mathewhe/aqua_rat huggingface dataset:
Question: Five kids were walking down the street. At a shop, they saw three brands of chocolates viz. Cadbury, Nestle and Ferrero being displayed. The shopkeeper has three chocolates which are of three different flavors of each brand. The kids bought all the chocolates available and decided to play a game. The chocolates will be distributed only to the winners of that game. Also they have decided that any winner cannot have all three brands of chocolates as his prize. Find the number of ways in which the chocolates can be distributed when there are four winners of the game and the best of them gets at least 4 chocolates?
(A) 12312
(B) 22536
(C) 4320
(D) 11268
(E) 45072
Rationale: Since, one child cannot have more than two brands of chocolates, therefore, one child can get a maximum of six chocolates.
When there are four winners, the winners can have the chocolates in the following possible way
Case I
One of them gets six chocolates and the other three get one each.
The one who gets six chocolates can be selected in 4C1 ways and he will get any two brands out of three in 3C2 ways.
The three chocolates of the same brand will be distributed among the other three in 3! ways.
Hence, the total number of ways = 4 × 3 × 6 = 72
Case II
One of them gets 5 chocolates, one of them gets 2 chocolates and the other two get 1 each.
Kid with 5 chocolates:
The one who gets five chocolates can be selected in 4C1 ways and he will get any two brands out of three in 3C2 ways.
After choosing the two brands (say AB), he can get all three chocolates of one brand in 2 ways (i.e. either A or B). The other two chocolates can be chosen from the second brand in 3 ways. Thus, there are 4 × 3 × 2 × 3 = 36 ways
Kid with 2 chocolates:
This person can be chosen in 3 ways. Now, he can either get two chocolates from the same brand or from two different brands.
Thus, there are 6 × 3 = 18 ways
Kids with 1 chocolate each
The remaining chocolates can be distributed between the two remaining winners in 2 ways.
Therefore, total number of ways = 36 × 18 × 2 = 1296 ways.
Case III
Similarly for four chocolates the following combinations are possible:
a) 4 3 1 1
The number of ways = 4 × 3 × [{6 × 3(1 + ( 6 + 3))} + {1 × 9 × 3 (1 + 6)}] × 2 = 8856
b) 4 2 2 1
The number of ways = 4 × 3 × [{6 × 3(2 × 6 × 3 + (3 + 9))} + {9 × (9 + 9)}] = 12312
Since, the best of them can’t have less than 4 chocolates the above are the only cases applicable.
Hence, the total number of ways = 72 + 1296 + (8856 + 12312) = 22536.
Option B
Answer: (B) 22536
Question: (12)^3 x 6^4 ÷ 432 = ?
(A) 5184
(B) 5060
(C) 5148
(D) 5084
(E) None of them
Rationale: =(12)^3 x 6^4/432
=(12)^3 x 6^4/12 x 6^2
=(12)^2 x 6^2
=(72)^2
=70
Answer is E
Answer: (E) None of them
Question: On dividing 122 by a number, the quotient is 6 and the remainder is 2. Find the divisor?
(A) 14
(B) 16
(C) 18
(D) 20
(E) 22
Rationale: d = (D-R)/Q
= (122 - 2)/6
= 122/6 = 20
D)
Answer: (D) 20
Question: A farmer needs 2400 ounces of corn to feed his pigs. How many pounds should he buy?
(A)  120
(B)  130
(C)  140
(D)  150
(E)  160
Rationale: 1 pound = 16 ounces.
2400 ounces / 16 = 150 pounds.
Answer: D.
Answer: (D)  150
Question: How many minutes does it take John to type z words if he types at the rate of y words per minute?
(A) z/y
(B) y/x
(C) xy
(D) 60x/y
(E) y/(60x)
Rationale: time*rate=job --> time*y=z --> time=z/y.
Answer: A.
Answer: (A) z/y
Question: Nine men went to a hotel. Eight of them spent Rs.3 each over their meals and the ninth spent Rs.2 more than the average expenditure of all the nine. Determine the total money spent by them?
