mathewhe/aqua_rat huggingface dataset:
Question: If a square and a rhombus stand on the same base, then what is the ratio of the areas of the square and the rhombus?
(A) equal to 12
(B) equal to 34
(C) greater than 1
(D) equal to 1
(E) None
Rationale: Explanation:
If a square and a rhombus lie on the same base, area of the square will be greater than area of the rhombus (In the special case when each angle of the rhombus is 90°90°, rhombus is also a square and therefore areas will be equal)
Hence greater than 11 is the more suitable choice from the given list
Answer: Option C
Answer: (C) greater than 1
Question: What decimal fraction is 50 ml of a litre ?
(A) .5
(B) .05
(C) .05
(D) 0.05
(E) None of these
Rationale: Answer
Required fraction = 50/1000
= 5/100
= .05
Correct Option: B
Answer: (B) .05
Question: how many internal diagonals does a hexagon (six sided polygon) have?
(A) 5
(B) 6
(C) 8
(D) 9
(E) 10
Rationale: Number of diagonals in any polygon can be found using this formula: n(n-3)/2
Here n = 6
No. of diagonals = 6(6 - 3)/2
= 9
Ans D
Answer: (D) 9
Question: A large tanker can be filled by two pipes A and B in 60 and 40 minutes respectively. How many minutes will it take to fill the tanker from empty state if B is used for half the time and A and B fill it together for the other half?
(A) 65 min
(B) 99 min
(C) 56 min
(D) 1Z min
(E) 12 min
Rationale: Part filled by (A + B) in 1 minute = (1/60 + 1/40) = 1/24
Suppose the tank is filled in x minutes.
Then, x/2(1/24 + 1/40) = 1
x/2 * 1/15 = 1 => x = 30 min.
Answer: D
Answer: (D) 1Z min
Question: The odds against ram solving the problem are 7 to 3 and the odds in favour of krishna solving the same are 7 to 5. What is the chance that it will be solved when they both try?
(A) 1/4
(B) 5/21
(C) 16/21
(D) 23/28
(E) 17/24
Rationale: Odds against Ram are 7:3 so probability that he will solve the problem is 3/10.
Odds in favor of Krishna are 7:5 so probability that he will solve it is 7/12
It will be solved means that either Ram or Krishna or both will be able to solve it.
P(A or B) = P(A) + P(B) - P(A and B) = 3/10 + 7/12 - (3/10)*(7/12) = 17/24
E
Answer: (E) 17/24
Question: Two vessels having volumes in the ratio 3:5 are filled with water and milk solutions. The ratio of milk and water in the two vessels are 1:2 and 3:1 respectively. If the contents of both the vessel are empties into a larger vessel, find the ratio of milk and water in the larger vessel.
(A) 18:13
(B) 16:13
(C) 19:13
(D) 14:11
(E) 13:11
Rationale: Vessel A = 300 gallons --> milk = 100, water = 200;
Vessel B = 500 gallons --> milk = 375, water = 125;
Vessel A + B = 800 gallons --> milk = 475, water 325.
The ratio = 475/325 --> 19/13
Answer: C
Answer: (C) 19:13
Question: The average of 11 results is 46, if the average of first six results is 49 and that of the last six is 52. Find the sixth result?
(A) 21
(B) 56
(C) 100
(D) 25
(E) 23
Rationale: 1 to 11 = 11 * 46 = 506
1 to 6 = 6 * 49 = 294
6 to 11 = 6 * 52 = 312
6th = 294 + 312 â€“ 506 = 100
Answer:C
Answer: (C) 100
Question: Village P’s population is 1200 greater than Village Q's population. If Village Q’s population were reduced by 800 people, then Village P’s population would be 6 times as large as Village Q's population. What is Village Q's current population?
(A) 1050
(B) 1100
(C) 1150
(D) 1200
(E) 1250
Rationale: P = Q+1200.
P=6(Q-800).
6(Q-800)=Q+1200.
5Q=6000.
Q=1200.
The answer is D.
Answer: (D) 1200
Question: 80 percent of the members of a study group are women, and 40 percent of those women are lawyers. If one member of the study group is to be selected at random, what is the probability that the member selected is a woman lawyer?
