mathewhe/aqua_rat huggingface dataset:
Question: A company assigns product codes consisting of all the letters in the alphabet.How many product codes are possible if the company uses at most 3 letters in its codes, and all letters can be repeated in any one code?
(A) 15600
(B) 16226
(C) 17576
(D) 18278
(E) 28572
Rationale: 1-letter codes
26 letters, so there are 26 possible codes
2-letter codes
There are 26 options for the 1st letter, and 26 options for the 2nd letter.
So, the number of 2-letter codes = (26)(26) = 26²
3-letter codes
There are 26 options for the 1st letter, 26 options for the 2nd letter, and 26 options for the 3rd letter.
So, the number of 3-letter codes = (26)(26)(26) = 26³
So, the TOTAL number of codes = 26 + 26² + 26³=18278
ANSWER:D
Answer: (D) 18278
Question: Oil cans x and y are right circular cylinders and the height and radius of y are each 10 times those of x. If the oil in can x filled to capacity sells for $1, how much does the oil in y sell for if y is only half filled?
(A) $400
(B) $450
(C) $500
(D) $550
(E) $600
Rationale: formula for vol of a cyl is PI*r^2*h
so Vy = 1000*Vy
y when half filled will cost 500 times x so ans is C
Answer: (C) $500
Question: If n divided by 11 has a remainder of 1, what is the remainder when 5 times n is divided by 11?
(A) 1
(B) 2
(C) 3
(D) 9
(E) 5
Rationale: As per question => N=11P+1 for some integer p
hence 5N => 55Q + 5 => remainder => 5 for some integer Q
hence E
Answer: (E) 5
Question: At the moment there are 54,000 tagged birds in a certain wildlife refuge. If exactly 20 percent of all birds in the refuge are tagged, what percent of the untagged birds must be tagged so that half of all birds in the refuge are tagged?
(A) 36.95
(B) 37.5
(C) 34.44
(D) 33.91
(E) 50
Rationale: All birds = 54000
Currently Tagged = 54000 * 20/100 = 10800
So Untagged birds = 54000 - 10800 = 43200
Half of all birds = 27000
The number of birds to be tagged to make half of all birds tagged = 27000 - 10800 = 16200
So now the question remains - 16200 is how much percentage of untagged birds (43200)
= 16200 * 100 /43200
= 37.5 %
Answer (B)
Answer: (B) 37.5
Question: How many kilograms of sugar costing Rs. 9 per kg must be mixed with 27kg of sugar costing Rs.7 per kg so that there may be gain of 10% by selling the mixture at Rs.9.24 per kg?
(A) 60 kg
(B) 63 kg
(C) 50 kg
(D) 77 kg
(E) None of these
Rationale: Explanation :
Let the rate of second quality be Rs x per Kg.
Step 1 :
S.P of 1 kg of mixture = Rs. 9.24
Gain = 10%
C.P of 1 kg of mixture =[100/(100+10)×9.24].
=> Rs. 8.40.
Thus, the mean price = Rs. 8.40.
Step 2 :
C.P of 1 kg of sugar of 1st kind = 900p
C.P of 1 kg of sugar of 2nd kind = 700p
Mean price = 840p
By the rule of alligation, we have:
C.P. of 1kg of C.P. of 1kg of
sugar of 1st sugar of 2nd
kind (900p) kind (700p)
\ /
Mean Price
(840p)
/ \
840 - 700 : 900 - 840
(140) (60)
=> Required ratio = 140 : 60 = 7 : 3.
Step 3:
Let, x kg of sugar of 1st kind be mixed with 27 kg of 2nd kind, then
=>7:3=x:27.
=>7/3=x/27.
=>x=(7/3)x 27.
=>x=63.
Answer : B
Answer: (B) 63 kg
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) 25/41
(D) 25/48
(E) 25/32
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: The length of the rectangular field is double its width. Inside the field there is square shaped pond 9m long. If the area of the pond is 1/8 of the area of the field. What is the length of the field?
