*2^3=80.
Answer: E.
Answer: (E) 80
Question: How many 4 digits number contain the number 2.
(A) 3170
(B) 3172
(C) 3174
(D) 3168
(E) 3167
Rationale: total no. of 4 digit nos are 9000(btwn 1000 and 9999).
consider the case where the nos contain no 2 in it.
so units place can be filled in 9 ways(0,1,3,4,5,6,7,8,9)
smlry,tenths place in 9 ways
hunderedths place in 9 ways
thousands place can be filled in 8 ways only(because 0 cannot come)
so total nos are (9000-(8*9*9*9))=3168
ANSWER:D
Answer: (D) 3168
Question: 3 candidates in an election and received 1136, 7636 and 11628 votes respectively. What % of the total votes did the winningcandidate got in that election?
(A) 30%
(B) 59%
(C) 57%
(D) 64%
(E) 69%
Rationale: Total number of votes polled = (1136 + 7636 + 11628) = 20400
So, Required percentage = 11628/20400 * 100 = 57%
C
Answer: (C) 57%
Question: Given positive integer x, which of the following CANNOT be evenly divisible by x?
(A) 7x
(B) x + 2
(C) 2x - 1/2
(D) 3x − 1
(E) x + 6
Rationale: This can be easily solved by substituting values:
Assume x to be 1
A. 7x: 7 is evenly divisible by 1
B. x + 2: 3 is evenly divisible by 1
C. 2x - 1/2: 3/2 is not evenly divisible by 1
D. 3x − 1: 2 is evenly divisible by 1
E. x + 6: 7 is not evenly divisible by 1
Option C
Answer: (C) 2x - 1/2
Question: If an object travels 80 feet in 2 seconds, what is the object’s approximate speed in miles per hour? (Note: 1 mile = 5280 feet)
(A) 21.21
(B) 24.24
(C) 27.27
(D) 30.35
(E) 33.33
Rationale: 80 feet/2 seconds = 40 feet/second
(40 feet/second)*(3600 seconds/hour)*(1 mile/5280 feet) = 27.27 miles/hour (approximately)
The answer is C.
Answer: (C) 27.27
Question: A bag contains 6 black and 8 white balls. One ball is drawn at random. What is the probability that the ball drawn is white?
(A) 4/7
(B) 3/7
(C) 2/7
(D) 7/7
(E) 4/3
Rationale: Let number of balls = (6 + 8) = 14.
Number of white balls = 8.
P (drawing a white ball) =8/14=4/7.
Answer: A
Answer: (A) 4/7
Question: Consider a quarter of a circle of radius 49. Let r be the radius of the circle inscribed in this quarter of a circle. Find r.
(A) 49*(sqr2 -1)
(B) 58*(sqr3 -1)
(C) 40*(sqr7 - 1)
(D) 12* (sqr7 -1)
(E) None of these
Rationale: I got 49/(sqr2 +1) and just forgot to multiply by (sqr2 -1).
Answer is A
Answer: (A) 49*(sqr2 -1)
Question: An urn contains 10 balls, numbered from 1 to 10. If 2 balls are selected at random with replacement from the urn, what is the probability G that the sum of the 2 numbers on the balls will be even?
(A) 25%
(B) 37.5%
(C) 50%
(D) 62.5%
(E) 75%
Rationale: Correct Answer: C
Since there are 5 even numbered balls and 5 odd numbered balls, the probability G of selecting either an even or an odd is 5/10= 1/2. In order for the sum of the numbers on the two balls to be even, either both numbers must be even or both numbers must be odd; one even and one odd number would add to an odd number. The probability of selecting two even numbers is:
1/2 * 1/2= 1/4
The probability of selecting two odd numbers is also:
1/2 * 1/2= 1/4
Adding both probabilities gives 1/4+1/4= 1/2 , or 50%, as the probability that the sum of the numbers will be even. Thus, the correct answer is (C).