(A) Rs.29.25
(B) Rs.39.25
(C) Rs.29.29
(D) Rs.23.25
(E) Rs.29.45
Rationale: Average of 9 = x
9x = 8 * 3 + x * 2 x = 3.25
Total = 9 * 3.25 = 29.25
Answer:A
Answer: (A) Rs.29.25
Question: Two pipes A and B can fill a cistern in 20 and 30 minutes respectively, and a third pipe C can empty it in 40 minutes. How long will it take to fill the cistern if all the three are opened at the same time?
(A) 17 1/7
(B) 17 1/9
(C) 17 8/7
(D) 17 8/8
(E) 17 2/7
Rationale: 1/20 + 1/30 - 1/40
= 7/120
120/7
= 17 1/7
Answer:C
Answer: (C) 17 8/7
Question: How long does a train 100 m long travelling at 60 kmph takes to cross a bridge of 80 m in length?
(A) 15.8 sec
(B) 14.9 sec
(C) 12.4 sec
(D) 10.8 sec
(E) 11.8 sec
Rationale: D
16.8 sec
D = 100 + 80 = 180 m
S = 60 * 5/18 = 50/3
T = 180 * 3/50 = 10.8 sec
Answer: (D) 10.8 sec
Question: Take number 1000 and then add 20 to it. Now add 1000 one more time. Now add 30. Now add 1000 one more time. Now add 40. Now add 1000 one more time. Now add 10. What is the total?
(A) 4100
(B) 3590
(C) 2800
(D) 3700
(E) 3600
Rationale: A
4100
Answer: (A) 4100
Question: Water boils at 212°F or 100°C and melts at 32°F or 0°C . If the temperature of the particular day is 35°C , it is equal to
(A) 50°F
(B) 76°F
(C) 95°F
(D) 110°F
(E) 120°F
Rationale: Let F and C denotes the temparature in Fahrenheit anid Celcsius respectively.
Then, (F - 32) /(212 - 32) = (C - 0)/(100 - 0), if c = 35, then F = 95.
C
Answer: (C) 95°F
Question: Three consecutive traffic signals each show either red or green. How many different arrangements of the three signals are possible? (Note: “Red-redgreen” is different from “green-red-red.”)
(A) 10
(B) 9
(C) 8
(D) 7
(E) 6
Rationale: The best way to do this Q would be to find the ways separately for each type of arrangements..
all three of same colour= 1*2(for green and red)= 2..
two of one colour and third different colour= 3!/2!=3..
total= 1*2+3*2=8
ANSWER:C
Answer: (C) 8
Question: A boat can travel with a speed of 24 km/hr in still water. If the speed of the stream is 4 km/hr, find the time taken by the boat to go 84 km downstream
(A) 3 hours
(B) 4 hours
(C) 5 hours
(D) 6 hours
(E) 7 hours
Rationale: Explanation:
Speed of the boat in still water = 24 km/hr
speed of the stream = 4 km/hr
Speed downstream = (22+5) = 28 km/hr
Distance travelled downstream = 84 km
Time taken = distance/speed = 84/28 = 3 hours
Answer: Option A
Answer: (A) 3 hours
Question: The average of first six prime numbers greater than 65 is?
(A) 55
(B) 77
(C) 56
(D) 67
(E) 98
Rationale: 67 + 71 + 73 + 79 + 83 + 89 = 462/6 = 77
Answer: B
Answer: (B) 77
Question: The length of the bridge, which a train 150 meters long and travelling at 45 km/hr can cross in 30 seconds, is?
(A) 766 m
(B) 156 m
(C) 245 m
(D) 225 m
(E) 156 m
Rationale: Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time
= 30 sec. Let the length of bridge be x meters. Then, (150 + X)/30 = 25/2
==> 2(150 + X) = 750 ==> X
= 225 m.
Answer: D
Answer: (D) 225 m
Question: A can do a piece of work in 12 days and B alone can do it in 14 days. How much time will both take to finish the work ?
(A) A)3.2222
(B) B)5
(C) C)6.46
(D) D)8.3333
(E) E)9
Rationale: This question can be solved by different methods. We need to conserve time in exams so solving this problem using equations is the good idea.