(A) 54
(B) 36
(C) 75
(D) 28
(E) 11
Rationale: A/8 = 9 * 9 => A = 9 * 9 * 8
x * 2x =9 * 9 * 8
x = 18 => 2x = 36
Answer:B
Answer: (B) 36
Question: A reduction of 20% in the price of salt enables a lady to obtain 10kgs more for Rs.100, find the original price per kg?
(A) 2.9
(B) 2.6
(C) 2.5
(D) 2.4
(E) 2.1
Rationale: 100*(20/100) = 20 --- 10
? --- 1 => Rs.2
100 --- 80
? --- 2 => Rs.2.5
Answer:C
Answer: (C) 2.5
Question: If 3x=2y=z, what is x+y, in terms of z?
(A) 5z/6
(B) 2z
(C) z/3
(D) 3z/5
(E) z/9
Rationale: 3x=2y=z
x = z/3
and y = z/2
x+y = z/3 + z/2 = 5z/6
Answer is A
Answer: (A) 5z/6
Question: A factory produces 5500 toys per week. If the workers at this factory work 5 days a week and if these workers make the same number of toys everyday, how many toys are produced each day?
(A) 1100 toys
(B) 5487 toys
(C) 6113 toys
(D) 2354 toys
(E) 1375 toys
Rationale: To find the number of toys produced every day, we divide the total number of toys produced in one week (of 5 days) by 5.
5500 /5 = 1100 toys
correct answer A
Answer: (A) 1100 toys
Question: 8 friends decides to eat pizza. 4 friends eat type 1 pizza which cost 100 each. Remaining friend buy pizza having off on it and saves 100 and each of them pay equal money .Total bill is 800. what is % of off on each pizza.
(A) 20%
(B) 30%
(C) 10%
(D) 15%
(E) 25%
Rationale: Solution: A.8 friend = 800. per friend 100. Saves 100 and each of them paid 100 and saved 100/4=25. so pizza had a 20% off
Answer: (A) 20%
Question: A family made a down payment of $55 and borrowed the balance on a set of encyclopedias that cost $400. The balance with interest was paid in 23 monthly payments of $16 each and a final payment of $9. The amount of interest paid was what percent of the amount borrowed?
(A)  6%
(B)  8%
(C)  7.7%
(D)  10%
(E)  5%
Rationale: borrowings = 400-50 = 350
total pmt = 23x16 + 9 = 377
so int = 377 - 350 = 27
interest in terms of borrowing = 27/350 = 7.7%
Answer is C
Answer: (C)  7.7%
Question: The average salary of all the workers in a workshop is Rs. 8000. The average salary of 9 technicians is Rs. 18000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is :
(A) 22
(B) 54
(C) 88
(D) 37
(E) 29
Rationale: Explanation:
Lot the total number of workers be v Then,
8OOOv = (18000 * 9) + 6000 (v - 9) <=> 2000v = 108000 <=> v = 54
Answer: B) 54
Answer: (B) 54
Question: which of the following could be the greatest common factor of positive integers 10 and 15 ? I) 5 II) 4 III) 2
(A) II only
(B) I only
(C) III only
(D) I,II only
(E) I,III only
Rationale: 10=2*5
15=3*5
GCF =5
Answer : B
Answer: (B) I only
Question: During 2001, a stock lost 90 percent of its value. During the following year, the stock's value increased by 200 percent. Which of the following is the percent change in the stock's value during those two years?
(A) 70 percent decrease
(B) 40 percent decrease
(C) 20 percent increase
(D) 60 percent increase
(E) 140 percent increase
Rationale: Let the value of the stock in 2000 be 100, then in 2001 its value would be 100*(1-90/100)=100*0.1=10 and in 2002 its value would be 10*(1+200/100)=30. Hence during those two years the value of the stock decreased from 100 to 30, so by 70%.
Answer: A.
Answer: (A) 70 percent decrease
Question: The H.C.F. and L.C.M. of two numbers are 12 and 5040 respectively If one of the numbers is 144, find the other number
(A) 400
(B) 256
(C) 120
(D) 420
(E) None of these
Rationale: Explanation:
Solve this question by using below formula.