Answer: (C) 50%
Question: Martin bought 10 concert tickets, some at the full price of $2.00 per ticket, and some at a discounted price of $1.60 per ticket. If he spent a total of $17.20, how many discounted tickets did he buy?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: Let x be the number of tickets he bought at $2 per ticket.
then 2 x + (10-x)1.6 = 17.2
0.4x = 1.2 => x = 3
discounted tickets = 10 -x = 7
Ans : E
Answer: (E) 7
Question: A and B can do a piece of work in 2 days. With the help of C they finish the work in 1 days. C alone can do that piece of work in?
(A) 1.5 DAYS
(B) 4 DAYS
(C) 3 DAYS
(D) 1 DAY
(E) 2 DAYS
Rationale: C = 1/1 – 1/2= 1/2 => 2 days
Answer:E
Answer: (E) 2 DAYS
Question: A can do a piece of work in 4 hours; B and C together can do it in 3 hours, while A and C together can do it in 2 hours. How long will B alone take to do it?
(A) 8 hours
(B) 10 hours
(C) 12 hours
(D) 24 hours
(E) 25 hours
Rationale: Explanation:
A's 1 hour's work =1/4
(B + C)'s 1 hour's work =1/3
(A + C)'s 1 hour's work =1/2
(A + B + C)'s 1 hour's work =1/4 +1/3=7/12
B's 1 hour's work =7/12-1/2=1/12
B alone will take 12 hours to do the work.
ANSWER IS C
Answer: (C) 12 hours
Question: If the average (arithmetic mean) of 5 positive temperatures is x degrees Fahrenheit, then the sum Q of the 3 greatest of these temperatures, in degrees Fahrenheit, could be
(A) 6x
(B) Q=4x
(C) Q=5x/3
(D) Q=3x/2
(E) 3x/5
Rationale: OA please. Yeah so 5x is the sum of the 5, then I guess 4x could be the answer (B)
But what about C,D,E? Any ideas why these could be wrong?
Note that we have 5 positive temperatures.
Next, as the average is x then the sum of the temperatures is 5x and as all the temperatures are positive then the sum of the 3 greatest must be more than (or equal to) 3x (as the average of the 3 greatest must be at least x) and less than 5x: 3x<SUM<5x --> only option B fits.
Answer: B.
Answer: (B) Q=4x
Question: Find the area of a parallelogram with base 21 cm and height 11 cm?
(A) 231 cm2
(B) 384 cm2
(C) 672 cm2
(D) 267 cm2
(E) 286 cm2
Rationale: Area of a parallelogram
= base * height
= 21 * 11
= 231 cm2
Answer: A
Answer: (A) 231 cm2
Question: A farmer built a fence around his square plot. He used 27 fence poles on each side of the square. How many poles did he need altogether ?
(A) 100
(B) 104
(C) 108
(D) 112
(E) None of these
Rationale: one side=2 corners( 1 nd 1 each) plus 25 ...
1 25 1
25 25
1 25 1
der4 ans=25*4+4=104
ANSWER:B
Answer: (B) 104
Question: Ram professes to sell his goods at the cost price but he made use of 500 grms instead of a kg, what is the gain percent?
A. 11%
(A) 11 1/9%
(B) 11 1/8%
(C) 11 9/9%
(D) 100%
(E) 11 1/5%
Rationale: 500 --- 500
100 --- ? => 100%
Answer:D
Answer: (D) 100%
Question: Two pipes A and B can separately fill a tank in 12 and 15 minutes respectively. A third pipe C can drain off 45 liters of water per minute. If all the pipes are opened, the tank can be filled in 15 minutes. What is the capacity of the tank?
(A) 542
(B) 540
(C) 542
(D) 829
(E) 279
Rationale: 1/12 + 1/15 - 1/x = 1/15
x = 12
12 * 45 = 540
Answer: B
Answer: (B) 540
Question: If x : y = 3 : 5, find the value of (2x + 4y) : (4x – y)
(A) 29:7
(B) 22:7
(C) 26:7
(D) 20:7
(E) 26:5
Rationale: Explanation:
Given: a/b = 3/5
(2*3 + 4*5) : (4*3 – 5)
= 26:7
ANSWER: C
Answer: (C) 26:7
Question: The average marks of 14 students was calculated as 71. But, it was discovered later that the marks of one student was taken as 42 instead of 56 and the marks of another student was wrongly taken as 74 while it was actually 32. If these corrections are now made then what is the average of the 14 students?