Time taken to finish the job = XY / (X + Y)
= 12 x 14 / (12 + 14)
= 150 / 25
= 6.46 days
Answer: C
Answer: (C) C)6.46
Question: The mean salary in ICM ltd. was Rs 1500, and the standard deviation was Rs 400. A year later each employee got a Rs 100 raise. After another year each employee's salary was increased by 20%. The standard deviation of the current salary is?
(A) Rs 400
(B) Rs 480
(C) Rs 600
(D) Rs 700
(E) Rs 800
Rationale: Mean salary was Rs 1500
Standard deviation = Rs 400
After 1 year all the employees got a uniform rise of Rs 100.
So, there will be no change in standard deviation.
After another year, every employee's salary was increased by 20%.
So, standard deviation will be increased by 20%.
Standard deviation=400×
120
100
= Rs 480
Answer B
Answer: (B) Rs 480
Question: Find the sum lend at C.I. at 5 p.c per annum will amount to Rs.240 in 2 years?
(A) 217
(B) 287
(C) 400
(D) 288
(E) 171
Rationale: Explanation:
240 = P(21/20)2
P = 217
Answer:A
Answer: (A) 217
Question: If k is a non-negative integer and 15^k is a divisor of 823,435 then 5^k - k^5 =
(A) 0
(B) 1
(C) 35
(D) 120
(E) 245
Rationale: 8+2+3+4+3+5 = 25, so this number is not divisible by 3 and thus not divisible by 15.
Therefore, k=0
5^k - k^5 =1-0=1
The answer is B.
Answer: (B) 1
Question: A can give B 100 meters start and C 200 meters start in a kilometer race. How much start can B give C in a kilometer race?
(A) 111.12
(B) 111.13
(C) 111.22
(D) 111.0
(E) 111.12
Rationale: A runs 1000 m while B runs 900 m and C runs 800 m.
The number of meters that C runs when B runs 1000 m,
= (1000 * 800)/900 = 8000/9
= 888.88 m.
B can give C = 1000 - 888.88
=111.12m.
Answer:A
Answer: (A) 111.12
Question: The perimeter of an equilateral triangle is 60. If one of the sides of the equilateral triangle is the side of an isosceles triangle of perimeter 65, then how long is the base of isosceles triangle?
(A) 10
(B) 15
(C) 20
(D) 25
(E) 30
Rationale: The base of the isosceles triangle is 65-20-20= 25 units
The answer is D.
Answer: (D) 25
Question: A train is moving at a speed of 132 km/hr. If the length of the train is 200 meters, how long will it take to cross a railway platform 295 meters long
(A) 6 ½ sec
(B) 7 ½ sec
(C) 8 sec
(D) 13 ½ sec
(E) 9 sec
Rationale: Explanation:
Speed of train = 132 ×(5/18) m/sec = 110/3 m/sec.
Distance covered in passing the platform = (200 + 295) m = 495 m.
Time taken =495 ×(3/110) sec =27/2 sec = 13 ½ sec
Answer: Option D
Answer: (D) 13 ½ sec
Question: A car traveling at a certain constant speed takes 2 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 225 kilometers per hour. At what speed, in kilometers per hour, is the car traveling?
(A) 220
(B) 200
(C) 210
(D) 225
(E) 230
Rationale: B
225 * T = 1 km => T = 1/225 km/h
V*(T+2/3600) = 1
V (1/225 + 2/3600) = 1 => V = 200 km/h
Answer: (B) 200
Question: Q is not equal to zero and k = (Q x n - s)/2.What is n?
(A) (2 x k + s)/Q
(B) (2 x s x k)/Q
(C) (2 x k - s)/Q
(D) (2 x k + s x Q)/Q
(E) (k + s)/Q
Rationale: k=(Q*n-s)/2
=> (2k+s)/Q = n
ANSWER:A
Answer: (A) (2 x k + s)/Q
Question: What is the measure of the radius of the circle inscribed in a triangle whose sides measure 8, 15 and 19 units?