Product of 2 numbers = product of their HCF and LCM
144 * x = 12 * 5040
x = (12*5040)/144 = 420
Option D
Answer: (D) 420
Question: A man sitting in a train which is traveling at 60 kmph observes that a goods train, traveling in opposite direction, takes 12 seconds to pass him. If the goods train is 300 m long, find its speed
(A) 52 kmph
(B) 56 kmph
(C) 58 kmph
(D) 30 kmph
(E) 34 kmph
Rationale: Explanation:
Relative speed = 300/12 m / sec = ((300/12)×(18/5)) kmph = 90 kmph.
Speed of goods train = (90 - 60) kmph = 30 kmph
Answer: Option D
Answer: (D) 30 kmph
Question: Insert the missing number. 34, 7, 37, 14, 40, 28, 43, (...)
(A) 56
(B) 40
(C) 30
(D) 22
(E) 25
Rationale: We have two series here
34, 37, 40, 43, ... (Increase by 3)
7, 14, 28, ... (Multiply by 2)
next term is 28 Ã— 2 = 56
ANSWER A
Answer: (A) 56
Question: A coin has two sides. One side has the number 1 on it and the other side has the number 2 on it. If the coin is flipped four times what is the probability that the sum of the numbers on the landing side of the coin will be greater than 4?
(A) 3/16
(B) 15/16
(C) 11/16
(D) 5/8
(E) 3/4
Rationale: There are 16 possible outcomes and only one (1111) has a sum equal or less than 4.
P(the sum is greater than 4) = 1 - 1/16 = 15/16
The answer is B.
Answer: (B) 15/16
Question: Jim is able to sell a hand-carved statue for $670 which was a 25% profit over his cost. How much did the statue originally cost him?
(A) $496.30
(B) $536.00
(C) $555.40
(D) $574.90
(E) $588.20
Rationale: 670 = 1.25*X
X = 670/1.25 = 536
$536, which is (B).
Answer: (B) $536.00
Question: A train crosses a tunnel of 1200 m in 45 sec, same train crosses another platform of length 180 m in 15 sec. then find the length of the train?
(A) 350m
(B) 400m
(C) 272m
(D) 330m
(E) 267m
Rationale: Length of the train be ‘X’
(X + 1200)/45 = (X + 180)/15
X + 1200 = 3X + 540
2X = 660
X = 330m
Answer: D
Answer: (D) 330m
Question: 5:3 is the present ratio between the ages of Rose and Jennie. In 5 years time Rose will be 20. What is the present age of Jennie?
(A) 9
(B) 5
(C) 4
(D) 7
(E) 9
Rationale: Let the present ages of Rose and Jennie be 5x years and 3x years respectively
5x+5 = 20
5x = 15
x = 3
Jennie's age = 3x = 9 years
Answer is E
Answer: (E) 9
Question: A group of men decided to do a work in 55 days, but 15 of them became absent. If the rest of the group did the work in 60 days, Find the original number of men?
(A) 180
(B) 150
(C) 140
(D) 100
(E) 25
Rationale: Original number of men = 15*60 / (60-55) = 180
Answer is A
Answer: (A) 180
Question: A group consists of 4 couples in which each of the 4 boys have one girl friend.In how many ways they can be arranged in a straight line such that boys and girls occupies alternate positions?
(A) 1142
(B) 1152
(C) 1252
(D) 1342
(E) 1424
Rationale: Total positions are 8.
In that boys can be arranged in 4 places and girls can be arranged in 4 places and hence this can be done in 2 ways.
i.e => 4! * 4! * 2 = 24*24*2=1152.
ANSWER:B
Answer: (B) 1152
Question: What is the probability of rolling a total of 9 with a single roll of two fair six-sided dice, each with the distinct numbers 1 through 6 on each side?
(A) 1/12
(B) 1/6
(C) 1/9
(D) 1/3
(E) 1/2
Rationale: Totalsample spacefrom two fair six-sided dice is 36.
There are six possible ways to be 7 i.e. (3+6), (4+5), (5+4), (6+3)
So, total probability is 4/36 or 1/9.