(A) 0.45
(B) 0.55
(C) 0.65
(D) 0.32
(E) 0.35
Rationale: Say there are 100 people in that group, then there would be 0.8*0.40*100=32 women lawyers, which means that the probability that the member selected is a woman lawyer is favorable/total=32/100.
Answer: D
Answer: (D) 0.32
Question: A baseball card decreased in value 40% in its first year and 10% in its second year. What was the total percent decrease of the card's value over the two years?
(A) 28%
(B) 30%
(C) 32%
(D) 46%
(E) 72%
Rationale: consider the initial value of the baseball card as $100
After first year price = 100*0.6 = 60
After second year price = 60 *0.9 = 54
final decrease = [(100 - 54)/100] * 100 = 46%
correct answer - D
Answer: (D) 46%
Question: What is the greatest value of x such that 4^x is a factor of 21! ?
(A) 5
(B) 6
(C) 3
(D) 2
(E) 4
Rationale: Pretty simple, really.
If m = 6, then 4m = 24, which is 12x2, both of which are included in 21!
Since 6 is the largest number here, its the answer.
Answer is B
Answer: (B) 6
Question: Taylor is making a bracelet. He Starts with 3 blue knots, 6 red knots, and 2 yellow knots, in that order, and repeats the pattern until there is no more string. If the last Knot is yellow which of the following could be the total number of knots on the bracelet.
(A) 89
(B) 90
(C) 95
(D) 97
(E) 87
Rationale: Repeating sequence = 3 + 6 + 2 = 11.
As the pattern ends in Y this could be the 10th thread or 11 thread (both are yellow)
Out of the answer choices, correct on should be a multiple of 11(since 11 threads are repeating) and if not, multiple of 11 + 10 (since 11 threads are repeating and last sequence end at first yellow)
none of the options is a direct multiple of 11 and only option that is multiple of 11; + 10 is 87 (11*7) + 10
Hence, answer is E
Answer: (E) 87
Question: A man can row with a speed of 13 kmph in still water. If the stream flows at 53 kmph, then the speed in downstream is?
(A) 28
(B) 16
(C) 20
(D) 87
(E) 24
Rationale: M = 13
S = 3
DS = 13 + 3
=16
Answer: B
Answer: (B) 16
Question: A man can row his boat with the stream at 6 km/h and against the stream in 4 km/h. The man's rate is?
(A) 1 kmph
(B) 2 kmph
(C) 7 kmph
(D) 8 kmph
(E) 9 kmph
Rationale: DS = 6
US = 4
S = ?
S = (6 - 4)/2 = 1 kmph
Answer: A
Answer: (A) 1 kmph
Question: How many words can be formed by using all letters of the word ‘DESK’ ?
(A) 16
(B) 20
(C) 24
(D) 28
(E) 32
Rationale: The word contains 4 different letters.
The number of permutations is 4! = 24
The answer is C.
Answer: (C) 24
Question: Find the ratio between whole surfaces of a sphere and a hemisphere?
(A) 4:9
(B) 4:3
(C) 4:6
(D) 4:2
(E) 4:1
Rationale: 4 πr2 : 3 πr2 => 4:3
Answer:B
Answer: (B) 4:3
Question: Find the average of all numbers between 5 and 37 which are divisible by 4
(A) 25
(B) 20
(C) 45
(D) 30
(E) 35
Rationale: Explanation:
Average=(4+8+12+16+20+24+28+32+36) / 4)=180 / 4=45
Option C
Answer: (C) 45
Question: The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 4% per annum is Re. 1. The sum (in Rs. ) is?
(A) 625
(B) 286
(C) 266
(D) 191
(E) 811
Rationale: Explanation:
Let the sum be Rs. x. Then,
[x (1 + 4/100)2 - x] = (676/625 x - x) = 51/625 x
S.I. = (x * 4 * 2)/100 = 2x/25
51x/625 - 2x/25 = 1 or x = 625.