(A) 2.8 units
(B) 6 units
(C) 3 units
(D) 5 units
(E) 12 units
Rationale: Sides are 8, 15 and 19...thus it is right angle triangle Since 19^2 = 8^2 + 15^2
therefore, area = 1/2 * 15 * 8 = 60
We have to find in-radius
Therefore, area of triangle = S*r ....where S=semi-perimeter and r= in-radius
Now S=semi-perimeter = 19+15+8 /2 = 21
Thus , 60 =21*r
and hence r=in-radius= 2.8
Option A
Answer: (A) 2.8 units
Question: Rs.1500 is divided into two parts such that if one part is invested at 6% and the other at 5% the whole annual interest from both the sum is Rs.84. How much was lent at 5%?
(A) 228
(B) 299
(C) 266
(D) 600
(E) 188
Rationale: (x*5*1)/100 + [(1500 - x)*6*1]/100 = 84
5x/100 + 90 â€“ 6x/100 = 84
x/100 = 6
=> x = 600
Answer:D
Answer: (D) 600
Question: A woman complete a journey in 10 hours. She travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km.
(A) 334 km.
(B) 216 km.
(C) 314 km.
(D) 224 km.
(E) 544 km.
Rationale: D
224 km.
0.5x/21 + 0.5x/24 = 10
--> x/21 + x/24 = 20
--> 15x = 168 x 20
--> x = (168 x 20)/15 = 224 km.
Answer: (D) 224 km.
Question: Pat and Cathy begin running at the same time and they start at the same place on a straight path. Pat runs at 9 miles per hour, and Cathy runs at 8 miles per hour. After 30 minutes, Pat stops to stretch. If it takes Pat 15 minutes to stretch and Cathy continues to run during this time, how many minutes will it take Pat to catch up to Cathy?
(A) 50
(B) 60
(C) 70
(D) 80
(E) 90
Rationale: In 30 minutes, Pat runs 4.5 miles.
In 45 minutes, Cathy runs 6 miles.
Pat can catch Cathy at a rate of 1 mile per hour.
Since Cathy is ahead by 1.5 miles, it will take Pat 1.5 / 1 = 1.5 hours = 90 minutes to catch Cathy.
the answer is E.
Answer: (E) 90
Question: An employer has 8 applicants for a programming position and 4 applicants for a manager position. If the employer must hire 3 programmers and 2 managers, what is the total number of ways the employer can make the selection?
(A) a) 1,490
(B) b) 132
(C) c) 336
(D) d) 60
(E) e) 23
Rationale: 8C3 * 4C2 = 336. Answer C.
Answer: (C) c) 336
Question: The calendar of the year 2060 can be used again in the year?
(A) 2081
(B) 2083
(C) 2088
(D) 1971
(E) 1973
Rationale: Explanation:
Given year 2060 when divided by 4, leaves a remainder 0.
NOTE: When remainder is 0, 28 is added to the given year to get the result.
So, 2060 + 28 = 2088
Answer: C
Answer: (C) 2088
Question: To be considered for “movie of the year,” a film must appear in at least 1/4 of the top-10-movies lists submitted by the Cinematic Academy’s 775 members. What is the smallest number of top-10 lists a film can appear on and still be considered for “movie of the year”?
(A) 191
(B) 194
(C) 193
(D) 212
(E) 213
Rationale: Total movies submitted are 775.
As per question we need to take 1/4 of 775 to be considered for top 10 movies = 193.75
approximate the value we 194.
IMO option B is the correct answer...
Answer: (B) 194
Question: A train 800 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 min, then the length of the tunnel is?
(A) 288 m
(B) 256 m
(C) 500 m
(D) 278 m
(E) 287 m
Rationale: Speed = 78 * 5/18 = 65/3 m/sec.
Time = 1 min = 60 sec.
Let the length of the train be x meters.
Then, (800 + x)/60
= 65/3
x = 500 m.
Answer:C
Answer: (C) 500 m
Question: The cost of a Personal computer was $2,000 in 1990. In 2000, the price had decreased to $500. What was the percent decrease in the cost of the Personal computer?