Answer is C.
Answer: (C) 1/9
Question: What is the angle of degree suspended when two hands of clock showing the time 2.30.
(A) 95 degree
(B) 105 degree
(C) 115 degree
(D) 125 degree
(E) 135 degree
Rationale: angle between 2 and 6 =30*4=120
andin half an hour hour hand moves forward by 30/2=15 degree
hence required ans= 120-15=105 degree
ANSWER:B
Answer: (B) 105 degree
Question: If m and n are positive integers and n ≠ 1, then mn(n −1) is
(A) m-n
(B) m+n
(C) mn
(D) mn^2 -mn
(E) mn^2
Rationale: mn(n-1) = mn^2 -mn
Answer : D
Answer: (D) mn^2 -mn
Question: A man can swim in still water at 7.5 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is?
(A) 1.7
(B) 1.4
(C) 1.1
(D) 1.5
(E) 2.5
Rationale: M = 7.5
S = x
DS = 7.5 + x
US = 7.5 + x
7.5 + x = (7.5 - x)2
7.5 + x = 15 -2x
3x = 7.5
x = 2.5
Answer:E
Answer: (E) 2.5
Question: Seema took a loan of 1800 with simple interest for as many years as the rate of interest. If she paid 162 as interest at the end of the loan period, what was the rate of interest?
(A) 4
(B) 3
(C) 5
(D) Can not be determined
(E) None
Rationale: Explanation: Let rate = R% and time = R years.
Then, (1800 x R x R)/100 = 162
18RÂ² = 162
RÂ² = 9
R = 3.
Answer: B
Answer: (B) 3
Question: If J is the interest on K and K is the interest on L, the rate and time is the same on both the cases. What is the relation between J, K and L ?
(A) JxJ = KL
(B) KxK= JL
(C) LxL = JK
(D) JKL = 1
(E) None of these
Rationale: Explanation:
Let the Time be 'N' and Rate be 'R'
J = (K x NR)/100 K = (L x NR)/100
J/K = NR/100 K/L = NR/100
J/K = K/L
K2= JL
ANSWER IS B
Answer: (B) KxK= JL
Question: P is 50% more efficient than Q. P can complete a work in 25 days. If P and Q work together, how many days will it take to complete the same work?
(A) 11
(B) 13
(C) 15
(D) 17
(E) 19
Rationale: The work done by P in 1 day = 1/25
Let work done by Q in 1 day = q
q × (150/100) = 1/25
q = 100/(25×150) = 10/(25×15)
The work done by P and Q in 1 day = 1/25 + 10/(25×15) = 25/(25×15)= 1/15
P and Q together can do the work in 15 days.
The answer is C.
Answer: (C) 15
Question: The distance between two cities A and B is 330 Km. A train starts from A at 8 a.m. and travel towards B at 60 km/hr. Another train starts from B at 9 a.m and travels towards A at 75 Km/hr. At what time do they meet?
(A) 10 a.m
(B) 09 a.m
(C) 11 a.m
(D) 05 a.m
(E) 06 a.m
Rationale: Explanation:
Suppose they meet x hrs after 8 a.m
then,
[Distance moved by first in x hrs] + [Distance moved by second in (x-1) hrs] = 330.
Therefore, 60x + 75(x-1) = 330.
=> x=3.
So,they meet at (8+3) i.e, 11a.m.
Answer: C
Answer: (C) 11 a.m
Question: A set A consists of 7 consecutive odd integers. If the sum of 5 largest integers of set A is -185 what is the sum of the 5 smallest integers of set A?
(A) 165
(B) 175
(C) 195
(D) 205
(E) 215
Rationale: Average of largest 5 = -185/5 =-37
So the largest numbers are -41, -39, -37, -35, -33
Now if we consider smallest 5, we have to eliminate last 2 numbers, which are -35 and -33
Notice here that the numbers are equally spaced.
So the average of smallest number will just shift 2 place to the left.