Answer: A
Answer: (A) 625
Question: Ramzi walked for 3 days. She walked 18 miles on the first day, walking 3 miles per hour. On the second day she walked for one less hour but she walked one mile per hour, faster than on the first day. On the third day she walked the same number of hours as on the first day, but at the same speed as on the second day. How many miles in total did she walk?
(A) 24
(B) 44
(C) 58
(D) 60
(E) 62
Rationale: Ramzi walked 18 miles on the first day, walking 3 miles per hour i.e. total time of walk on Day-1 = 18/3 = 6 Hours
Second day time of walk = 6-1 = 5 hours and Speed = 3+1=4 miles per hour i.e. Distance walked on second day = 5*4 = 20 miles
Third day time of walk = 6 hours and Speed = 4 miles per hour i.e. Distance walked on second day = 6*4 = 24 miles
Total Distance travelled on three days = 18+20+24 = 62
Answer: Option E
Answer: (E) 62
Question: Walking with 4/5 of my usual speed, I miss the bus by 5 minutes. What is my usual time?
(A) 35 min
(B) 30 min
(C) 25 min
(D) 20 min
(E) 40 min
Rationale: Explanation:
Speed Ratio = 1:4/5 = 5:4Time Ratio = 4:51 -------- 5 4 --------- ? è 20
ANSWER IS D
Answer: (D) 20 min
Question: Amit and Ananthu can do a work in 15 days and 60 days respectively. Amit started the work and left after 3 days. Ananthu took over and completed the work. In how many days was the total work completed?
(A) 38 days
(B) 40 days
(C) 43 days
(D) 45 days
(E) 51 days
Rationale: Amit’s one day’s work= 1/15
Amit’s 3 day’s work = 1/15 *3 = 1/5
Work left= 1-1/5 = 4/5
Ananthu’s one day’s work= 1/60
Ananthu can do work in = 4/5 *60 = 48 days
So total days = 48+3 = 51 days
ANSWER:E
Answer: (E) 51 days
Question: What approximate value should come in place of question mark (?) in the following equation
287.532 + 1894.029 – 657.48 = 543.095 + ?
(A) 870
(B) 790
(C) 980
(D) 770
(E) 890
Rationale: ? = 285 + 1895 – 655 – 545 or, ? = 980
Answer C
Answer: (C) 980
Question: If the cost price is 25% of selling price. Then what is the profit percent
(A) 238
(B) 278
(C) 300
(D) 166
(E) 129
Rationale: Explanation:
Let the S.P = 100
then C.P. = 25
Profit = 75
Profit% = (75/25) * 100 = 300%
Answer: C
Answer: (C) 300
Question: Two men A and B start from place X walking at 4 ½ kmph and 5 ¾ kmph respectively. How many km apart they are at the end of 3 ½ hours if they are walking in the same direction?
(A) 2 3/8 km
(B) 4 3/6 km
(C) 4 3/8 km
(D) 4 7/8 km
(E) 4 1/8 km
Rationale: RS = 5 ¾ - 4 ½ = 1 ¼
T = 3 ½ h.
D = 5/4 * 7/2 = 35/8
= 4 3/8 km
Answer:C
Answer: (C) 4 3/8 km
Question: Is y is a positive number? Statement–1: 2x+y > 27; Statement–2: x–3y < 24
(A) 22
(B) 62
(C) 28
(D) 16
(E) 11
Rationale: Answer:B
Answer: (B) 62
Question: A word consists of 9 letters; 5 consonants and 4 vowels.Three letters are choosen at random. What is the probability that more than one vowel will be selected ?
(A) 17/49
(B) 17/42
(C) 17/87
(D) 17/29
(E) 17/12
Rationale: Explanation:
3 letters can be choosen out of 9 letters in {\color{Black} {^9}C_3} ways.
More than one vowels ( 2 vowels + 1 consonant or 3 vowels ) can be choosen in {\color{Black} \left ( {^4}C_2\times {^5}C_1 \right )+{^4}C_3} ways
Hence,required probability = {\color{Black} \frac{\left ( {^4}C_2\times {^5}C_1 \right )+{^4}C_3}{{^9}C_3}} = 17/42
Answer: B) 17/42
Answer: (B) 17/42
Question: A goods train leaves a station at a certain time and at a fixed speed. After ^hours, an express train leaves the same station and moves in the same direction at a uniform speed of 90 kmph. This train catches up the goods train in 4 hours. Find the speed of the goods train.