(A) 25%
(B) -30%
(C) -75%
(D) 40%
(E) 90%
Rationale: Decrease = 2000-500 = 1500
% decrease = 1500*100/2000 = -75%
Answer: option C
Answer: (C) -75%
Question: A man rows his boat 105 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream?
(A) 5 kmph
(B) 7 kmph
(C) 12 kmph
(D) 8 kmph
(E) 1 kmph
Rationale: Speed downstream = d/t = 105/(2 1/2) = 42 kmph
Speed upstream = d/t = 45/(2 1/2) = 18 kmph
The speed of the stream = (42 - 18)/2 = 12 kmph
Answer:C
Answer: (C) 12 kmph
Question: The first train leaves the station at 6:00 am with a speed of 60 km/hr. The second train leaves at 7:15 am, in the same direction from the same station, with a speed of 75 km/hr. What time will the second train catch the first train?
(A) 11:15 am
(B) 11:45 am
(C) 12:15 pm
(D) 12:45 pm
(E) 1:15 pm
Rationale: In seventy-five minutes, the first train travels 75 km.
The second train catches the first train with a relative speed of 15 km/h.
The second train will catch the first train in 5 hours.
The second train will catch the first train at 12:15 pm.
The answer is C.
Answer: (C) 12:15 pm
Question: How many such letter-pairs are there in the word SERVANT having the same no. of letters left between them in the word as they have in the series?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: 1 pair is S & V
1 pair is N &S
total 2 pair
ANSWER: A
Answer: (A) 2
Question: At 1:00 pm, there were 10.0 grams of bacteria. The bacteria increased to x grams at 4:00 pm, and 22.5 grams at 7:00 pm. If the amount of bacteria present increased by the same fraction during each of the 3-hour periods, how many grams of bacteria were present at 4:00 pm?
(A) 14.4
(B) 14.7
(C) 15.0
(D) 15.3
(E) 15.6
Rationale: Let x be the factor by which the bacteria increases every three hours.
At 4:00 pm, the amount of bacteria was 10x and at 7:00 pm it was 10x^2.
10x^2 = 22.5
x^2=2.25
x=1.5
At 4:00 pm, the amount of bacteria was 10(1.5)=15 grams.
The answer is C.
Answer: (C) 15.0
Question: In a division sum, the remainder is 6 and the divisor is 5 times the quotient and is obtained by adding 27 to the thrice of the remainder. The dividend is
(A) 74
(B) 78
(C) 186
(D) 92
(E) 98
Rationale: Divisor = (6 * 3) + 27 = 45
5 * Quotient = 45
Quotient = 9.
Dividend = (Divisor * Quotient) + Remainder
Dividend = (20 * 9) + 6 = 186.
C)
Answer: (C) 186
Question: A 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 18 sec. What is the length of the platform?
(A) 300
(B) 350
(C) 360
(D) 370
(E) 380
Rationale: Speed = 300/18 = 50/3 m/sec.
Let the length of the platform be x meters.
Then, (x + 300)/39 = 50/3
3x + 900 = 1950 => x = 350 m.
Answer: Option B
Answer: (B) 350
Question: A man started driving at a constant speed, from the site of a blast, the moment he heard the blast. He heard a second blast after a time of 30 mins and 12 seconds. If the second blast occurred exactly 30 mins after the first, how many meters was he from the site when he heard the second blast? ( speed of sound = 330 m/s)
(A) 3120
(B) 3330
(C) 3540
(D) 3750
(E) 3960
Rationale: The distance the sound traveled to the man is 12*330 = 3960 meters
The answer is E.
Answer: (E) 3960
Question: A man sells two articles for Rs.3300 each and he gains 21% on the first and loses 21% on the next. Find his total gain or loss?
(A) 9%loss
(B) 2%loss
(C) 7%loss
(D) 8%loss
(E) 4%loss
Rationale: Explanation:
(21*21)/100
= 4%loss
Answer:E
Answer: (E) 4%loss
Question: Marisa is taking a cash deposit to the bank. She has $10 bills and $5 bills in a deposit
pouch. Altogether, she has 130 bills with a total value of $890. How many ten dollar bills are in the pouch?