Avg= -41
Therefore, total = -41*5= -205
Answer:D
Answer: (D) 205
Question: Four brothers Adam, Bill, Charles and David together contributed certain amount of money and purchased a car. The contribution made by Adam is half that of the total contribution made by the other three brothers, contribution made by Bill is one-fourth of the total contribution made by the other three brothers and the contribution made by Charles is two-third of the total contribution made by the other three brothers. If the total price of the car is $9750, find the contribution made by David.
(A) $540
(B) $580
(C) $600
(D) $650
(E) $680
Rationale: Given that A:(B+C+D)= 1:2.
Hence A contributed 1/3rd of the total price.
Given B:(A+C+D)=1:4
Hence B contributed 1/5th of the total price.
Given C:(A+B+D)=2:3
Hence C contributed 2/5th of the total price.
Thus the contribution made by A,B and C= 1/3+1/5+2/5=14/15
So, the remaining 1/15th of the price is contributed by David.
Hence David's contribution= 1/15×9750=$650.
The answer is D.
Answer: (D) $650
Question: In a game of 50 points; A can give B 5 points and C 15 points. Then how many points B can give C in a game of 90 ?
(A) can give C 1 points
(B) can give C 4 points
(C) can give C 2 points
(D) can give C 6 points
(E) can give C 20 points
Rationale: A: B = 50 : 45, A : C = 50 : 35.
B/C = ( B/ A * A/C) = (45 / 50 * 50 / 35) = 9/7 = 90 /70
Therefore ,In a game of 90, B can give C 20 points.
Answer is E.
Answer: (E) can give C 20 points
Question: If 1^3 + 2^3 + 3^3 +......+ 10^3 = 516 then the value of 2^3 + 4^3 + 63 + ..... + 203 is
(A) 1032
(B) 1030
(C) 1034
(D) 1035
(E) 1036
Rationale: 2(13 + 23 + 33 + ---------- + 103)
2 × 516 = 1032
A
Answer: (A) 1032
Question: A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
(A) 248 m
(B) 240 m
(C) 277 m
(D) 765 m
(E) 176 m
Rationale: Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train = (15 x 20)m = 300 m. Let the length of the platform be x meters. Then, (x + 300)/36 = 15 ==> x + 300 = 540 ==> x
= 240 m.
Answer: B
Answer: (B) 240 m
Question: Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is
(A) 2:5
(B) 3:5
(C) 4:5
(D) 6:5
(E) 7:5
Rationale: Explanation:
Let the third number be x.
First Number (120/100)*x = 6x/5
Second Number (150/100)*x = 3x/2
Ratio = 6x/5:3x/2
=> 4:5
Option C
Answer: (C) 4:5
Question: Quentin's income is 60% less than Rex's income, and Ram's income is 25% less than Quentin's income. If Rex gave 60% of his income to Ram and 40% of his income to Quentin, Quentin's new income would be what fraction of Ram's new income?
(A) 8/9
(B) 11/12
(C) 8/13
(D) 11/13
(E) 12/13
Rationale: We can take some easy numbers and make calculations simpler.
Let R ( Rex's income) = 100
Q (Quentin's income) = 40%R = 40
S (Ram's income) = 75% Q = (3/4)*40 = 30
Now, if Rex gives 40% to Quentin --> Q = 40 + 40 = 80
60% given to Ram --> S = 30+60 = 90
The ratio is : Q/S = 80/90 = 8/9=A
Answer: (A) 8/9
Question: On a certain road 10% of the motorists exceed the posted speed limit and receive speeding tickets, but 40% of the motorists who exceed the posted speed limit do not receive speeding tickets. What percent of the motorists on the road exceed the posted speed limit?
(A) 10.5%
(B) 12.5%
(C) 15%
(D) 22%
(E) 16%
Rationale: 0.1 M = 0.60 E
=> E/M = 1/6 * 100 = 16%
So answer is E.
M - # of Motorists
E - # of Motorists exceeding speed
Answer: (E) 16%
Question: In one hour, a boat goes 11 km/hr along the stream and 7 km/hr against the stream. The speed of the boat in still water (in km/hr) is:
(A) 3 km/hr
(B) 4 km/hr
(C) 5 km/hr
(D) 6 km/hr
(E) 9 km/hr
Rationale: Upstream relative speed is u + v=11km/hr
Downstream speed is u-v = 7
Where u = speed of boat in still water and v is speed of stream
Then adding two equations u+v + u-v =11+7
2u=18
Finally, u=9.