(A) 67
(B) 68
(C) 69
(D) 80
(E) 71
Rationale: total marks =14*71 = 994
marks with out that two studnts = 994-42-74 = 878
total marks ith corrections = 878+56+32 = 966
the average marks = 966/14 =69
ANSWER:C
Answer: (C) 69
Question: If s is the product of the integers from 40 to 50 inclusive, and if t is the product of the integers from 40 to 51 inclusive, what is 1/s + 1/t in terms of t?
(A) 32/t
(B) 42/t
(C) 52/t
(D) 62/t
(E) 72/t
Rationale: Similarly in the actual problem
s =t/51. 1/s = 1/(t/51) or 1/s = 51/t
1/s + 1/t = 51/t + 1/t = 52/t
C
Answer: (C) 52/t
Question: A train starts full of passengers at the first station it drops 1/3 of the passengers and takes 280 more at the second station it drops one half the new total and takes twelve more .on arriving at the third station it is found to have 248 passengers. Find the no of passengers in the beginning?
(A) 258
(B) 288
(C) 248
(D) 278
(E) 238
Rationale: Let no of passengers in the beginning be x
After first station no passengers=(x-x/3)+280=2x/3 +280
After second station no passengers =1/2(2x/3+280)+12
½(2x/3+280)+12=248
2x/3+280=2*236
2x/3=192
x=288
Answer is B.
Answer: (B) 288
Question: 19/6 = 4/27. Which method did you use to determine whether this proportion is true or false?
(A) 24
(B) 77
(C) 88
(D) 26
(E) 91
Rationale: 19/6 = 4/27.
Cross multiplication:
19 × 27 = 513.
6 × 4 = 24.
Answer:A
We see that 513 are not equal to 24.
Therefore, we determine 19/6 = 4/27 is not proportion so, the answer is false.
Answer: (A) 24
Question: Balls of equal size are arranged in rows to form an equilateral triangle. the top most row consists of one ball, the 2nd row of two balls and so on. If 253 balls are added, then all the balls can be arranged in the shape of square and each of the sides of the square contain 8 balls less than the each side of the triangle did. How many balls made up the triangle?
(A) 903
(B) 2209
(C) 2878
(D) 1210
(E) 1560
Rationale: As expected, this question boils down to 2 equation,
Consider total number of Balls in Triangle = T and number of balls in last row = x.
1+2+3+...+x = T
x(x+1)/2 = T ----(a)
As mentioned in the question, side of a square will be (x-8) and total number of Balls in square will be (T+253)
(x-8)^2 = T+253 -----(b)
Now the hardest part of the question will be to solve these 2 equations and this looks like time consuming BUT the easy way will be plug and play. Also, we've to find a value of T (from 5 optiosn given below) which can make a square of a a number. One we know this, it will be a cake walk.
We can see that option A fits this criteria in eq (b). Add - 903+253 = 1156 = 34^2 = (x-8)^2 Hence, x = 42.
Cross check by putting in eq (a) = x(x+1)/2 = T = > 42*43/2=903
Hence, answer is A.
Answer: (A) 903
Question: 2 gears one with 12 teeth and other one with 14 teeth are engaged with each other. One teeth in smaller and one tooth in bigger are marked and initially those 2 marked teeth are in contact with each other. After how many rotations of the smaller gear with the marked teeth in the other gear will again come into contact for the first time?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 2
Rationale: Assume the distance between the teeth is 1 cm. Then the circumference of first gear is 12 cm and the second is 14 cm.