(A) 26 kmph
(B) 16 kmph
(C) 36 kmph
(D) 46 kmph
(E) 13 kmph
Rationale: Let the speed of the goods train be x kmph.
Distance covered by goods train in 10 hours= Distance covered by express train in 4 hours
10x = 4 x 90 or x =36.
So, speed of goods train = 36kmph.
Option C
Answer: (C) 36 kmph
Question: How many seconds will a 400 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
(A) 24 sec
(B) 30 sec
(C) 27 sec
(D) 28 sec
(E) 29 sec
Rationale: Speed of train relative to man = 63 - 3
= 60 km/hr.
= 60 * 5/18
= 50/3 m/sec.
Time taken to pass the man = 400 * 3/50
= 24 sec.
Answer:A
Answer: (A) 24 sec
Question: Each person who attended a company meeting was either a stockholder in the company, an employee of the company, or both. If 60 percent of those who attended the meeting were stockholders and 47 percent were employees, what percent were stockholders who were not employees?
(A) 53
(B) 54
(C) 55
(D) 56
(E) 57
Rationale: 60+47=107 so 7% were both stockholders and employees.
The percent who were stockholders but not employees is 60-7=53%
The answer is A.
Answer: (A) 53
Question: A and B invests Rs.3000 and Rs.4000 respectively in a business. If A doubles his capital after 6 months. In what ratio should A and B divide that year's profit?
(A) 8:8
(B) 9:8
(C) 9:9
(D) 9:5
(E) 9:1
Rationale: (3*6 + 6*6): (4*12)
54:48 => 9:8
Answer: B
Answer: (B) 9:8
Question: A woman bought books at 30% discount on its original price. He sold it at a 90% increase on the price he bought it. What percent of profit did he make on the original price?
(A) 33%
(B) 22%
(C) 44%
(D) 55%
(E) 66%
Rationale: Original price = 100
CP = 70
S = 70*(190/100) = 133
100 - 133 = 33%
Answer: A
Answer: (A) 33%
Question: A towel, when bleached, lost 20%20% of its length and 10%10% of its breadth. What is the percentage decrease in area?
(A) 30%
(B) 28%
(C) 32%
(D) 26%
(E) 28%
Rationale: Explanation:
Let original length =10
original breadth =10
Then, original area =10×10=100
Lost 20%20% of length
⇒ New length =10−2=8 (∵ 2 is 20% of 1010)
Lost 10% of breadth
⇒ New breadth =10−1=9 (∵ 1 is 10% of 10)
New area =8×9=72
Decrease in area
= original area - new area
=100−72=28
Percentage decrease in area
=decrease in area /original area×100
=28/100×100=28%
Answer: Option B
Answer: (B) 28%
Question: Alfred started a business investing Rs. 45,000. After 3 months, Peter joined him with a capital of Rs. 60,000. After another 6 months, Ronald joined them with a capital of Rs. 90,000. At the end of the year, they made a profit of Rs. 16,500. Find the lire of each.
(A) 2300
(B) 3300
(C) 4300
(D) 1300
(E) None of them
Rationale: Clearly, Alfred invested his capital for 12 months, Peter for 9 months and Ronald for 3 months.
So, ratio of their capitals = (45000 x 12) : (60000 x 9) : (90000 x 3)
= 540000 : 540000 : 270000 = 2 : 2 : 1.
Alfred's share = Rs. (16500 x (2/5)) = Rs. 6600
Peter's share = Rs. (16500 x (2/5)) = Rs. 6600
Ronald's share = Rs. (16500 x (1/5)) = Rs. 3300.
Answer is B.