ANSWER : E
Answer: (E) 9 km/hr
Question: A watch is sold for Rs.440 cash or for Rs.200 cash down payment together with Rs.244 to be paid after one month. Find the rate of interest charged in the installment scheme.
(A) 10%
(B) 15%
(C) 20%
(D) 25%
(E) None
Rationale: Explanation:
Principal for the next month = 440 - 200 = 240
Amount paid after next month = 244
Therefore interest charged at Rs.240 = 240×1×R/12×100=4
Rate of interest (R) = 20% per annum
Answer C
Answer: (C) 20%
Question: The MegaTek Corporation is displaying its distribution of employees by department in a circle graph. The size of each sector of the graph representing a department is proportional to the percentage of total employees in that department. If the section of the circle graph representing the manufacturing department takes up 108° of the circle, what percentage of MegaTek employees are in manufacturing?
(A) 20%
(B) 25%
(C) 30%
(D) 35%
(E) 72%
Rationale: ANSWER: C
108° divided by 360° equals 0.3, therefore the sector is equal to 30% of the total
Answer: (C) 30%
Question: Jagtap purchases 30 kg of wheat at the rate of 11.50 per kg and 20 kg of wheat at the rate of 14.25 per kg. He mixed the two and sold the mixture. Approximately at what price per kg should he sell the mixture to make 30 per cent profit?
(A) 16.3
(B) 18.2
(C) 15.6
(D) 14.8
(E) 15.4
Rationale: CP = 30 × 11.50 + 20 × 14.25 = 630
SP = 630 × 130⁄100 × 1⁄50 ≈ 16.30
Answer A
Answer: (A) 16.3
Question: Ram professes to sell his goods at the cost price but he made use of 900 grms instead of a kg, what is the gain percent?
(A) 11 1/8
(B) 11 1/7
(C) 11 1/9
(D) 11 1/1
(E) 11 1/2
Rationale: 900 --- 100
100 --- ? => 11 1/9%.Answer: C
Answer: (C) 11 1/9
Question: There is a 20% chance that Lions will not win at all during the whole season. There is a 20% chance that Federer will not play at all in the whole season. What is the greatest possible probability that the Lions will win and Federer will play during the season?
(A) A)55%
(B) B)60%
(C) C)70%
(D) D)72%
(E) E)80%
Rationale: There is a 20% chance that Lions will not win at all during the whole season
We can infer that there is 80% chance Lions will win .
Similarly There is a 20% chance that Federer will not play at all in the whole season
We can also infer that there is 80% chance that Federer will play.
Answer E
Answer: (E) E)80%
Question: If the C.I. on a sum for 2 years at 12 1/2 % per annum is Rs. 510, the S.I. on the same sum at the same rate for the same period of time is?
(A) 488
(B) 485
(C) 470
(D) 480
(E) 482
Rationale: Let the sum be Rs. P. Then,
[P(1 + 25/(2 * 100))2 - P] = 510
P[(9/8)2 - 1] = 510.
Sum = Rs. 1920
So, S.I. = (1920 * 25 * 2) / (2 * 100) = Rs. 480.Answer: D
Answer: (D) 480
Question: In a group of 100 adults, 75 percent of the women are left-handed. If there are 11 right-handed women in the group, how many men are in the group?
(A) 48
(B) 52
(C) 56
(D) 60
(E) 62
Rationale: 12 left-haded women compose 100-75=25% (or 1/4) of all women, so there are total of 4*11=44 women --> 100-44=56 men.
Answer: C.
Answer: (C) 56
Question: An unbiased die is tossed. Find the probability of getting a multiple of 3
(A) 1/3
(B) 2/3
(C) 1
(D) 4/3
(E) 5/3
Rationale: Here S={1,2,3,4,5,6}
Let E be the event of getting the multiple of 3
then ,E={3,6}
P(E)=n(E)/n(S)=2/6=1/3
answer option A) 1/3.