Now LCM (12, 14) = 84. So to cover 84 cm, the first gear has to rotate 84128412 = 7 rounds (the second gear rotates 84 / 14 = 6 rounds as it is bigger)
Correct Option : A
Answer: (A) 6
Question: A total of m different points are selected on a particular line, and a total of n different points are selected on another line parallel to the first, where each of m and n is greater than 1. In how many different ways can a triangle be made with its vertices at three of the selected points?
(A) m^2n+mn^2
(B) mn(m+n-2)
(C) mn(m+n−2)/2
(D) (m+n)(m+n−1)(m+n−2)/6
(E) (m+n)!/m!n!
Rationale: ase 1: One point on particular line and other 2 points on parallel line. #ways=
m* nc2
Case 2: one point on parallel line and other 2 on particular line.
n* mc2
Total
m* nc2+ n* mc2
mn(m+n-2)
ANS:B
Answer: (B) mn(m+n-2)
Question: A basket has 5 apples and 4 oranges. Three fruits are picked at random. The probability that at least 2 apples are picked is?
(A) 25/42
(B) 25/46
(C) 25/48
(D) 25/18
(E) 25/29
Rationale: Total fruits = 9
Since there must be at least two apples,
(⁵C₂ * ⁴C₁)/⁹C₃ + ⁵C₃/⁹C₃
= 25/42.
Answer: A
Answer: (A) 25/42
Question: At what rate percent on simple interest will Rs.1750 amount to Rs.2000 in 5 years?
(A) 4 %
(B) 3 6/7 %
(C) 2 6/7 %
(D) 5 %
(E) 6 %
Rationale: Explanation:
250 = (1750x5xR)/100
250 = (175xR)/2
500 = (175xR)
R = 500/175
R = 2 6/7 %
Answer: Option C
Answer: (C) 2 6/7 %
Question: How many times the keys of a writter haveto be pressedin order to write first 400 counting no.'s?
(A) 998
(B) 1000
(C) 1092 times
(D) 1100
(E) 1200
Rationale: 1 to 9 = 9 * 1 = 9
10 to 99 = 90 * 2 = 180
100 to 400 = 301 * 3 = 903
-----------
1092
C
Answer: (C) 1092 times
Question: In a box, there are 8 red, 7 blue and 6 green balls. One ball is picked up randomly. What is the probability that it is neither red nor green?
(A) 1/3
(B) 2/3
(C) 1/4
(D) 1/5
(E) 2/5
Rationale: Total number of balls = (8 + 7 + 6) = 21.
Let E	= event that the ball drawn is neither red nor green
= event that the ball drawn is blue.
n(E) = 7
=>7/21 = 1/3
ANSWER A
Answer: (A) 1/3
Question: The average age of 25 students of a class is 25 years. Out of these, the average age of 10 students is 22 years and that of the other 14 students is 28 years. The age of the 25th student is?
(A) 10
(B) 15
(C) 13
(D) 11
(E) 9
Rationale: Age of the 25th student = 25*25 - (10*22+14*28) = 625-612 = 13 years
Answer is C
Answer: (C) 13
Question: A teacher gave the same test to three history classes: A, B, and C. The average (arithmetic mean) scores for the three classes were 65, 95, and 77, respectively. The ratio of the numbers of students in each class who took the test was 4 to 6 to 5, respectively. What was the average score for the three classes combined?
(A) 74
(B) 75
(C) 76
(D) 77
(E) 81
Rationale: ratio is 4:6:5 , numbers are 4x, 6x, 5x
total scores of each class is (65*4x + 6x * 95 + 77*5x) = 260x+570x+385x = 1215x
total number of students = 15x
average = 1215x/15x = 81
E is the answer
Answer: (E) 81
Question: A train 280 m long is running with a speed of 60 km/hr. In what time will it pass a man who is running at 6 km/hr in the direction opposite to that in which the train is going?
(A) 15
(B) 6
(C) 7
(D) 9
(E) 5
Rationale: Speed of train relative to man = 60 + 6 = 66 km/hr.
= 66 * 5/18 = 55/3 m/sec.
Time taken to pass the men = 280 * 3/55 = 15 sec.Answer: A
Answer: (A) 15
Question: How many integers between 324,805 and 458,705 have tens digit 1 and units digit 3?