Answer: (B) 3300
Question: On a scale of map,0.6 cm represent 6.6 km.If the distance between the points on the map is 80.5 cm,the actual distance between these points is :
(A) 9 km
(B) 72.5 km
(C) 190.75 km
(D) 885.5 km
(E) None of these
Rationale: Solution
Let the actual distance be x km.Then,
More distance on the map,More is the actual distance (Direct Proportion)
∴ 0.6 : 80.5 : : 6.6 : x ⇔ 0.6x = 80.5 × 6.6 ⇔ x = ⇔ x = 80.5x6.6/0.6=x=885.5. Answer D
Answer: (D) 885.5 km
Question: The security lock requires a five-digit lock code. If the lock code must consist only of digits from 1 through 6, inclusive, with no repeated digits, and the first and last digits of the code must be odd, how many lock codes are possible?
(A) 120
(B) 240
(C) 360
(D) 720
(E) 144
Rationale: X-X-X-X-X --> there are 3 odd digits from 1 to 6, inclusive thus options for the first and the last X's are: 3-X-X-X-2. Other X's can take following values: 3-4-3-2-2 --> 3*4*3*2*2=144.
Answer: E.
Answer: (E) 144
Question: Jamboree and GMAT Club Contest Starts
QUESTION #12:
How many words (with or without meaning) can be formed using all the letters of the word “SELFIE” so that the two E’s are not together?
(A)  660
(B)  600
(C) 400
(D)  300
(E)  240
Rationale: The question is asking the total number of arrangements possible with the letters of the word “SELFIE” where two E’s are not together.
Arrangements when two E’s are not together = Total arrangements - Arrangements when two E’s are together
In total there are 6 letters but two are identical. so we can arrange in 6! ways. but we divide for those objects that are identical. so divide by 2!. Hence,
Total arrangements = 6!/2!
Now two E's are coupled together. Consider this couple (EE) as one letter. apart from this there are 4 more letters. so we can arrange these 5 different objects in 5! ways.
Two E's can arrange themselves in 2! ways, but we divide for those objects that are identical. so divide by 2!. so arrangement for E's would be 2!/2!.
Hence, Arrangements when two E’s are together = 5! * (2!/2!)
Arrangements when two E’s are not together = 6!/2! - 5! = 5! * ( 6/2 -1 ) = 120 * 2 = 240.
Option C is correct!
Answer: (C) 400
Question: 23, 29, 31, 37, 41, 43, 47, 53, (...)
(A) 53
(B) 47
(C) 48
(D) 59
(E) 45
Rationale: Explanation :
All are prime numbers in their order, starting from 23
Hence, next number is 59
Answer : D
Answer: (D) 59
Question: If s and t are positive integers such that s/t = 58.32, which of the following could be the remainder when s is divided by t ?
(A) 22
(B) 42
(C) 18
(D) 40
(E) 45
Rationale: s/t= 58.32
s = 58.32t
s = (58 + 0.32)t
s = 58t + (32/100)t
s = 58t + (8/25)t
So remainder will be multiple of 8. The only multiple of 8 is 40.
Ans. D
Answer: (D) 40
Question: 2 men and 4 boys can complete a work in 4 days. 5 men and 6 boys can complete the same work in 3 days. The work done by 2 boys is equal to the work of how many men?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: Exp: (2m + 4b)’s one day’s work = 1/4
(5m + 6b)’s one day’s work = 1/3
=> (8m + 16b)’s one day’s work = (15m + 18b) ’s one day’s work
=> 7 men’s work = 2 boy’s work
So, we should be employ 5 more men to be completed the work.
Answer: B
Answer: (B) 5
Question: A club wants to mix 10 pounds of candy worth $8.00 per pound with candy worth $5.00 per pound to reduce the cost of the mixture to $6.00 per pound. How many pounds of the $5.00 per pound candy should be used?
(A) 20
(B) 30
(C) 40
(D) 50
(E) 60
Rationale: Let number of pounds of 5$ candy to be used be w
6 = (10*8 + 5*w)/(10 +w)
=> 60 + 6w = 80 + 5w
=> w = 20
Answer A
Answer: (A) 20
Question: Six years ago, the ratio of ages of Kunal and Sagar was 6:5. Four years hence, the ratio of their ages will be 11:10. What is Sagar's age at present?