Answer: (A) 1/3
Question: A thief is noticed by a policeman from a distance of 200 m. The thief starts running and the policeman chases him. The thief and the policeman run at the rate of 10 km and 11 km per hour respectively. What is the distance between them after 6 minutes?
(A) 100
(B) 377
(C) 399
(D) 277
(E) 271
Rationale: Explanation:
Relative speed of the thief and policeman = (11 – 10) km/hr = 1 km/hr
Distance covered in 6 minutes = {\color{Blue} \left ( \frac{1}{60}\times 6 \right )} km = {\color{Blue} \frac{1}{10}} km = 100 m
{\color{Blue} \therefore } Distance between the thief and policeman = (200 – 100) m = 100 m.
Answer: A) 100 m
Answer: (A) 100
Question: If Bob has $20 in his pocket and a bowl of ice creams sells for $5 and pizza sells for $12, which of the following COULD be true?
I. Bob can buy 4 bowls of ice cream.
II. Bob can buy 2 bowls of ice cream and pizza.
III. Bob can buy 3 bowls of ice cream and pizza.
(A)  I only
(B)  I and II only
(C)  I and III only
(D)  II and III only
(E)  I, II and III
Rationale: Let’s check each statement.
Statement I:Bob can buy 4 bowls of ice cream. the cost of one bowl of ice cream is $5, 4 bowls of ice cream will cost $5 * 4 = $20, in which case Statement I is be TRUE.
Statement II: Bob can buy 2 bowls of icecream and pizza. The cost of ice cream is $5 and pizza is $12, 2 bowls of ice cream will cost $5 * 2 = $10 and Pizza will cost $12. Total is $10 + $12 = $22 in which case Statement II can NEVER BE TRUE.
Statement III: Bob can buy 3 bowls of ice cream and pizza. 3 bowls of ice cream = $5 * 3 = $15 and pizza = $12. Total = $15 + $12 = $27, in which case Statement III ca NEVER BE TRUE.
Only Statement I is true.
So,the correct answer is A
Answer: (A)  I only
Question: Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 22 seconds. The ratio of their speeds is?
(A) 3/1
(B) 3/1
(C) 1/1
(D) 3/5
(E) 5/2
Rationale: Let the speeds of the two trains be x m/sec and y m/sec respectively. Then, length of the first train
= 27 x meters, and length of the second train
= 17 y meters. (27 x + 17 y) / (x + y) = 22 ==> 27 x + 17 y = 22 x + 22 y
==> 5 x = 5 y ==> x/y
= 1/1.
Answer:C
Answer: (C) 1/1
Question: An order was placed for the supply of a carper whose length and breadth were in the ratio of 3 : 2. Subsequently, the dimensions of the carpet were altered such that its length and breadth were in the ratio 7 : 3 but were was no change in its parameter. Find the ratio of the areas of the carpets in both the cases?
(A) 8:7
(B) 8:7
(C) 8:3
(D) 8:1
(E) 8:9
Rationale: Let the length and breadth of the carpet in the first case be 3x units and 2x units respectively.
Let the dimensions of the carpet in the second case be 7y, 3y units respectively.
From the data,.
2(3x + 2x) = 2(7y + 3y)
=> 5x = 10y
=> x = 2y
Required ratio of the areas of the carpet in both the cases
= 3x * 2x : 7y : 3y
= 6x2 : 21y2
= 6 * (2y)2 : 21y2
= 6 * 4y2 : 21y2
= 8:7
Answer:B
Answer: (B) 8:7
Question: A certain store sells only black shoes and brown shoes. In a certain week, the store sold x black shoes and y brown shoes. If 1/4 of all shoes sold that week were black, which of the following expressions represents the value of y, in terms of x?
(A) x/3
(B) x/2
(C) 2x/3
(D) 3x
(E) 2x
Rationale: x/(x+y) = 1/4
4x = x+y
3x = y
y = 3x
Answer D
Answer: (D) 3x