(A) 1,349
(B) 1,353
(C) 10,040
(D) 1,354
(E) 10,400
Rationale: There is one number in hundred with 1 in the tens digit and 3 in the units digit: 13, 113, 213, 313, ...
The difference between 324,805 and 458,705 is 458,705-324,805=134,900 - one number per each hundred gives 134,900/100=1,349 numbers.
Answer: A.
Answer: (A) 1,349
Question: Two trains of length 100 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 90 kmph. In how much time will the trains cross each other?
(A) 11
(B) 10
(C) 12
(D) 13
(E) 14
Rationale: Relative speed = (54 + 90)* 5/18 = 7 * 5 = 40 mps.
The time required = d/s = (100 + 100 + 200)/40
= 400/40 = 10 sec.
Answer: B
Answer: (B) 10
Question: Find the least number which when divided by 35 and 11 leaves a remainder of 1 in each case.
(A) 366
(B) 236
(C) 367
(D) 365
(E) 386
Rationale: Explanation:
The least number which when divided by different divisors leaving the same remainder in each case
= LCM(different divisors) + remainder left in each case.
Hence the required least number
= LCM(35, 11) + 1 = 386.
Answer: E
Answer: (E) 386
Question: A man whose speed is 4.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph, find his average speed for the total journey?
(A) 8
(B) 4
(C) 3
(D) 2
(E) 6
Rationale: M = 45
S = 1.5
DS = 6
US = 3
AS = (2 * 6 * 3) /9 = 4
Answer: B
Answer: (B) 4
Question: A tank is filled in 5 hours by three pipes A, B and C. The pipe C is twice as fast as B and B is twice as fast as A. How much time will pipe A alone take to fill the tank?
(A) 76 hrs
(B) 97 hrs
(C) 35 hrs
(D) 16 hrs
(E) 12 hrs
Rationale: Suppose pipe A alone takes x hours to fill the tank.
Then, pipes B and C will take x/2 and x/4 hours respectively to fill the tank.
1/x + 2/x + 4/x
= 1/5
7/x = 1/5 => x = 35 hrs.
Answer: C
Answer: (C) 35 hrs
Question: If a positive even number n is not divisible by 3 or 4, then the product (n + 6)(n + 8)(n + 10) must be divisible by which of the following?
I. 24
II. 32
III. 96
(A) None
(B) I only
(C) II only
(D) I and II only
(E) I, II, and III
Rationale: n is a multiple of 2 but not a multiple of 3 or 4
Possible values of n = 10, 14, 22.....
@n=10 : (n + 6)(n + 8)(n + 10) = 16*18*20 i.e. Divisible by 24, 32 and 96 all
@n=14 : (n + 6)(n + 8)(n + 10) = 20*22*24 i.e. Divisible by 24, 32 and 96 all
@n=22 : (n + 6)(n + 8)(n + 10) = 28*30*32 i.e. Divisible by 24, 32 and 96 all
Answer: Option E
Answer: (E) I, II, and III
Question: Mysoon collects glass ornaments. Ten more than 1/6 of the ornaments in her collection are handmade, and 1/2 of the handmade ornaments are antiques. If 1/10 of the ornaments in her collection are handmade antiques, how many ornaments are in her collection?
(A) 36
(B) 60
(C) 108
(D) 144
(E) 300
Rationale: The number of ornaments = a
Ten more than 1/6 of the ornaments in her collection are handmade => Handmade = 10+a/6
1/2 of the handmade ornaments are antiques => Handmade ornaments = 1/2*(10+a/6) = 5 + a/12
1/10 of the ornaments in her collection are handmade antiques => Handmade ornaments = a/10
=> 5 + a/12 = a/10 => a = 300
Ans: E
Answer: (E) 300
Question: Every letter in the alphabet has a number value that is equal to its place in the alphabet. Thus, the letter A has a value of 1, the letter B has a value of 2, the letter C has a value of 3, etc... The number value of a word is obtained by adding up the value of the letters in the word and then multiplying that sum by the length of the word. What is the number value of the word "COW"?