(A) 18
(B) 15
(C) 16
(D) 20
(E) 25
Rationale: [(6x + 6) + 4] / [(5x + 6) + 4] = 11/10
10(6x + 10) = 11(5x + 10) => x = 2
Sagar's present age = (5x + 6) = 16 years.
ANSWER C
Answer: (C) 16
Question: The length of the bridge, which a train 130 meters long and travelling at 45 km/hr can cross in 30 seconds, is:
(A) 230
(B) 244
(C) 245
(D) 238
(E) 236
Rationale: Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (130 + X)/30 = 25/2 ==> 2(130 + X) = 750 ==> X = 245 m.
Answer: Option C
Answer: (C) 245
Question: Bill downloads the movieRevenge of the Avengersto his computer in 2.5 hours, using a download manager that downloads from 3 sources marked A, B and C. Each source provides download at a constant rate, but the rates of different sources are not necessarily identical. If the movie was downloaded from sources A and C alone, it would take 4 hours to complete the download. The next day, source B is available, but the other sources are inactive. How long will it take to download the trailer of the movie, a file that is 10 times smaller, from source B alone?
(A) 40 minutes
(B) 15 minutes
(C) 12 minutes
(D) 10 minutes
(E) 3 minutes
Rationale: Let the movie size be 400 u.
Given,A+C=4 hrs.
A+C=100 u/hr
And A+B+C=2.5 hrs or 400/2.5=160 u/hr
B alone=160-100=60 u/hr
Trailer=40 times smaller or400/10=40 u
B will take 40/60 hrs or 40 minutes.
Ans A
Answer: (A) 40 minutes
Question: A company has 3 directors and 5 managers. How many different committees with 5 people can be chosen having at least 1 director?
(A) 500
(B) 720
(C) 4500
(D) 25
(E) 55
Rationale: at least one means exactly one and more than one.
different committees with 5 people can be chosen having at least 1 director is
(3c1*5c4) + (3c2*5c3) + (3c3*5c2) = 55;
Hence E.
Answer: (E) 55
Question: The present age of a father is 3 years more than three times the age of his son.Three years hence,father as age will be 11 years more than twice the age of the son.Find the present age of the father.
(A) 36
(B) 77
(C) 33
(D) 44
(E) 55
Rationale: Explanation:
Let the present age be 'x' years. Then father's present age is 3x+3 years. Three years hence (3x+3)+3=2(x+3)+11 x=11 Hence father's present age = 3x+3 =[ (3 x 11) + 3] = 36 years.
Answer: A
Answer: (A) 36
Question: A starts a business with a capital of Rs. 85,000. B joins in the business with Rs.42500 after some time. For how much period does B join, if the profits at the end of the year are divided in the ratio of 3 : 1?
(A) 5 months
(B) 6 months
(C) 7 months
(D) 8 months
(E) None of these
Rationale: Explanation :
Let B joins for x months. Then
A:B = 85000*12 : x* 42500 = 3 : 1
=> 850*12 : 425x= 3 : 1
=> 850*12/ 425x = 3/1 = 3
=> 850*4 /425x = 1
=> 2*4/x = 1
=> x = 8. Answer : Option D
Answer: (D) 8 months
Question: Which of the following expressions CANNOT be equal to 0 when x^2 − 8x = 15?
(A) x^2 − 3x
(B) x^2 − 3x -10
(C) x^2 − 4x +5
(D) x^2 − 4x - 5
(E) x^2 − 2x - 3
Rationale: x^2 − 8x = 15
x^2 − 8x - 15= 0
x=3 or x=5
All other choices result in a possibility of 0 when you plug in 3 or 5 for x
Except x^2 − 4x +5
Answer is C
Answer: (C) x^2 − 4x +5
Question: Salad dressing P is made up of 30% vinegar and 70% oil, and salad dressing Q contains 10% vinegar and 90% oil. If the two dressings are combined to produce a salad dressing that is 18% vinegar, dressing P comprises what percentage of the new dressing?
(A) 20%
(B) 30%
(C) 40%
(D) 50%
(E) 60%
Rationale: Let x be the percentage of dressing P in the new dressing.