(A) 28
(B) 58
(C) 48
(D) 67
(E) 76
Rationale: Let x represent the number of $10 bills in the bag. Next, use the same variable to represent the
number of $5 bills. If there are 130 bills in all, then 130 x represents the number of $5 bills.
Now you need to establish a relationship between the number of bills and their value.
Using the expression above, the total value of the $10 bills is 10x, and the total value of
the $5 bills is 5(130 x).
Write an equation and solve. 10x 5(130 x) 890 Multiply both terms in parentheses by 5.
10x 650 5x 890 Combine like terms.
5x 650 890 Subtract 650 from both sides.
5x 240 Divide both sides by 5 to get the
x 48 number of $10 bills.
130 x 82 Subtract to find the number of $5 bills.
Answer: There are 48 ten-dollar bills and 82 five-dollar bills.
Check: (48 $10) (82 $5) $480 $410 $890. The answer is correct.
correct answer C
Answer: (C) 48
Question: The ratio of the ages of Anil and his son at present is 7:3. Six years hence, the ratio of the ages of the Anil's wife and the son will be 2:1. Find the ratio of the present ages of Anil and his wife?
(A) 7
(B) 8
(C) 9
(D) 6
(E) 5
Rationale: Let the present ages of Anil and his son be 7x and 3x years respectively.
Let the present age of the son's mother be m years.
(m + 6)/(3x + 6) = 2/1
m = 6x + 6
Ratio of the present ages of Anil and his son's mother = 7x/(6x + 6).
This cannot be found uniquely.
Answer:D
Answer: (D) 6
Question: There are 7 pairs of socks and 2 socks are worn from that such that the pair of socks worn are not of the same pair. what is the number of pair that can be formed.
(A) 40
(B) 49
(C) 41
(D) 56
(E) 42
Rationale: First of all you should remember that there is a difference in left and right sock.
now no. of way to select any of the sock = 7
and for second = 6
so total methods = 7*6 = 42
ANSWER:E
Answer: (E) 42
Question: There are 60 supermarkets in the FGH chain. All of them are either in the US or Canada. If there are 22 more FGH supermarkets in the US than in Canada, how many FGH supermarkets are there in the US?
(A) 20
(B) 31
(C) 41
(D) 53
(E) 64
Rationale: x + (x - 22) = 60 --> x =41.
Answer: C.
Answer: (C) 41
Question: A company consists of 10 senior and 5 junior staff officers. If a committee is created with 3 senior and 2 junior staff officers, in how many ways can the committee be formed?
(A)  120
(B)  300
(C)  450
(D)  800
(E)  1200
Rationale: Choose 3 senior from 10 senior and choose 2 junior from 5 junior:
10C3 * 5C2 = 120 * 10= 1200
Ans: E
Answer: (E)  1200
Question: A certain animal in the zoo has consumed 39 pounds of food in six days. If it continues to eat at the same rate, in how many more days will its total consumption be 143 pounds?
(A) 8
(B) 7
(C) 12
(D) 16
(E) none of the above
Rationale: Ans is D:
39 pounds --> 6 days
143 pounds --> x days
x = 143*6/39 = 22
the animal has already consumed food in 6 days so the the number of days
for it's total consumption be 143 pounds is 22-6 = 16
Answer: (D) 16
Question: Mr. Kramer, the losing candidate in a two-candidate election, received 942,568 votes, which was exactly 30 percent of all votes cast. Approximately what percent of the remaining votes would he need to have received in order to have won at least 50 percent of all the votes cast?
(A) 10%
(B) 12%
(C) 15%
(D) 17%
(E) 28%
Rationale: Lets assume that candidate got 30% votes and total votes is 100.
Candidate won = 30
Remaining = 70
To get 50%, candidate requires 20 votes from 100 which is 20% and 20 votes from 70.
20/70 = 28.57%
Which is approx 28%. Hence the answer is E
Answer: (E) 28%
Question: 8 men can do a piece of work in 12 days. 4 women can do it in 48 days and 10 children can do it in 24 days. In how many days can 10 men, 4 women and 18 children together complete the piece of work?