(A) 120
(B) 123
(C) 126
(D) 129
(E) 132
Rationale: "COW" = (3+15+23)*3=123.
The answer is B.
Answer: (B) 123
Question: The owner of a cell phone shop charges his customer 23% more than the cost price. If a customer paid Rs.7,011 for a cell phone, then what was the cost price of the cell phone?
(A) Rs.5,845
(B) Rs.6,750
(C) Rs.5,700
(D) Rs.6,925
(E) None of these
Rationale: Explanation:
123% of CP =SP
Therefore, CP = Rs.7,011x100/123 = Rs.5700
Answer: Option C
Answer: (C) Rs.5,700
Question: A cube of edge 5 cm is cut into cubes of each edge 1 cm. The ratio of the total surface area of one of the small cubes to that of the large cube is equal to
(A) 1 : 5
(B) 1 : 25
(C) 1 : 125
(D) 1 : 625
(E) None
Rationale: Solution
Required ratio	=(6x1x1 / 6x5x5)
‹=› 1/ 25
‹=› 1 : 125.
Answer B
Answer: (B) 1 : 25
Question: In a school of 650 boys, 44% of Muslims, 28% Hindus, 10% Sikhs and the remaining of other communities. How many belonged to the other communities?
(A) 173
(B) 163
(C) 153
(D) 143
(E) 117
Rationale: 44 + 28 + 10 = 82%
100 – 82 = 18%
650 * 18/100 = 117
ANSWER:E
Answer: (E) 117
Question: Mr Amin borrowed some money from Mr Vishwas. The rate of interest for first two years is 8% p.a., for the next three years is 11 % p.a. and for the period beyond 5 years 14% p.a. Mr Vishwas got an amount of 10920 as an interest at the end of eight years. Then what amount was borrowed by Mr Amin ?
(A) 12000
(B) 15000
(C) 1400
(D) Data inadequate
(E) None of these
Rationale: Let ‘x’ be the amount borrowed by Mr Amin.
∴ x×2×8/100+x×3×11/100+x×3×14/100=10920
or, 91⁄100x = 10920 or x = 10920×100/91=12000
Answer A
Answer: (A) 12000
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 W 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 W is:
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: In a graduating class of 232 students, 144 took geometry and 119 took biology. What is the difference between the greatest possible number and the smallest possible number of students that could have taken both geometry and biology?
(A) 144
(B) 119
(C) 113
(D) 88
(E) 31
Rationale: Greatest Possible Number taken both should be 144 (As it is maximum for One)
Smallest Possible Number taken both should be given by
Total - Neither = A + B - Both
Both = A+B+Neither - Total (Neither must be 0 to minimize the both)
So 144 + 119 + 0 - 232 = 31
Greatest - Smallest is 144-31 = 113
So answer must be C. 113
Answer: (C) 113
Question: In a certain circle there are 9 points. What is the number of the triangles connecting 3 points of the 9 points?
(A) 12
(B) 84
(C) 108
(D) 120
(E) 132
Rationale: IMO : B
HERE we have to select 3 points out of 9 points. Order is not important
So the answer will be 9c3 = 84
answer B
Answer: (B) 84
Question: In an office, 10 percent of the workers have at least 5 years of service, and a total of 16 workers have at least 10 years of service. If 90 percent of the workers have fewer than 10 years of service, how many of the workers have at least 5 but fewer than 10 years of service?
(A)  16
(B)  64
(C)  50
(D)  144
(E)  160
Rationale: (10/100)Workers = 16 = > number of workers = 160
(10/100)*Workers = x+16 = > x = 16
Answer A
Answer: (A)  16
Question: John makes $50 a week from his job. He earns a raise andnow makes $75 a week. What is the % increase?
(A) 15%
(B) 16.66%
(C) 50%
(D) 19%
(E) 21%
Rationale: Increase = (25/50)*100 = (1/2)*100 = 50%.
C
Answer: (C) 50%