0.3x + 0.1(1-x) = 0.18
0.2x = 0.08
x = 0.4 = 40%
The answer is C.
Answer: (C) 40%
Question: A man can row upstream at 20 kmph and downstream at 28 kmph, and then find the speed of the man in still water?
(A) 24
(B) 37
(C) 30
(D) 27
(E) 18
Rationale: US = 20
DS = 28
M = (28 + 20)/2 = 24
Answer:A
Answer: (A) 24
Question: Which among 2^1/2, 3^1/3, 4^1/4 , 6^1/6 and 12^1/12 is the largest ?
(A) 2^1/2
(B) 3^1/3
(C) 4^1/4
(D) 6^1/6
(E) 12^1/12
Rationale: 2^1/2, 3^1/3, 4^1/4 , 6^1/6 and 12^1/12
Multiply each number raised to the power of 12
So,
2^1/2 = 2^6 = 64
3^1/3 = 3^4 = 81
4^1/4 = 4^3 = 64
6^1/6 = 6^2 = 36
12^1/12 = 12^1 = 12
So, the greatest is 3^1/3
ANSWER:B
Answer: (B) 3^1/3
Question: Susan, John, Daisy, Tim and Kim need to be seated in 5 identical chairs in straight line so that Susan is seated always left to Tim. How many such arrangements are possible ?
(A) 360
(B) 120
(C) 80
(D) 240
(E) 60
Rationale: Total # of arrangement of 5 people is 5!.
In half of the cases Susan will be seated left to Tim and in half of the cases Susan will be seated right to Tim (why should one seating arrangement have more ways to occur than another?).
So, # of arrangements to satisfy the given condition is 5!/2=60.
Answer: E.
Answer: (E) 60
Question: If a / b is an integer, which of the following statements must be true?
(A) q is an integer
(B) a = nb where n is an integer
(C) both a and b are integers
(D) b / a is an integer
(E) either a or b is negative
Rationale: Let a = 1/4; b = 1/8 --> a/b = 2
a = nb where n is an integer --> 1/4 = 2*(1/8) --> Correct
Answer: B
Answer: (B) a = nb where n is an integer
Question: Boy sells a book for Rs. 450 he gets a loss of 10%, find CP of the book?
(A) Rs.350
(B) Rs.400
(C) Rs.500
(D) Rs.550
(E) Rs.620
Rationale: Find cost price
Let C.P. of book = x and S.P. = Rs. 450
S.P. of book = C.P. – (10% of C.P.)
S.P. = x – (0.10x)
450 = 0.9 x
x i.e cost price = Rs.500
C
Answer: (C) Rs.500
Question: there are two kind of professional in a company software & personal. If the personal are 15% of the total .a party is going .in a party if 50% of the total professional left and all are software then what is the ratio of the software professional left to total software professional.
(A) 7:15
(B) 7:16
(C) 7:17
(D) 7:18
(E) 7:19
Rationale: let there are 100 professionals.
15 are personal 85 are software
in party 50% left means 50 professionals are there and all are software.
85-50=35 have gone then ratio
35:85
7:17
ANSWER:C
Answer: (C) 7:17
Question: The smallest number which when diminished by 7, is divisible 12, 16, 18, 21 and 28 is:
(A) 1008
(B) 1015
(C) 1022
(D) 1032
(E) None of these
Rationale: EXPLANATION
Required number = (L.C.M. of 12,16, 18, 21, 28) + 7
= 1008 + 7
= 1015
Answer B
Answer: (B) 1015
Question: A library branch originally contained 18365 volumes, 30% of which were fiction novels. 1/3 of the volumes were transferred to another location and 1/3 of the volumes transferred were fiction novels. What percent of the remaining collection was fiction novels?
(A) 2.5%
(B) 17.67%
(C) 28.3%
(D) 45.2%
(E) 73.6%
Rationale: Fiction Novels = 5,509
Transferred to another location = 6,121
Transferred fiction novels = 2,040
Non Transferred Fiction Novels = 3,469
Percent of the remaining collection was fiction novels = 3469/(18365 - 6121 ) * 100 => 28.332...%
Hence answer will be (C)
Answer: (C) 28.3%