(A) 5 days
(B) 15 days
(C) 28 days
(D) 6 days
(E) 7 days
Rationale: Explanation:
1 man’s 1 day’s work = 1/8 × 12 = 1/96
10 men’s 1 day’s work = 1 × 10/96 = 5/48
1 woman’s 1 day’s work = 1/192
4 women’s 1 day’s work = 1/192 × 4 = 1/48
1 child’s 1 day’s work = 1/240
18 children’s 1 day’s work = 3/40
Therefore, (10 men + 4 women + 18 children)’s 1 day’s work = 5/48 + 1/48 + 3/40
= 1/5
The required No. of days = 5 days
Answer: Option A
Answer: (A) 5 days
Question: In a colony of 70 residents, the ratio of the number of men and women is 4 : 2. Among the women, the ratio of the educated to the uneducated is 1 : 4. If the ratio of the number of educated to uneducated persons is 8 : 27, then find the ratio of the number of educated to uneducated men in the colony?
(A) A)1:6
(B) B)1:1
(C) C)1:8
(D) D)1:9
(E) E)1:3
Rationale: Number of men in the colony = 4/7 * 70 = 40.
Number of women in the colony = 2/7 * 70 = 20.
Number educated women in the colony = 1/5 * 30 = 6.
Number of uneducated women in the colony = 4/5 * 50 = 24.
Number of educated persons in the colony = 8 /35 * 70 = 16.
As 6 females are educated, remaining 10 educated persons must be men.
Number of uneducated men in the colony = 40 - 10 = 30.
Number of educated men and uneducated men are in the ratio 10 : 30 i.e., 1:3.
Answer:E
Answer: (E) E)1:3
Question: Two employees X and Y are paid a total of Rs. 880 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week?
(A) s.150
(B) s.200
(C) s.250
(D) s.350
(E) s.400
Rationale: Let the amount paid to X per week = x
and the amount paid to Y per week = y
Then x + y = 880
But x = 120% of y = 120y/100 = 12y/10
âˆ´12y/10 + y = 880
â‡’ y[12/10 + 1] = 880
â‡’ 22y/10 = 880
â‡’ 22y = 8800
â‡’ y = 8800/22 = 800/2 = Rs.400
E)
Answer: (E) s.400
Question: Last year a certain bond yielded 10 percent of its face value in interest. If that interest was approximately 4 percent of the bonds selling price of $7,500, what is the bonds face value?
(A) $3,000
(B) $6,750
(C) $7,425
(D) $7,500
(E) $9,375
Rationale: Interest = 0.10*face value = 0.04*7,500 --> face value = 0.04*7,500/0.1 = 3,000.
Answer: A.
Answer: (A) $3,000
Question: An order was placed for a carpet whose length and width were in the ratio of 3 : 2. Subsequently, the dimensions of the carpet were altered such that its length and width were in the ratio 3 : 1 but were was no change in its perimeter. What is the ratio of the areas of the carpets?
(A) 12:7
(B) 15:11
(C) 25:16
(D) 30:23
(E) 32:25
Rationale: Let the length and width of one carpet be 3x and 2x.
Let the length and width of the other carpet be 3y and y.
2(3x + 2x) = 2(3y + y)
5x = 4y
(5/4) * x = y
The ratio of the areas of the carpet in both cases:
= 3x * 2x : 3y * y
= 6x^2 : 3y^2
= 6x^2 : 3*(25/16) * x^2
= 96 : 75
= 32 : 25
The answer is E.
Answer: (E) 32:25
Question: A motorist knows seven different routes from Bristol to Birmingham. From Birmingham to Sheffield he knows three different routes and from Sheffield to Carlisle he knows two different routes. How many routes does he know from Bristol to Carlisle ?
(A) 4
(B) 8
(C) 12
(D) 24
(E) 42
Rationale: Explanation:
Total number of routes from Bristol to Carlisle = (7 x 3 x 2) = 42.
Answer: E
Answer: (E) 42